assignment fill in the blank exercise 2.04

4.1 Writing and Balancing Chemical Equations

What does it mean to say an equation is balanced? Why is it important for an equation to be balanced?

Consider molecular, complete ionic, and net ionic equations.

(a) What is the difference between these types of equations?

(b) In what circumstance would the complete and net ionic equations for a reaction be identical?

Balance the following equations:

(a) PCl 5 ( s ) + H 2 O ( l ) ⟶ POCl 3 ( l ) + HCl ( a q ) PCl 5 ( s ) + H 2 O ( l ) ⟶ POCl 3 ( l ) + HCl ( a q )

(b) Cu ( s ) + HNO 3 ( a q ) ⟶ Cu ( NO 3 ) 2 ( a q ) + H 2 O ( l ) + NO ( g ) Cu ( s ) + HNO 3 ( a q ) ⟶ Cu ( NO 3 ) 2 ( a q ) + H 2 O ( l ) + NO ( g )

(c) H 2 ( g ) + I 2 ( s ) ⟶ HI ( s ) H 2 ( g ) + I 2 ( s ) ⟶ HI ( s )

(d) Fe ( s ) + O 2 ( g ) ⟶ Fe 2 O 3 ( s ) Fe ( s ) + O 2 ( g ) ⟶ Fe 2 O 3 ( s )

(e) Na ( s ) + H 2 O ( l ) ⟶ NaOH ( a q ) + H 2 ( g ) Na ( s ) + H 2 O ( l ) ⟶ NaOH ( a q ) + H 2 ( g )

(f) ( NH 4 ) 2 Cr 2 O 7 ( s ) ⟶ Cr 2 O 3 ( s ) + N 2 ( g ) + H 2 O ( g ) ( NH 4 ) 2 Cr 2 O 7 ( s ) ⟶ Cr 2 O 3 ( s ) + N 2 ( g ) + H 2 O ( g )

(g) P 4 ( s ) + Cl 2 ( g ) ⟶ PCl 3 ( l ) P 4 ( s ) + Cl 2 ( g ) ⟶ PCl 3 ( l )

(h) PtCl 4 ( s ) ⟶ Pt ( s ) + Cl 2 ( g ) PtCl 4 ( s ) ⟶ Pt ( s ) + Cl 2 ( g )

(a) Ag ( s ) + H 2 S ( g ) + O 2 ( g ) ⟶ Ag 2 S ( s ) + H 2 O ( l ) Ag ( s ) + H 2 S ( g ) + O 2 ( g ) ⟶ Ag 2 S ( s ) + H 2 O ( l )

(b) P 4 ( s ) + O 2 ( g ) ⟶ P 4 O 10 ( s ) P 4 ( s ) + O 2 ( g ) ⟶ P 4 O 10 ( s )

(c) Pb ( s ) + H 2 O ( l ) + O 2 ( g ) ⟶ Pb(OH) 2 ( s ) Pb ( s ) + H 2 O ( l ) + O 2 ( g ) ⟶ Pb(OH) 2 ( s )

(d) Fe ( s ) + H 2 O ( l ) ⟶ Fe 3 O 4 ( s ) + H 2 ( g ) Fe ( s ) + H 2 O ( l ) ⟶ Fe 3 O 4 ( s ) + H 2 ( g )

(e) Sc 2 O 3 ( s ) + SO 3 ( l ) ⟶ Sc 2 ( S O 4 ) 3 ( s ) Sc 2 O 3 ( s ) + SO 3 ( l ) ⟶ Sc 2 ( S O 4 ) 3 ( s )

(f) Ca 3 ( P O 4 ) 2 ( a q ) + H 3 PO 4 ( a q ) ⟶ Ca ( H 2 PO 4 ) 2 ( a q ) Ca 3 ( P O 4 ) 2 ( a q ) + H 3 PO 4 ( a q ) ⟶ Ca ( H 2 PO 4 ) 2 ( a q )

(g) Al ( s ) + H 2 SO 4 ( a q ) ⟶ Al 2 ( S O 4 ) 3 ( s ) + H 2 ( g ) Al ( s ) + H 2 SO 4 ( a q ) ⟶ Al 2 ( S O 4 ) 3 ( s ) + H 2 ( g )

(h) TiCl 4 ( s ) + H 2 O ( g ) ⟶ TiO 2 ( s ) + HCl ( g ) TiCl 4 ( s ) + H 2 O ( g ) ⟶ TiO 2 ( s ) + HCl ( g )

Write a balanced molecular equation describing each of the following chemical reactions.

(a) Solid calcium carbonate is heated and decomposes to solid calcium oxide and carbon dioxide gas.

(b) Gaseous butane, C 4 H 10 , reacts with diatomic oxygen gas to yield gaseous carbon dioxide and water vapor.

(c) Aqueous solutions of magnesium chloride and sodium hydroxide react to produce solid magnesium hydroxide and aqueous sodium chloride.

(d) Water vapor reacts with sodium metal to produce solid sodium hydroxide and hydrogen gas.

Write a balanced equation describing each of the following chemical reactions.

(a) Solid potassium chlorate, KClO 3 , decomposes to form solid potassium chloride and diatomic oxygen gas.

(b) Solid aluminum metal reacts with solid diatomic iodine to form solid Al 2 I 6 .

(c) When solid sodium chloride is added to aqueous sulfuric acid, hydrogen chloride gas and aqueous sodium sulfate are produced.

(d) Aqueous solutions of phosphoric acid and potassium hydroxide react to produce aqueous potassium dihydrogen phosphate and liquid water.

Colorful fireworks often involve the decomposition of barium nitrate and potassium chlorate and the reaction of the metals magnesium, aluminum, and iron with oxygen.

(a) Write the formulas of barium nitrate and potassium chlorate.

(b) The decomposition of solid potassium chlorate leads to the formation of solid potassium chloride and diatomic oxygen gas. Write an equation for the reaction.

(c) The decomposition of solid barium nitrate leads to the formation of solid barium oxide, diatomic nitrogen gas, and diatomic oxygen gas. Write an equation for the reaction.

(d) Write separate equations for the reactions of the solid metals magnesium, aluminum, and iron with diatomic oxygen gas to yield the corresponding metal oxides. (Assume the iron oxide contains Fe 3+ ions.)

Fill in the blank with a single chemical formula for a covalent compound that will balance the equation:

Aqueous hydrogen fluoride (hydrofluoric acid) is used to etch glass and to analyze minerals for their silicon content. Hydrogen fluoride will also react with sand (silicon dioxide).

(a) Write an equation for the reaction of solid silicon dioxide with hydrofluoric acid to yield gaseous silicon tetrafluoride and liquid water.

(b) The mineral fluorite (calcium fluoride) occurs extensively in Illinois. Solid calcium fluoride can also be prepared by the reaction of aqueous solutions of calcium chloride and sodium fluoride, yielding aqueous sodium chloride as the other product. Write complete and net ionic equations for this reaction.

A novel process for obtaining magnesium from sea water involves several reactions. Write a balanced chemical equation for each step of the process.

(a) The first step is the decomposition of solid calcium carbonate from seashells to form solid calcium oxide and gaseous carbon dioxide.

(b) The second step is the formation of solid calcium hydroxide as the only product from the reaction of the solid calcium oxide with liquid water.

(c) Solid calcium hydroxide is then added to the seawater, reacting with dissolved magnesium chloride to yield solid magnesium hydroxide and aqueous calcium chloride.

(d) The solid magnesium hydroxide is added to a hydrochloric acid solution, producing dissolved magnesium chloride and liquid water.

(e) Finally, the magnesium chloride is melted and electrolyzed to yield liquid magnesium metal and diatomic chlorine gas.

