6.5: End of Chapter Problems

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

The number of moles and the mass of chlorine, Cl₂, required to react with 10.0 g of sodium metal, Na, to produce sodium chloride, NaCl.
The number of moles and the mass of oxygen formed by the decomposition of 1.252 g of mercury(II) oxide.
The number of moles and the mass of sodium nitrate, NaNO₃, required to produce 128 g of oxygen. (NaNO₂ is the other product.)
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.
The number of moles and the mass of copper(II) carbonate needed to produce 1.500 kg of copper(II) oxide. (CO₂ is the other product.)

Write the balanced equation, then outline the steps necessary to determine the information requested in each of the following:
1. The number of moles and the mass of Mg required to react with 5.00 g of HCl and produce MgCl₂ and H₂.
2. The number of moles and the mass of oxygen formed by the decomposition of 1.252 g of silver(I) oxide.
3. The number of moles and the mass of magnesium carbonate, MgCO₃, required to produce 283 g of carbon dioxide. (MgO is the other product.)
4. The number of moles and the mass of water formed by the combustion of 20.0 kg of acetylene, C₂H₂, in an excess of oxygen.
5. The number of moles and the mass of barium peroxide, BaO₂, needed to produce 2.500 kg of barium oxide, BaO (O₂ is the other product.)

Answer: a. 0.0686 mol Mg, 1.67 g Mg; b. 2.701 × 10⁻³ mol O₂, 0.08644 g O₂; c. 6.43 mol MgCO₃, 542 g MgCO₃ ; d. 713 mol H₂O, 12.8 kg H₂O; e. 16.31 mol BaO₂, 2762 g BaO₂

H₂ is produced by the reaction of 118.5 mL of a 0.8775-M solution of H₃PO₄ according to the following equation: $\ce{2Cr + 2H3PO4 \rightarrow 3H2 + 2CrPO4}$.

Outline the steps necessary to determine the number of moles and mass of H₂.
Perform the calculations outlined.

Answer

a.)

Convert mL to L Multiply L by the molarity to determine moles of H₃PO₄ Convert moles of H₃PO₄to moles of H₂ Multiply moles of H₂ by the molar mass of H₂ to get the answer in grams

b.)

1. $118.5\: mL\times \dfrac{1\: L}{1000\: mL} = 0.1185\: L$

2. $0.1185\: L \times \dfrac{0.8775\: moles\: \ce{H3PO4}}{1\: L} = 0.1040\: moles\: \ce{H3PO4}$

3. $0.1040\: moles\: \ce{H3PO4} \times \dfrac{3\: moles\:\ce{H_2}}{2\: moles\: \ce{H3PO4}} = 0.1560\: moles\: \ce{H2}$

4. $0.1560\: moles\: \ce{H2} \times \dfrac{2.02 g}{1\: mole} = 0.3151g\: \ce{H2}$

Gallium chloride is formed by the reaction of 2.6 L of a 1.44 M solution of HCl according to the following equation: $\ce{2Ga + 6HCl \rightarrow 2GaCl3 + 3H2}$.

Outline the steps necessary to determine the number of moles and mass of gallium chloride.
Perform the calculations outlined.

Answer: $\mathrm{volume\: HCl\: solution \rightarrow mol\: HCl \rightarrow mol\: GaCl_3}$; 1.25 mol GaCl₃, 2.2 × 10² g GaCl₃

I₂ is produced by the reaction of 0.4235 mol of CuCl₂ according to the following equation: $\ce{2CuCl2 + 4KI \rightarrow 2CuI + 4KCl + I2}$.

How many molecules of I₂ are produced?
What mass of I₂ is produced?

Silver is often extracted from ores as K[Ag(CN)₂] and then recovered by the reaction

$\ce{2K[Ag(CN)2]}(aq)+\ce{Zn}(s)\rightarrow \ce{2Ag}(s)+\ce{Zn(CN)2}(aq)+\ce{2KCN}(aq)$

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

Answer: 5.337 × 10²² molecules; 10.41 g Zn(CN)₂

What mass of silver oxide, Ag₂O, is required to produce 25.0 g of silver sulfadiazine, AgC₁₀H₉N₄SO₂, from the reaction of silver oxide and sulfadiazine?