From the balanced molecular equations, write the complete ionic and net ionic equations for the following:

(a) K 2 C 2 O 4 ( a q ) + Ba (OH) 2 ( a q ) ⟶ 2 KOH ( a q ) + BaC 2 O 4 ( s ) K 2 C 2 O 4 ( a q ) + Ba (OH) 2 ( a q ) ⟶ 2 KOH ( a q ) + BaC 2 O 4 ( s )

(b) Pb ( N O 3 ) 2 ( a q ) + H 2 SO 4 ( a q ) ⟶ PbSO 4 ( s ) + 2 HNO 3 ( a q ) Pb ( N O 3 ) 2 ( a q ) + H 2 SO 4 ( a q ) ⟶ PbSO 4 ( s ) + 2 HNO 3 ( a q )

(c) CaCO 3 ( s ) + H 2 SO 4 ( a q ) ⟶ CaSO 4 ( s ) + CO 2 ( g ) + H 2 O ( l ) CaCO 3 ( s ) + H 2 SO 4 ( a q ) ⟶ CaSO 4 ( s ) + CO 2 ( g ) + H 2 O ( l )

4.2 Classifying Chemical Reactions

Use the following equations to answer the next four questions:

i. H 2 O ( s ) ⟶ H 2 O ( l ) H 2 O ( s ) ⟶ H 2 O ( l )

ii. Na + ( a q ) + Cl − ( aq ) + Ag + ( a q ) + NO 3 − ( a q ) ⟶ AgCl ( s ) + Na + ( a q ) + NO 3 − ( a q ) Na + ( a q ) + Cl − ( aq ) + Ag + ( a q ) + NO 3 − ( a q ) ⟶ AgCl ( s ) + Na + ( a q ) + NO 3 − ( a q )

iii. CH 3 OH ( g ) + O 2 ( g ) ⟶ CO 2 ( g ) + H 2 O ( g ) CH 3 OH ( g ) + O 2 ( g ) ⟶ CO 2 ( g ) + H 2 O ( g )

iv. 2 H 2 O ( l ) ⟶ 2 H 2 ( g ) + O 2 ( g ) 2 H 2 O ( l ) ⟶ 2 H 2 ( g ) + O 2 ( g )

v. H + ( a q ) + OH − ( a q ) ⟶ H 2 O ( l ) H + ( a q ) + OH − ( a q ) ⟶ H 2 O ( l )

(a) Which equation describes a physical change?

(b) Which equation identifies the reactants and products of a combustion reaction?

(c) Which equation is not balanced?

(d) Which is a net ionic equation?

Indicate what type, or types, of reaction each of the following represents:

(a) Ca ( s ) + Br 2 ( l ) ⟶ CaBr 2 ( s ) Ca ( s ) + Br 2 ( l ) ⟶ CaBr 2 ( s )

(b) Ca (OH) 2 ( a q ) + 2 HBr ( a q ) ⟶ CaBr 2 ( a q ) + 2 H 2 O ( l ) Ca (OH) 2 ( a q ) + 2 HBr ( a q ) ⟶ CaBr 2 ( a q ) + 2 H 2 O ( l )

(c) C 6 H 12 ( l ) + 9 O 2 ( g ) ⟶ 6 CO 2 ( g ) + 6 H 2 O ( g ) C 6 H 12 ( l ) + 9 O 2 ( g ) ⟶ 6 CO 2 ( g ) + 6 H 2 O ( g )

(a) H 2 O ( g ) + C ( s ) ⟶ CO ( g ) + H 2 ( g ) H 2 O ( g ) + C ( s ) ⟶ CO ( g ) + H 2 ( g )

(b) 2KClO 3 ( s ) ⟶ 2 KCl ( s ) + 3 O 2 ( g ) 2KClO 3 ( s ) ⟶ 2 KCl ( s ) + 3 O 2 ( g )

(c) Al (OH) 3 ( a q ) + 3 HCl ( a q ) ⟶ AlCl 3 ( a q ) + 3 H 2 O ( l ) Al (OH) 3 ( a q ) + 3 HCl ( a q ) ⟶ AlCl 3 ( a q ) + 3 H 2 O ( l )

(d) Pb ( NO 3 ) 2 ( a q ) + H 2 SO 4 ( a q ) ⟶ PbSO 4 ( s ) + 2 HNO 3 ( a q ) Pb ( NO 3 ) 2 ( a q ) + H 2 SO 4 ( a q ) ⟶ PbSO 4 ( s ) + 2 HNO 3 ( a q )

Silver can be separated from gold because silver dissolves in nitric acid while gold does not. Is the dissolution of silver in nitric acid an acid-base reaction or an oxidation-reduction reaction? Explain your answer.

Determine the oxidation states of the elements in the following compounds:

(e) Mg 2 Si

(f) RbO 2 , rubidium superoxide

Determine the oxidation states of the elements in the compounds listed. None of the oxygen-containing compounds are peroxides or superoxides.

(a) H 3 PO 4

(b) Al(OH) 3

(e) In 2 S 3

(f) P 4 O 6

(a) H 2 SO 4

(b) Ca(OH) 2

Classify the following as acid-base reactions or oxidation-reduction reactions:

(a) Na 2 S ( a q ) + 2 HCl ( a q ) ⟶ 2 NaCl ( a q ) + H 2 S ( g ) Na 2 S ( a q ) + 2 HCl ( a q ) ⟶ 2 NaCl ( a q ) + H 2 S ( g )

(b) 2 Na ( s ) + 2 HCl ( a q ) ⟶ 2 NaCl ( a q ) + H 2 ( g ) 2 Na ( s ) + 2 HCl ( a q ) ⟶ 2 NaCl ( a q ) + H 2 ( g )

(c) Mg ( s ) + Cl 2 ( g ) ⟶ MgCl 2 ( s ) Mg ( s ) + Cl 2 ( g ) ⟶ MgCl 2 ( s )

(d) MgO ( s ) + 2 HCl ( a q ) ⟶ MgCl 2 ( a q ) + H 2 O ( l ) MgO ( s ) + 2 HCl ( a q ) ⟶ MgCl 2 ( a q ) + H 2 O ( l )

(e) K 3 P ( s ) + 2 O 2 ( g ) ⟶ K 3 PO 4 ( s ) K 3 P ( s ) + 2 O 2 ( g ) ⟶ K 3 PO 4 ( s )

(f) 3 KOH ( a q ) + H 3 PO 4 ( a q ) ⟶ K 3 PO 4 ( a q ) + 3 H 2 O ( l ) 3 KOH ( a q ) + H 3 PO 4 ( a q ) ⟶ K 3 PO 4 ( a q ) + 3 H 2 O ( l )

Identify the atoms that are oxidized and reduced, the change in oxidation state for each, and the oxidizing and reducing agents in each of the following equations:

(a) Mg ( s ) + NiCl 2 ( a q ) ⟶ MgCl 2 ( a q ) + Ni ( s ) Mg ( s ) + NiCl 2 ( a q ) ⟶ MgCl 2 ( a q ) + Ni ( s )

(b) PCl 3 ( l ) + Cl 2 ( g ) ⟶ PCl 5 ( s ) PCl 3 ( l ) + Cl 2 ( g ) ⟶ PCl 5 ( s )

(c) C 2 H 4 ( g ) + 3 O 2 ( g ) ⟶ 2 CO 2 ( g ) + 2 H 2 O ( g ) C 2 H 4 ( g ) + 3 O 2 ( g ) ⟶ 2 CO 2 ( g ) + 2 H 2 O ( g )

(d) Zn ( s ) + H 2 SO 4 ( a q ) ⟶ ZnSO 4 ( a q ) + H 2 ( g ) Zn ( s ) + H 2 SO 4 ( a q ) ⟶ ZnSO 4 ( a q ) + H 2 ( g )

(e) 2 K 2 S 2 O 3 ( s ) + I 2 ( s ) ⟶ K 2 S 4 O 6 ( s ) + 2 KI ( s ) 2 K 2 S 2 O 3 ( s ) + I 2 ( s ) ⟶ K 2 S 4 O 6 ( s ) + 2 KI ( s )

(f) 3 Cu ( s ) + 8 HNO 3 ( a q ) ⟶ 3 Cu ( NO 3 ) 2 ( a q ) + 2 NO ( g ) + 4 H 2 O ( l ) 3 Cu ( s ) + 8 HNO 3 ( a q ) ⟶ 3 Cu ( NO 3 ) 2 ( a q ) + 2 NO ( g ) + 4 H 2 O ( l )

Complete and balance the following acid-base equations:

(a) HCl gas reacts with solid Ca(OH) 2 ( s ).

(b) A solution of Sr(OH) 2 is added to a solution of HNO 3 .

(a) A solution of HClO 4 is added to a solution of LiOH.

(b) Aqueous H 2 SO 4 reacts with NaOH.

(c) Ba(OH) 2 reacts with HF gas.

Complete and balance the following oxidation-reduction reactions, which give the highest possible oxidation state for the oxidized atoms.

(a) Al ( s ) + F 2 ( g ) ⟶ Al ( s ) + F 2 ( g ) ⟶

(b) Al ( s ) + CuBr 2 ( a q ) ⟶ Al ( s ) + CuBr 2 ( a q ) ⟶ (single displacement)

(c) P 4 ( s ) + O 2 ( g ) ⟶ P 4 ( s ) + O 2 ( g ) ⟶

(d) Ca ( s ) + H 2 O ( l ) ⟶ Ca ( s ) + H 2 O ( l ) ⟶ (products are a strong base and a diatomic gas)

(a) K ( s ) + H 2 O ( l ) ⟶ K ( s ) + H 2 O ( l ) ⟶

(b) Ba ( s ) + HBr ( a q ) ⟶ Ba ( s ) + HBr ( a q ) ⟶

(c) Sn ( s ) + I 2 ( s ) ⟶ Sn ( s ) + I 2 ( s ) ⟶

Complete and balance the equations for the following acid-base neutralization reactions. If water is used as a solvent, write the reactants and products as aqueous ions. In some cases, there may be more than one correct answer, depending on the amounts of reactants used.

(a) Mg (OH) 2 ( s ) + HClO 4 ( a q ) ⟶ Mg (OH) 2 ( s ) + HClO 4 ( a q ) ⟶

(b) SO 3 ( g ) + H 2 O ( l ) ⟶ (assume an excess of water and that the product dissolves) SO 3 ( g ) + H 2 O ( l ) ⟶ (assume an excess of water and that the product dissolves)

(c) SrO ( s ) + H 2 SO 4 ( l ) ⟶ SrO ( s ) + H 2 SO 4 ( l ) ⟶

When heated to 700–800 °C, diamonds, which are pure carbon, are oxidized by atmospheric oxygen. (They burn!) Write the balanced equation for this reaction.

The military has experimented with lasers that produce very intense light when fluorine combines explosively with hydrogen. What is the balanced equation for this reaction?

Write the molecular, total ionic, and net ionic equations for the following reactions:

(a) Ca (OH) 2 ( a q ) + HC 2 H 3 O 2 ( a q ) ⟶ Ca (OH) 2 ( a q ) + HC 2 H 3 O 2 ( a q ) ⟶

(b) H 3 PO 4 ( a q ) + CaCl 2 ( a q ) ⟶ H 3 PO 4 ( a q ) + CaCl 2 ( a q ) ⟶

Great Lakes Chemical Company produces bromine, Br 2 , from bromide salts such as NaBr, in Arkansas brine by treating the brine with chlorine gas. Write a balanced equation for the reaction of NaBr with Cl 2 .

In a common experiment in the general chemistry laboratory, magnesium metal is heated in air to produce MgO. MgO is a white solid, but in these experiments it often looks gray, due to small amounts of Mg 3 N 2 , a compound formed as some of the magnesium reacts with nitrogen. Write a balanced equation for each reaction.

Lithium hydroxide may be used to absorb carbon dioxide in enclosed environments, such as manned spacecraft and submarines. Write an equation for the reaction that involves 2 mol of LiOH per 1 mol of CO 2 . (Hint: Water is one of the products.)

Calcium propionate is sometimes added to bread to retard spoilage. This compound can be prepared by the reaction of calcium carbonate, CaCO 3 , with propionic acid, C 2 H 5 CO 2 H, which has properties similar to those of acetic acid. Write the balanced equation for the formation of calcium propionate.

Complete and balance the equations of the following reactions, each of which could be used to remove hydrogen sulfide from natural gas:

(a) Ca ( OH ) 2 ( s ) + H 2 S ( g ) ⟶ Ca ( OH ) 2 ( s ) + H 2 S ( g ) ⟶

(b) Na 2 CO 3 ( a q ) + H 2 S ( g ) ⟶ Na 2 CO 3 ( a q ) + H 2 S ( g ) ⟶

Copper(II) sulfide is oxidized by molecular oxygen to produce gaseous sulfur trioxide and solid copper(II) oxide. The gaseous product then reacts with liquid water to produce liquid dihydrogen sulfate as the only product. Write the two equations which represent these reactions.

Write balanced chemical equations for the reactions used to prepare each of the following compounds from the given starting material(s). In some cases, additional reactants may be required.

(a) solid ammonium nitrate from gaseous molecular nitrogen via a two-step process (first reduce the nitrogen to ammonia, then neutralize the ammonia with an appropriate acid)

(b) gaseous hydrogen bromide from liquid molecular bromine via a one-step redox reaction

(c) gaseous H 2 S from solid Zn and S via a two-step process (first a redox reaction between the starting materials, then reaction of the product with a strong acid)

Calcium cyclamate Ca(C 6 H 11 NHSO 3 ) 2 is an artificial sweetener used in many countries around the world but is banned in the United States. It can be purified industrially by converting it to the barium salt through reaction of the acid C 6 H 11 NHSO 3 H with barium carbonate, treatment with sulfuric acid (barium sulfate is very insoluble), and then neutralization with calcium hydroxide. Write the balanced equations for these reactions.

Complete and balance each of the following half-reactions (steps 2–5 in half-reaction method):

(a) Sn 4+ ( a q ) ⟶ Sn 2+ ( a q ) Sn 4+ ( a q ) ⟶ Sn 2+ ( a q )

(b) [ Ag ( NH 3 ) 2 ] + ( a q ) ⟶ Ag ( s ) + NH 3 ( a q ) [ Ag ( NH 3 ) 2 ] + ( a q ) ⟶ Ag ( s ) + NH 3 ( a q )

(c) Hg 2 Cl 2 ( s ) ⟶ Hg ( l ) + Cl − ( a q ) Hg 2 Cl 2 ( s ) ⟶ Hg ( l ) + Cl − ( a q )

(d) H 2 O ( l ) ⟶ O 2 ( g ) H 2 O ( l ) ⟶ O 2 ( g ) (in acidic solution)

(e) IO 3 − ( a q ) ⟶ I 2 ( s ) IO 3 − ( a q ) ⟶ I 2 ( s ) (in basic solution)

(f) SO 3 2− ( a q ) ⟶ SO 4 2− ( a q ) SO 3 2− ( a q ) ⟶ SO 4 2− ( a q ) (in acidic solution)

(g) MnO 4 − ( a q ) ⟶ Mn 2+ ( a q ) MnO 4 − ( a q ) ⟶ Mn 2+ ( a q ) (in acidic solution)

(h) Cl − ( a q ) ⟶ ClO 3 − ( a q ) Cl − ( a q ) ⟶ ClO 3 − ( a q ) (in basic solution)

(a) Cr 2+ ( a q ) ⟶ Cr 3+ ( a q ) Cr 2+ ( a q ) ⟶ Cr 3+ ( a q )

(b) Hg ( l ) + Br − ( a q ) ⟶ HgBr 4 2− ( a q ) Hg ( l ) + Br − ( a q ) ⟶ HgBr 4 2− ( a q )

(c) ZnS ( s ) ⟶ Zn ( s ) + S 2− ( a q ) ZnS ( s ) ⟶ Zn ( s ) + S 2− ( a q )

(d) H 2 ( g ) ⟶ H 2 O ( l ) H 2 ( g ) ⟶ H 2 O ( l ) (in basic solution)

(e) H 2 ( g ) ⟶ H 3 O + ( a q ) H 2 ( g ) ⟶ H 3 O + ( a q ) (in acidic solution)

(f) NO 3 − ( a q ) ⟶ HNO 2 ( a q ) NO 3 − ( a q ) ⟶ HNO 2 ( a q ) (in acidic solution)

(g) MnO 2 ( s ) ⟶ MnO 4 − ( a q ) MnO 2 ( s ) ⟶ MnO 4 − ( a q ) (in basic solution)

(h) Cl − ( a q ) ⟶ ClO 3 − ( a q ) Cl − ( a q ) ⟶ ClO 3 − ( a q ) (in acidic solution)

Balance each of the following equations according to the half-reaction method:

(a) Sn 2+ ( a q ) + Cu 2+ ( a q ) ⟶ Sn 4+ ( a q ) + Cu + ( a q ) Sn 2+ ( a q ) + Cu 2+ ( a q ) ⟶ Sn 4+ ( a q ) + Cu + ( a q )

(b) H 2 S ( g ) + Hg 2 2+ ( a q ) ⟶ H g ( l ) + S ( s ) (in acid) H 2 S ( g ) + Hg 2 2+ ( a q ) ⟶ H g ( l ) + S ( s ) (in acid)

(c) CN − ( a q ) + ClO 2 ( a q ) ⟶ CNO − ( a q ) + Cl − ( a q ) (in acid) CN − ( a q ) + ClO 2 ( a q ) ⟶ CNO − ( a q ) + Cl − ( a q ) (in acid)

(d) Fe 2+ ( a q ) + Ce 4+ ( a q ) ⟶ Fe 3+ ( a q ) + Ce 3+ ( a q ) Fe 2+ ( a q ) + Ce 4+ ( a q ) ⟶ Fe 3+ ( a q ) + Ce 3+ ( a q )

(e) HBrO ( a q ) ⟶ Br − ( a q ) + O 2 ( g ) (in acid) HBrO ( a q ) ⟶ Br − ( a q ) + O 2 ( g ) (in acid)

(a) Zn ( s ) + NO 3 − ( a q ) ⟶ Zn 2+ ( a q ) + N 2 ( g ) (in acid) Zn ( s ) + NO 3 − ( a q ) ⟶ Zn 2+ ( a q ) + N 2 ( g ) (in acid)

(b) Zn ( s ) + NO 3 − ( a q ) ⟶ Zn 2+ ( a q ) + NH 3 ( a q ) (in base) Zn ( s ) + NO 3 − ( a q ) ⟶ Zn 2+ ( a q ) + NH 3 ( a q ) (in base)

(c) CuS ( s ) + NO 3 − ( a q ) ⟶ Cu 2+ ( a q ) + S ( s ) + NO ( g ) (in acid) CuS ( s ) + NO 3 − ( a q ) ⟶ Cu 2+ ( a q ) + S ( s ) + NO ( g ) (in acid)

(d) NH 3 ( a q ) + O 2 ( g ) ⟶ NO 2 ( g ) (gas phase) NH 3 ( a q ) + O 2 ( g ) ⟶ NO 2 ( g ) (gas phase)

(e) H 2 O 2 ( a q ) + MnO 4 − ( a q ) ⟶ Mn 2+ ( a q ) + O 2 ( g ) (in acid) H 2 O 2 ( a q ) + MnO 4 − ( a q ) ⟶ Mn 2+ ( a q ) + O 2 ( g ) (in acid)

(f) NO 2 ( g ) ⟶ NO 3 − ( a q ) + NO 2 − ( a q ) (in base) NO 2 ( g ) ⟶ NO 3 − ( a q ) + NO 2 − ( a q ) (in base)

(g) Fe 3+ ( a q ) + I − ( a q ) ⟶ Fe 2+ ( a q ) + I 2 ( a q ) Fe 3+ ( a q ) + I − ( a q ) ⟶ Fe 2+ ( a q ) + I 2 ( a q )

(a) MnO 4 − ( a q ) + NO 2 − ( a q ) ⟶ MnO 2 ( s ) + NO 3 − ( a q ) (in base) MnO 4 − ( a q ) + NO 2 − ( a q ) ⟶ MnO 2 ( s ) + NO 3 − ( a q ) (in base)

(b) MnO 4 2− ( a q ) ⟶ MnO 4 − ( a q ) + MnO 2 ( s ) (in base) MnO 4 2− ( a q ) ⟶ MnO 4 − ( a q ) + MnO 2 ( s ) (in base)

(c) Br 2 ( l ) + SO 2 ( g ) ⟶ Br − ( a q ) + SO 4 2− ( a q ) (in acid) Br 2 ( l ) + SO 2 ( g ) ⟶ Br − ( a q ) + SO 4 2− ( a q ) (in acid)

4.3 Reaction Stoichiometry

Write the balanced equation, then outline the steps necessary to determine the information requested in each of the following:

(a) The number of moles and the mass of chlorine, Cl 2 , required to react with 10.0 g of sodium metal, Na, to produce sodium chloride, NaCl.

(b) The number of moles and the mass of oxygen formed by the decomposition of 1.252 g of mercury(II) oxide.

(c) The number of moles and the mass of sodium nitrate, NaNO 3 , required to produce 128 g of oxygen. (NaNO 2 is the other product.)

(d) The number of moles and the mass of carbon dioxide formed by the combustion of 20.0 kg of carbon in an excess of oxygen.

(e) The number of moles and the mass of copper(II) carbonate needed to produce 1.500 kg of copper(II) oxide. (CO 2 is the other product.)

Determine the number of moles and the mass requested for each reaction in Exercise 4.42 .

(a) The number of moles and the mass of Mg required to react with 5.00 g of HCl and produce MgCl 2 and H 2 .

(b) The number of moles and the mass of oxygen formed by the decomposition of 1.252 g of silver(I) oxide.

(c) The number of moles and the mass of magnesium carbonate, MgCO 3 , required to produce 283 g of carbon dioxide. (MgO is the other product.)

(d) The number of moles and the mass of water formed by the combustion of 20.0 kg of acetylene, C 2 H 2 , in an excess of oxygen.

(e) The number of moles and the mass of barium peroxide, BaO 2 , needed to produce 2.500 kg of barium oxide, BaO (O 2 is the other product.)

Determine the number of moles and the mass requested for each reaction in Exercise 4.44 .

H 2 is produced by the reaction of 118.5 mL of a 0.8775-M solution of H 3 PO 4 according to the following equation: 2 Cr + 2 H 3 PO 4 ⟶ 3 H 2 + 2 CrPO 4 . 2 Cr + 2 H 3 PO 4 ⟶ 3 H 2 + 2 CrPO 4 .

(a) Outline the steps necessary to determine the number of moles and mass of H 2 .

(b) Perform the calculations outlined.

Gallium chloride is formed by the reaction of 2.6 L of a 1.44 M solution of HCl according to the following equation: 2 Ga + 6 HCl ⟶ 2 GaCl 3 + 3 H 2 . 2 Ga + 6 HCl ⟶ 2 GaCl 3 + 3 H 2 .

(a) Outline the steps necessary to determine the number of moles and mass of gallium chloride.

I 2 is produced by the reaction of 0.4235 mol of CuCl 2 according to the following equation: 2 CuCl 2 + 4 KI ⟶ 2 CuI + 4 KCl + I 2 . 2 CuCl 2 + 4 KI ⟶ 2 CuI + 4 KCl + I 2 .

(a) How many molecules of I 2 are produced?

(b) What mass of I 2 is produced?

Silver is often extracted from ores such as K[Ag(CN) 2 ] and then recovered by the reaction 2 K [ Ag ( CN ) 2 ] ( a q ) + Zn ( s ) ⟶ 2Ag ( s ) + Zn ( CN ) 2 ( a q ) + 2 KCN ( a q ) 2 K [ Ag ( CN ) 2 ] ( a q ) + Zn ( s ) ⟶ 2Ag ( s ) + Zn ( CN ) 2 ( a q ) + 2 KCN ( a q )

(a) How many molecules of Zn(CN) 2 are produced by the reaction of 35.27 g of K[Ag(CN) 2 ]?

(b) What mass of Zn(CN) 2 is produced?

What mass of silver oxide, Ag 2 O, is required to produce 25.0 g of silver sulfadiazine, AgC 10 H 9 N 4 SO 2 , from the reaction of silver oxide and sulfadiazine? 2 C 10 H 10 N 4 SO 2 + Ag 2 O ⟶ 2 AgC 10 H 9 N 4 SO 2 + H 2 O 2 C 10 H 10 N 4 SO 2 + Ag 2 O ⟶ 2 AgC 10 H 9 N 4 SO 2 + H 2 O

Carborundum is silicon carbide, SiC, a very hard material used as an abrasive on sandpaper and in other applications. It is prepared by the reaction of pure sand, SiO 2 , with carbon at high temperature. Carbon monoxide, CO, is the other product of this reaction. Write the balanced equation for the reaction, and calculate how much SiO 2 is required to produce 3.00 kg of SiC.

Automotive air bags inflate when a sample of sodium azide, NaN 3 , is very rapidly decomposed. 2 NaN 3 ( s ) ⟶ 2 Na ( s ) + 3 N 2 ( g ) 2 NaN 3 ( s ) ⟶ 2 Na ( s ) + 3 N 2 ( g ) What mass of sodium azide is required to produce 2.6 ft 3 (73.6 L) of nitrogen gas with a density of 1.25 g/L?

Urea, CO(NH 2 ) 2 , is manufactured on a large scale for use in producing urea-formaldehyde plastics and as a fertilizer. What is the maximum mass of urea that can be manufactured from the CO 2 produced by combustion of 1.00 × 10 3 kg 1.00 × 10 3 kg of carbon followed by the reaction? CO 2 ( g ) + 2 NH 3 ( g ) ⟶ CO ( NH 2 ) 2 ( s ) + H 2 O ( l ) CO 2 ( g ) + 2 NH 3 ( g ) ⟶ CO ( NH 2 ) 2 ( s ) + H 2 O ( l )

In an accident, a solution containing 2.5 kg of nitric acid was spilled. Two kilograms of Na 2 CO 3 was quickly spread on the area and CO 2 was released by the reaction. Was sufficient Na 2 CO 3 used to neutralize all of the acid?

A compact car gets 37.5 miles per gallon on the highway. If gasoline contains 84.2% carbon by mass and has a density of 0.8205 g/mL, determine the mass of carbon dioxide produced during a 500-mile trip (3.785 liters per gallon).

What volume of 0.750 M hydrochloric acid solution can be prepared from the HCl produced by the reaction of 25.0 g of NaCl with excess sulfuric acid? NaCl ( s ) + H 2 SO 4 ( l ) ⟶ HCl ( g ) + NaHSO 4 ( s ) NaCl ( s ) + H 2 SO 4 ( l ) ⟶ HCl ( g ) + NaHSO 4 ( s )

What volume of a 0.2089 M KI solution contains enough KI to react exactly with the Cu(NO 3 ) 2 in 43.88 mL of a 0.3842 M solution of Cu(NO 3 ) 2 ? 2 Cu ( NO 3 ) 2 + 4 KI ⟶ 2 CuI + I 2 + 4 KNO 3 2 Cu ( NO 3 ) 2 + 4 KI ⟶ 2 CuI + I 2 + 4 KNO 3

A mordant is a substance that combines with a dye to produce a stable fixed color in a dyed fabric. Calcium acetate is used as a mordant. It is prepared by the reaction of acetic acid with calcium hydroxide. 2 CH 3 CO 2 H + Ca (OH) 2 ⟶ Ca ( CH 3 CO 2 ) 2 + 2 H 2 O 2 CH 3 CO 2 H + Ca (OH) 2 ⟶ Ca ( CH 3 CO 2 ) 2 + 2 H 2 O

What mass of Ca(OH) 2 is required to react with the acetic acid in 25.0 mL of a solution having a density of 1.065 g/mL and containing 58.0% acetic acid by mass?

The toxic pigment called white lead, Pb 3 (OH) 2 (CO 3 ) 2 , has been replaced in white paints by rutile, TiO 2 . How much rutile (g) can be prepared from 379 g of an ore that contains 88.3% ilmenite (FeTiO 3 ) by mass? 2 FeTiO 3 + 4 HCl + Cl 2 ⟶ 2 FeCl 3 + 2 TiO 2 + 2 H 2 O 2 FeTiO 3 + 4 HCl + Cl 2 ⟶ 2 FeCl 3 + 2 TiO 2 + 2 H 2 O

4.4 Reaction Yields

The following quantities are placed in a container: 1.5 × × 10 24 atoms of hydrogen, 1.0 mol of sulfur, and 88.0 g of diatomic oxygen.

(a) What is the total mass in grams for the collection of all three elements?

(b) What is the total number of moles of atoms for the three elements?

(c) If the mixture of the three elements formed a compound with molecules that contain two hydrogen atoms, one sulfur atom, and four oxygen atoms, which substance is consumed first?

(d) How many atoms of each remaining element would remain unreacted in the change described in (c)?

What is the limiting reactant in a reaction that produces sodium chloride from 8 g of sodium and 8 g of diatomic chlorine?

Which of the postulates of Dalton's atomic theory explains why we can calculate a theoretical yield for a chemical reaction?

A student isolated 25 g of a compound following a procedure that would theoretically yield 81 g. What was his percent yield?

A sample of 0.53 g of carbon dioxide was obtained by heating 1.31 g of calcium carbonate. What is the percent yield for this reaction?

CaCO 3 ( s ) ⟶ CaO ( s ) + CO 2 ( s ) CaCO 3 ( s ) ⟶ CaO ( s ) + CO 2 ( s )

Freon-12, CCl 2 F 2 , is prepared from CCl 4 by reaction with HF. The other product of this reaction is HCl. Outline the steps needed to determine the percent yield of a reaction that produces 12.5 g of CCl 2 F 2 from 32.9 g of CCl 4 . Freon-12 has been banned and is no longer used as a refrigerant because it catalyzes the decomposition of ozone and has a very long lifetime in the atmosphere. Determine the percent yield.

Citric acid, C 6 H 8 O 7 , a component of jams, jellies, and fruity soft drinks, is prepared industrially via fermentation of sucrose by the mold Aspergillus niger . The equation representing this reaction is C 12 H 22 O 11 + H 2 O + 3 O 2 ⟶ 2 C 6 H 8 O 7 + 4 H 2 O C 12 H 22 O 11 + H 2 O + 3 O 2 ⟶ 2 C 6 H 8 O 7 + 4 H 2 O

What mass of citric acid is produced from exactly 1 metric ton (1.000 × × 10 3 kg) of sucrose if the yield is 92.30%?

Toluene, C 6 H 5 CH 3 , is oxidized by air under carefully controlled conditions to benzoic acid, C 6 H 5 CO 2 H, which is used to prepare the food preservative sodium benzoate, C 6 H 5 CO 2 Na. What is the percent yield of a reaction that converts 1.000 kg of toluene to 1.21 kg of benzoic acid?

2 C 6 H 5 CH 3 + 3 O 2 ⟶ 2 C 6 H 5 CO 2 H + 2 H 2 O 2 C 6 H 5 CH 3 + 3 O 2 ⟶ 2 C 6 H 5 CO 2 H + 2 H 2 O

In a laboratory experiment, the reaction of 3.0 mol of H 2 with 2.0 mol of I 2 produced 1.0 mol of HI. Determine the theoretical yield in grams and the percent yield for this reaction.

Outline the steps needed to solve the following problem, then do the calculations. Ether, (C 2 H 5 ) 2 O, which was originally used as an anesthetic but has been replaced by safer and more effective medications, is prepared by the reaction of ethanol with sulfuric acid.

2C 2 H 5 OH + H 2 SO 4 ⟶ (C 2 H 5 ) 2 O + H 2 SO 4 ·H 2 O

What is the percent yield of ether if 1.17 L (d = 0.7134 g/mL) is isolated from the reaction of 1.500 L of C 2 H 5 OH (d = 0.7894 g/mL)?

Outline the steps needed to determine the limiting reactant when 30.0 g of propane, C 3 H 8 , is burned with 75.0 g of oxygen.

Determine the limiting reactant.

Outline the steps needed to determine the limiting reactant when 0.50 mol of Cr and 0.75 mol of H 3 PO 4 react according to the following chemical equation. 2 Cr + 2 H 3 PO 4 ⟶ 2 CrPO 4 + 3 H 2 2 Cr + 2 H 3 PO 4 ⟶ 2 CrPO 4 + 3 H 2

What is the limiting reactant when 1.50 g of lithium and 1.50 g of nitrogen combine to form lithium nitride, a component of advanced batteries, according to the following unbalanced equation? Li + N 2 ⟶ Li 3 N Li + N 2 ⟶ Li 3 N

Uranium can be isolated from its ores by dissolving it as UO 2 (NO 3 ) 2 , then separating it as solid UO 2 (C 2 O 4 )·3H 2 O. Addition of 0.4031 g of sodium oxalate, Na 2 C 2 O 4 , to a solution containing 1.481 g of uranyl nitrate, UO 2 (NO 3 ) 2 , yields 1.073 g of solid UO 2 (C 2 O 4 )·3H 2 O.

Na 2 C 2 O 4 + UO 2 (NO 3 ) 2 + 3H 2 O ⟶ UO 2 (C 2 O 4 )·3H 2 O + 2NaNO 3

Determine the limiting reactant and the percent yield of this reaction.

How many molecules of C 2 H 4 Cl 2 can be prepared from 15 C 2 H 4 molecules and 8 Cl 2 molecules?

How many molecules of the sweetener saccharin can be prepared from 30 C atoms, 25 H atoms, 12 O atoms, 8 S atoms, and 14 N atoms?

The phosphorus pentoxide used to produce phosphoric acid for cola soft drinks is prepared by burning phosphorus in oxygen.

(a) What is the limiting reactant when 0.200 mol of P 4 and 0.200 mol of O 2 react according to P 4 + 5 O 2 ⟶ P 4 O 10 P 4 + 5 O 2 ⟶ P 4 O 10

(b) Calculate the percent yield if 10.0 g of P 4 O 10 is isolated from the reaction.

Would you agree to buy 1 trillion (1,000,000,000,000) gold atoms for $5? Explain why or why not. Find the current price of gold at http://money.cnn.com/data/commodities/ ( 1 troy ounce = 31.1 g ) ( 1 troy ounce = 31.1 g )

4.5 Quantitative Chemical Analysis

What volume of 0.0105-M HBr solution is required to titrate 125 mL of a 0.0100- M Ca(OH) 2 solution? Ca ( OH ) 2 ( a q ) + 2 HBr ( a q ) ⟶ CaBr 2 ( a q ) + 2 H 2 O ( l ) Ca ( OH ) 2 ( a q ) + 2 HBr ( a q ) ⟶ CaBr 2 ( a q ) + 2 H 2 O ( l )

Titration of a 20.0-mL sample of acid rain required 1.7 mL of 0.0811 M NaOH to reach the end point. If we assume that the acidity of the rain is due to the presence of sulfuric acid, what was the concentration of sulfuric acid in this sample of rain?

What is the concentration of NaCl in a solution if titration of 15.00 mL of the solution with 0.2503 M AgNO 3 requires 20.22 mL of the AgNO 3 solution to reach the end point? AgNO 3 ( a q ) + NaCl ( a q ) ⟶ AgCl ( s ) + NaNO 3 ( a q ) AgNO 3 ( a q ) + NaCl ( a q ) ⟶ AgCl ( s ) + NaNO 3 ( a q )

In a common medical laboratory determination of the concentration of free chloride ion in blood serum, a serum sample is titrated with a Hg(NO 3 ) 2 solution. 2 Cl − ( a q ) + Hg ( NO 3 ) 2 ( a q ) ⟶ 2 NO 3 − ( a q ) + HgCl 2 ( s ) 2 Cl − ( a q ) + Hg ( NO 3 ) 2 ( a q ) ⟶ 2 NO 3 − ( a q ) + HgCl 2 ( s )

What is the Cl − concentration in a 0.25-mL sample of normal serum that requires 1.46 mL of 8.25 × × 10 −4 M Hg(NO 3 ) 2 ( aq ) to reach the end point?

Potatoes can be peeled commercially by soaking them in a 3-M to 6-M solution of sodium hydroxide, then removing the loosened skins by spraying them with water. Does a sodium hydroxide solution have a suitable concentration if titration of 12.00 mL of the solution requires 30.6 mL of 1.65 M HCl to reach the end point?

A sample of gallium bromide, GaBr 3 , weighing 0.165 g was dissolved in water and treated with silver nitrate, AgNO 3 , resulting in the precipitation of 0.299 g AgBr. Use these data to compute the %Ga (by mass) GaBr 3 .

The principal component of mothballs is naphthalene, a compound with a molecular mass of about 130 amu, containing only carbon and hydrogen. A 3.000-mg sample of naphthalene burns to give 10.3 mg of CO 2 . Determine its empirical and molecular formulas.

A 0.025-g sample of a compound composed of boron and hydrogen, with a molecular mass of ~28 amu, burns spontaneously when exposed to air, producing 0.063 g of B 2 O 3 . What are the empirical and molecular formulas of the compound?

Sodium bicarbonate (baking soda), NaHCO 3 , can be purified by dissolving it in hot water (60 °C), filtering to remove insoluble impurities, cooling to 0 °C to precipitate solid NaHCO 3 , and then filtering to remove the solid, leaving soluble impurities in solution. Any NaHCO 3 that remains in solution is not recovered. The solubility of NaHCO 3 in hot water of 60 °C is 164 g/L. Its solubility in cold water of 0 °C is 69 g/L. What is the percent yield of NaHCO 3 when it is purified by this method?

What volume of 0.600 M HCl is required to react completely with 2.50 g of sodium hydrogen carbonate? NaHCO 3 ( a q ) + HCl ( a q ) ⟶ NaCl ( a q ) + CO 2 ( g ) + H 2 O ( l ) NaHCO 3 ( a q ) + HCl ( a q ) ⟶ NaCl ( a q ) + CO 2 ( g ) + H 2 O ( l )

What volume of 0.08892 M HNO 3 is required to react completely with 0.2352 g of potassium hydrogen phosphate? 2 HNO 3 ( a q ) + K 2 HPO 4 ( a q ) ⟶ H 3 PO 4 ( a q ) + 2 KNO 3 ( a q ) 2 HNO 3 ( a q ) + K 2 HPO 4 ( a q ) ⟶ H 3 PO 4 ( a q ) + 2 KNO 3 ( a q )

What volume of a 0.3300- M solution of sodium hydroxide would be required to titrate 15.00 mL of 0.1500 M oxalic acid? C 2 O 4 H 2 ( a q ) + 2 NaOH ( a q ) ⟶ Na 2 C 2 O 4 ( a q ) + 2 H 2 O ( l ) C 2 O 4 H 2 ( a q ) + 2 NaOH ( a q ) ⟶ Na 2 C 2 O 4 ( a q ) + 2 H 2 O ( l )

What volume of a 0.00945- M solution of potassium hydroxide would be required to titrate 50.00 mL of a sample of acid rain with a H 2 SO 4 concentration of 1.23 × × 10 −4 M . H 2 SO 4 ( a q ) + 2 KOH ( a q ) ⟶ K 2 SO 4 ( a q ) + 2 H 2 O ( l ) H 2 SO 4 ( a q ) + 2 KOH ( a q ) ⟶ K 2 SO 4 ( a q ) + 2 H 2 O ( l )

A sample of solid calcium hydroxide, Ca(OH) 2 , is allowed to stand in water until a saturated solution is formed. A titration of 75.00 mL of this solution with 5.00 × × 10 −2 M HCl requires 36.6 mL of the acid to reach the end point. Ca ( OH ) 2 ( a q ) + 2 HCl ( a q ) ⟶ CaCl 2 ( a q ) + 2 H 2 O ( l ) Ca ( OH ) 2 ( a q ) + 2 HCl ( a q ) ⟶ CaCl 2 ( a q ) + 2 H 2 O ( l )

What is the molarity?

What mass of Ca(OH) 2 will react with 25.0 g of butanoic to form the preservative calcium butanoate according to the equation?

How many milliliters of a 0.1500- M solution of KOH will be required to titrate 40.00 mL of a 0.0656- M solution of H 3 PO 4 ? H 3 PO 4 ( a q ) + 2 KOH ( a q ) ⟶ K 2 HPO 4 ( a q ) + 2 H 2 O ( l ) H 3 PO 4 ( a q ) + 2 KOH ( a q ) ⟶ K 2 HPO 4 ( a q ) + 2 H 2 O ( l )

Potassium hydrogen phthalate, KHC 8 H 4 O 4 , or KHP, is used in many laboratories, including general chemistry laboratories, to standardize solutions of base. KHP is one of only a few stable solid acids that can be dried by warming and weighed. A 0.3420-g sample of KHC 8 H 4 O 4 reacts with 35.73 mL of a NaOH solution in a titration. What is the molar concentration of the NaOH? KHC 8 H 4 O 4 ( a q ) + NaOH ( a q ) ⟶ KNaC 8 H 4 O 4 ( a q ) + H 2 O ( a q ) KHC 8 H 4 O 4 ( a q ) + NaOH ( a q ) ⟶ KNaC 8 H 4 O 4 ( a q ) + H 2 O ( a q )

The reaction of WCl 6 with Al at ~400 °C gives black crystals of a compound containing only tungsten and chlorine. A sample of this compound, when reduced with hydrogen, gives 0.2232 g of tungsten metal and hydrogen chloride, which is absorbed in water. Titration of the hydrochloric acid thus produced requires 46.2 mL of 0.1051 M NaOH to reach the end point. What is the empirical formula of the black tungsten chloride?

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• Authors: Paul Flowers, Klaus Theopold, Richard Langley, William R. Robinson, PhD
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• Book title: Chemistry 2e
• Publication date: Feb 14, 2019
• Location: Houston, Texas
• Book URL: https://openstax.org/books/chemistry-2e/pages/1-introduction
• Section URL: https://openstax.org/books/chemistry-2e/pages/4-exercises

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2.4: Exercise 2.4

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• Rosanna Hartline
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13.5 g ("thirteen point five grams")

• Calculation setup: 300 mL x [45 g /1000 mL]
• Calculate parentheses first: 300 mL x 0.045 g/mL
• Multiply (mL units cancel out): 13.5 g

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10.E: Nuclear Chemistry (Exercises)

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Nuclear Structure and Stability

1. Write the following isotopes in hyphenated form (e.g., “carbon-14”)

2. Write the following isotopes in nuclide notation (e.g., " C614 ")

• tantalum-175
• francium-217

3. For the following isotopes that have missing information, fill in the missing information to complete the notation

4.For each of the isotopes in teh previous question, determine the numbers of protons, neutrons, and electrons in a neutral atom of the isotope.

5. Write the nuclide notation, including charge if applicable, for atoms with the following characteristics:

• 25 protons, 20 neutrons, 24 electrons
• 45 protons, 24 neutrons, 43 electrons
• 53 protons, 89 neutrons, 54 electrons
• 97 protons, 146 neutrons, 97 electrons

6. Calculate the density of the Mg1224 nucleus in g/mL, assuming that it has the typical nuclear diameter of 1 × 10 –13 cm and is spherical in shape.

7. What are the two principal differences between nuclear reactions and ordinary chemical changes?

8. The mass of the atom Na1123Na1123 is 22.9898 amu.

a. Calculate its binding energy per atom in millions of electron volts.

b. Calculate its binding energy per nucleon.

9. Which of the following nuclei lie within the band of stability?

• chlorine-37

10. Which of the following nuclei lie within the band of stability?

• magnesium-24

Nuclear Equations

11. Write a brief description or definition of each of the following:

• α particle
• β particle
• γ ray
• mass number
• atomic number

12. Which of the various particles (α particles, β particles, and so on) that may be produced in a nuclear reaction are actually nuclei?

13. Complete each of the following equations by adding the missing species:

• Al1327+He24⟶?+n01
• Pu94239+?⟶Cm96242+n01
• N714+He24⟶?+H11
• U92235⟶?+Cs55135+401n

14. Complete each of the following equations:

• Li37+?⟶224He
• C614⟶N714+?
• Cm96250⟶?+Sr3898+401n

15. Write a balanced equation for each of the following nuclear reactions:

• the production of 17 O from 14 N by α particle bombardment
• the production of 14 C from 14 N by neutron bombardment
• the production of 233 Th from 232 Th by neutron bombardment
• the production of 239 U from 238 U by H12H12 bombardment

16. Technetium-99 is prepared from 98 Mo. Molybdenum-98 combines with a neutron to give molybdenum-99, an unstable isotope that emits a β particle to yield an excited form of technetium-99, represented as 99 Tc * . This excited nucleus relaxes to the ground state, represented as 99 Tc, by emitting a γ ray. The ground state of 99 Tc then emits a β particle. Write the equations for each of these nuclear reactions.

17. The mass of the atom F919F919 is 18.99840 amu.

• Calculate its binding energy per atom in millions of electron volts.
• Calculate its binding energy per nucleon.

18. For the reaction C614⟶N714+?C614⟶N714+?, if 100.0 g of carbon reacts, what volume of nitrogen gas (N 2 ) is produced at 273 K and 1 atm?

Radioactive Decay

19. What are the types of radiation emitted by the nuclei of radioactive elements?

20. What changes occur to the atomic number and mass of a nucleus during each of the following decay scenarios?

• an α particle is emitted
• a β particle is emitted
• γ radiation is emitted
• a positron is emitted
• an electron is captured

21. What is the change in the nucleus that results from the following decay scenarios?

• emission of a β particle
• emission of a β + particle
• capture of an electron

22. any nuclides with atomic numbers greater than 83 decay by processes such as electron emission. Explain the observation that the emissions from these unstable nuclides also normally include α particles.

23. Why is electron capture accompanied by the emission of an X-ray?

24. Explain how unstable heavy nuclides (atomic number > 83) may decompose to form nuclides of greater stability (a) if they are below the band of stability and (b) if they are above the band of stability.

25. Which of the following nuclei is most likely to decay by positron emission? Explain your choice.

• chromium-53
• manganese-51

26. The following nuclei do not lie in the band of stability. How would they be expected to decay? Explain your answer.

27. The following nuclei do not lie in the band of stability. How would they be expected to decay?

28. Predict by what mode(s) of spontaneous radioactive decay each of the following unstable isotopes might proceed:

29. Write a nuclear reaction for each step in the formation of Po84218 from U92238, which proceeds by a series of decay reactions involving the step-wise emission of α, β, β, α, α, α, α particles, in that order.

30. Write a nuclear reaction for each step in the formation of Pb82208 from Th90228, which proceeds by a series of decay reactions involving the step-wise emission of α, α, α, α, β, β, α particles, in that order.

31. Define the term half-life and illustrate it with an example.

32. A 1.00 × 10 –6 -g sample of nobelium, No102254No102254, has a half-life of 55 seconds after it is formed. What is the percentage of No102254No102254 remaining at the following times?

• 5.0 min after it forms
• 1.0 h after it forms

33. 239 Pu is a nuclear waste byproduct with a half-life of 24,000 y. What fraction of the 239 Pu present today will be present in 1000 y?

34. The isotope 208 Tl undergoes β decay with a half-life of 3.1 min.

• What isotope is produced by the decay?
• How long will it take for 99.0% of a sample of pure 208 Tl to decay?
• What percentage of a sample of pure 208 Tl remains un-decayed after 1.0 h?

36. If 1.000 g of Ra88226 produces 0.0001 mL of the gas Rn86222 at STP (standard temperature and pressure) in 24 h, what is the half-life of 226 Ra in years?

37. The isotope Sr3890 is one of the extremely hazardous species in the residues from nuclear power generation. The strontium in a 0.500-g sample diminishes to 0.393 g in 10.0 y. Calculate the half-life.

38. Technetium-99 is often used for assessing heart, liver, and lung damage because certain technetium compounds are absorbed by damaged tissues. It has a half-life of 6.0 h. Calculate the rate constant for the decay of Tc4399Tc4399.

39. What is the age of mummified primate skin that contains 8.25% of the original quantity of 14 C?

40. A sample of rock was found to contain 8.23 mg of rubidium-87 and 0.47 mg of strontium-87.

a. Calculate the age of the rock if the half-life of the decay of rubidium by β emission is 4.7 × 10 10 y.

b. If some Sr3887 was initially present in the rock, would the rock be younger, older, or the same age as the age calculated in (a)? Explain your answer.

41. A laboratory investigation shows that a sample of uranium ore contains 5.37 mg of U92238U92238 and 2.52 mg of Pb82206Pb82206. Calculate the age of the ore. The half-life of U92238 is 4.5 × 10 9 yr.

42. Plutonium was detected in trace amounts in natural uranium deposits by Glenn Seaborg and his associates in 1941. They proposed that the source of this 239 Pu was the capture of neutrons by 238 U nuclei. Why is this plutonium not likely to have been trapped at the time the solar system formed 4.7 × 10 9 years ag

43. A Be47 atom (mass = 7.0169 amu) decays into a Li37 atom (mass = 7.0160 amu) by electron capture. How much energy (in millions of electron volts, MeV) is produced by this reaction?

44. A B58 atom (mass = 8.0246 amu) decays into a Be48 atom (mass = 8.0053 amu) by loss of a β + particle (mass = 0.00055 amu) or by electron capture. How much energy (in millions of electron volts) is produced by this reaction?

45. Isotopes such as 26 Al (half-life: 7.2 × 10 5 years) are believed to have been present in our solar system as it formed, but have since decayed and are now called extinct nuclides.

a. 26 Al decays by β + emission or electron capture. Write the equations for these two nuclear transformations.

b. The earth was formed about 4.7 × 10 9 (4.7 billion) years ago. How old was the earth when 99.999999% of the 26 Al originally present had decayed?

46. Write a balanced equation for each of the following nuclear reactions:

• bismuth-212 decays into polonium-212
• beryllium-8 and a positron are produced by the decay of an unstable nucleus
• neptunium-239 forms from the reaction of uranium-238 with a neutron and then spontaneously converts into plutonium-239
• strontium-90 decays into yttrium-90

47. Write a balanced equation for each of the following nuclear reactions:

• mercury-180 decays into platinum-176
• zirconium-90 and an electron are produced by the decay of an unstable nucleus
• thorium-232 decays and produces an alpha particle and a radium-228 nucleus, which decays into actinium-228 by beta decay
• neon-19 decays into fluorine-19

Transmutation and Nuclear Energy

48. Write the balanced nuclear equation for the production of the following transuranium elements:

• berkelium-244, made by the reaction of Am-241 and He-4
• fermium-254, made by the reaction of Pu-239 with a large number of neutrons
• lawrencium-257, made by the reaction of Cf-250 and B-11
• dubnium-260, made by the reaction of Cf-249 and N-15

49. How does nuclear fission differ from nuclear fusion? Why are both of these processes exothermic?

50. Both fusion and fission are nuclear reactions. Why is a very high temperature required for fusion, but not for fission?

51. Cite the conditions necessary for a nuclear chain reaction to take place. Explain how it can be controlled to produce energy, but not produce an explosion.

52. Describe the components of a nuclear reactor.

53. In usual practice, both a moderator and control rods are necessary to operate a nuclear chain reaction safely for the purpose of energy production. Cite the function of each and explain why both are necessary.

54. Describe how the potential energy of uranium is converted into electrical energy in a nuclear power plant.

55. The mass of a hydrogen atom (11H) is 1.007825 amu; that of a tritium atom (13H) is 3.01605 amu; and that of an α particle is 4.00150 amu. How much energy in kilojoules per mole of He24 produced is released by the following fusion reaction: H11+H13⟶He24.

Uses of Radioisotopes

56. How can a radioactive nuclide be used to show that the equilibrium:

AgCl(s)⇌Ag+(aq)+Cl−(aq)

is a dynamic equilibrium?

57. Technetium-99m has a half-life of 6.01 hours. If a patient injected with technetium-99m is safe to leave the hospital once 75% of the dose has decayed, when is the patient allowed to leave?

58. Iodine that enters the body is stored in the thyroid gland from which it is released to control growth and metabolism. The thyroid can be imaged if iodine-131 is injected into the body. In larger doses, I-131 is also used as a means of treating cancer of the thyroid. I-131 has a half-life of 8.70 days and decays by β − emission.

• Write a nuclear equation for the decay.
• How long will it take for 95.0% of a dose of I-131 to decay?

Biological Effects of Radiation

59. If a hospital were storing radioisotopes, what is the minimum containment needed to protect against:

• cobalt-60 (a strong γ emitter used for irradiation)
• molybdenum-99 (a beta emitter used to produce technetium-99 for imaging)

60. Based on what is known about Radon-222’s primary decay method, why is inhalation so dangerous?

61. Given specimens uranium-232 (t1/2=68.9yt1/2=68.9y) and uranium-233 (t1/2=159,200yt1/2=159,200y) of equal mass, which one would have greater activity and why?

62. A scientist is studying a 2.234 g sample of thorium-229 ( t 1/2 = 7340 y) in a laboratory.

• What is its activity in Bq?
• What is its activity in Ci?

63. Given specimens neon-24 (t1/2=3.38mint1/2=3.38min) and bismuth-211 (t1/2=2.14mint1/2=2.14min) of equal mass, which one would have greater activity and why?

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2.20: Present Perfect Tense - Fill in the Blanks and Explain

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• Nooshi Borhan
• Contra Costa College

Fill in the blanks with the present perfect tense of the given verb. Highlight any key words or expressions. Then explain why the verb tense is used.

I  have  always   loved   [always/love] to go hiking in the mountains.

My friend ______________________________ [go] to New York many times.

We ___________________________ [know] each other since the beginning of the semester.

I _______________________________________ [already/receive] 5 calls today.

How long _________________ [be] you _________________ [be] here?

Jane_____________________________ [love] to read since she ________________ [be] a child.

I __________________________________ [never/find] money in the street.

She ______________________________________ [already/finish] her homework.

He ______________________________________ [be] extremely busy for 2 weeks.

I ____________________________ [write] you many times.

She _______________________________ [finish] her chores yet.

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2.4: Exercises

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• Thomas W. Judson
• Stephen F. Austin State University via Abstract Algebra: Theory and Applications

\[ 1^2 + 2^2 + \cdots + n^2 = \frac{n(n + 1)(2n + 1)}{6} \nonumber \]

for \(n \in {\mathbb N}\text{.}\)

\[ 1^3 + 2^3 + \cdots + n^3 = \frac{n^2(n + 1)^2}{4} \nonumber \]

Prove that \(n! \gt 2^n\) for \(n \geq 4\text{.}\)

\[ x + 4x + 7x + \cdots + (3n - 2)x = \frac{n(3n - 1)x}{2} \nonumber \]

Prove that \(10^{n + 1} + 10^n + 1\) is divisible by \(3\) for \(n \in {\mathbb N}\text{.}\)

Prove that \(4 \cdot 10^{2n} + 9 \cdot 10^{2n - 1} + 5\) is divisible by \(99\) for \(n \in {\mathbb N}\text{.}\)

\[ \sqrt[n]{a_1 a_2 \cdots a_n} \leq \frac{1}{n} \sum_{k = 1}^{n} a_k\text{.} \nonumber \]

Prove the Leibniz rule for \(f^{(n)} (x)\text{,}\) where \(f^{(n)}\) is the \(n\)th derivative of \(f\text{;}\) that is, show that

\[ (fg)^{(n)}(x) = \sum_{k = 0}^{n} \binom{n}{k} f^{(k)}(x) g^{(n - k)}(x)\text{.} \nonumber \]

Use induction to prove that \(1 + 2 + 2^2 + \cdots + 2^n = 2^{n + 1} - 1\) for \(n \in {\mathbb N}\text{.}\)

\[ \frac{1}{2}+ \frac{1}{6} + \cdots + \frac{1}{n(n + 1)} = \frac{n}{n + 1} \nonumber \]

If \(x\) is a nonnegative real number, then show that \((1 + x)^n - 1 \geq nx\) for \(n = 0, 1, 2, \ldots\text{.}\)

12. Power Sets

Let \(X\) be a set. Define the power set of \(X\text{,}\) denoted \({\mathcal P}(X)\text{,}\) to be the set of all subsets of \(X\text{.}\) For example,

\[ {\mathcal P}( \{a, b\} ) = \{ \emptyset, \{a\}, \{b\}, \{a, b\} \}\text{.} \nonumber \]

For every positive integer \(n\text{,}\) show that a set with exactly \(n\) elements has a power set with exactly \(2^n\) elements.

Prove that the two principles of mathematical induction stated in Section 2.1 are equivalent.

Show that the Principle of Well-Ordering for the natural numbers implies that 1 is the smallest natural number. Use this result to show that the Principle of Well-Ordering implies the Principle of Mathematical Induction; that is, show that if \(S \subset {\mathbb N}\) such that \(1 \in S\) and \(n + 1 \in S\) whenever \(n \in S\text{,}\) then \(S = {\mathbb N}\text{.}\)

For each of the following pairs of numbers \(a\) and \(b\text{,}\) calculate \(\gcd(a,b)\) and find integers \(r\) and \(s\) such that \(\gcd(a,b) = ra + sb\text{.}\)

• \(14\) and \(39\)
• \(234\) and \(165\)
• \(1739\) and \(9923\)
• \(471\) and \(562\)
• \(23771\) and \(19945\)
• \(-4357\) and \(3754\)

Let \(a\) and \(b\) be nonzero integers. If there exist integers \(r\) and \(s\) such that \(ar + bs =1\text{,}\) show that \(a\) and \(b\) are relatively prime.

17. Fibonacci Numbers

The Fibonacci numbers are

\[ 1, 1, 2, 3, 5, 8, 13, 21, \ldots\text{.} \nonumber \]

We can define them inductively by \(f_1 = 1\text{,}\) \(f_2 = 1\text{,}\) and \(f_{n + 2} = f_{n + 1} + f_n\) for \(n \in {\mathbb N}\text{.}\)

• Prove that \(f_n \lt 2^n\text{.}\)
• Prove that \(f_{n + 1} f_{n - 1} = f^2_n + (-1)^n\text{,}\) \(n \geq 2\text{.}\)
• Prove that \(f_n = [(1 + \sqrt{5}\, )^n - (1 - \sqrt{5}\, )^n]/ 2^n \sqrt{5}\text{.}\)
• Show that \(\phi = \lim_{n \rightarrow \infty} f_{n + 1} / f_n = (\sqrt{5} + 1)/2\text{.}\) The constant \(\phi\) is known as the golden ratio .
• Prove that \(f_n\) and \(f_{n + 1}\) are relatively prime.

Let \(a\) and \(b\) be integers such that \(\gcd(a,b) = 1\text{.}\) Let \(r\) and \(s\) be integers such that \(ar + bs = 1\text{.}\) Prove that

\[ \gcd(a,s) = \gcd(r,b) = \gcd(r,s) = 1\text{.} \nonumber \]

Let \(x, y \in {\mathbb N}\) be relatively prime. If \(xy\) is a perfect square, prove that \(x\) and \(y\) must both be perfect squares.

Using the division algorithm, show that every perfect square is of the form \(4k\) or \(4k + 1\) for some nonnegative integer \(k\text{.}\)

Suppose that \(a, b, r, s\) are pairwise relatively prime and that

\begin{align*} a^2 + b^2 & = r^2\\ a^2 - b^2 & = s^2\text{.} \end{align*}

Prove that \(a\text{,}\) \(r\text{,}\) and \(s\) are odd and \(b\) is even.

Let \(n \in {\mathbb N}\text{.}\) Use the division algorithm to prove that every integer is congruent mod \(n\) to precisely one of the integers \(0, 1, \ldots, n-1\text{.}\) Conclude that if \(r\) is an integer, then there is exactly one \(s\) in \({\mathbb Z}\) such that \(0 \leq s \lt n\) and \([r] = [s]\text{.}\) Hence, the integers are indeed partitioned by congruence mod \(n\text{.}\)

Define the least common multiple of two nonzero integers \(a\) and \(b\text{,}\) denoted by \(\operatorname{lcm}(a, b)\text{,}\) to be the nonnegative integer \(m\) such that both \(a\) and \(b\) divide \(m\text{,}\) and if \(a\) and \(b\) divide any other integer \(n\text{,}\) then \(m\) also divides \(n\text{.}\) Prove there exists a unique least common multiple for any two integers \(a\) and \(b\text{.}\)

If \(d= \gcd(a, b)\) and \(m = \operatorname{lcm}(a, b)\text{,}\) prove that \(dm = |ab|\text{.}\)

Show that \(\operatorname{lcm}(a, b) = ab\) if and only if \(\gcd(a,b) = 1\text{.}\)

Prove that \(\gcd(a,c) = \gcd(b,c) =1\) if and only if \(\gcd(ab,c) = 1\) for integers \(a\text{,}\) \(b\text{,}\) and \(c\text{.}\)

Let \(a, b, c \in {\mathbb Z}\text{.}\) Prove that if \(\gcd(a,b) = 1\) and \(a \mid bc\text{,}\) then \(a \mid c\text{.}\)

Let \(p \geq 2\text{.}\) Prove that if \(2^p - 1\) is prime, then \(p\) must also be prime.

Prove that there are an infinite number of primes of the form \(6n + 5\text{.}\)

Prove that there are an infinite number of primes of the form \(4n - 1\text{.}\)

Using the fact that \(2\) is prime, show that there do not exist integers \(p\) and \(q\) such that \(p^2 = 2 q^2\text{.}\) Demonstrate that therefore \(\sqrt{2}\) cannot be a rational number.