$\ce{2C10H10N4SO2 + Ag2O \rightarrow 2AgC10H9N4SO2 + H2O}$

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, SiO₂, 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 SiO₂ is required to produce 3.00 kg of SiC.

Answer: $\ce{SiO2 + 3C \rightarrow SiC + 2CO}$, 4.50 kg SiO₂

Automotive air bags inflate when a sample of sodium azide, NaN₃, is very rapidly decomposed.

$\ce{2NaN3}(s) \rightarrow \ce{2Na}(s) + \ce{3N2}(g)$

What mass of sodium azide is required to produce 2.6 ft³ (73.6 L) of nitrogen gas with a density of 1.25 g/L?

Answer: 142g NaN₃

Urea, CO(NH₂)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 CO₂ produced by combustion of 1.00×10³ kg of carbon followed by the reaction?

\[\ce{CO2}(g)+\ce{2NH3}(g)\rightarrow \ce{CO(NH2)2}(s)+\ce{H2O}(l)\]

Answer: 5.00 × 10³ kg

In an accident, a solution containing 2.5 kg of nitric acid was spilled. Two kilograms of Na₂CO₃ was quickly spread on the area and CO₂ was released by the reaction. Was sufficient Na₂CO₃ 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).

Answer: 1.28 × 10⁵ g CO₂

What volume of a 0.750 M solution of hydrochloric acid, a solution of HCl, can be prepared from the HCl produced by the reaction of 25.0 g of NaCl with an excess of sulfuric acid?

\[\ce{NaCl}(s)+\ce{H2SO4}(l)\rightarrow \ce{HCl}(g)+\ce{NaHSO4}(s)\]

What volume of a 0.2089 M KI solution contains enough KI to react exactly with the Cu(NO₃)₂ in 43.88 mL of a 0.3842 M solution of Cu(NO₃)₂?

\[\ce{2Cu(NO3)2 + 4KI \rightarrow 2CuI + I2 + 4KNO3}\]

Answer: 161.40 mL KI solution

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.

\[\ce{2CH3CO2H + Ca(OH)2 \rightarrow Ca(CH3CO2)2 + 2H2O}\]

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, Pb₃(OH)₂(CO₃)₂, has been replaced in white paints by rutile, TiO₂. How much rutile (g) can be prepared from 379 g of an ore that contains 88.3% ilmenite (FeTiO₃) by mass?

\[\ce{2FeTiO3 + 4HCl + Cl2 \rightarrow 2FeCl3 + 2TiO2 + 2H2O}\]

Answer: 176 g TiO₂

The following quantities are placed in a container: 1.5 × 10²⁴ atoms of hydrogen, 1.0 mol of sulfur, and 88.0 g of diatomic oxygen.
1. What is the total mass in grams for the collection of all three elements?
2. What is the total number of moles of atoms for the three elements?
3. 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?
4. How many atoms of each remaining element would remain unreacted in the change described in ?
What is the limiting reactant in a reaction that produces sodium chloride from 8 g of sodium and 8 g of diatomic chlorine?

Answer: The limiting reactant is Cl₂.

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?

Answer: $\mathrm{Percent\: yield = 31\%}$

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?

\[\ce{CaCO3}(s)\rightarrow \ce{CaO}(s)+\ce{CO2}(s)\]

Freon-12, CCl₂F₂, is prepared from CCl₄ 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 CCl₂F₂ from 32.9 g of CCl₄. 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.

Answer: $\ce{g\: CCl4\rightarrow mol\: CCl4\rightarrow mol\: CCl2F2 \rightarrow g\: CCl2F2}, \mathrm{\:percent\: yield=48.3\%}$

Citric acid, C₆H₈O₇, 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

\[\ce{C12H22O11 + H2O + 3O2 \rightarrow 2C6H8O7 + 4H2O}\]

What mass of citric acid is produced from exactly 1 metric ton (1.000 × 10³ kg) of sucrose if the yield is 92.30%?

Toluene, C₆H₅CH₃, is oxidized by air under carefully controlled conditions to benzoic acid, C₆H₅CO₂H, which is used to prepare the food preservative sodium benzoate, C₆H₅CO₂Na. What is the percent yield of a reaction that converts 1.000 kg of toluene to 1.21 kg of benzoic acid?

\[\ce{2C6H5CH3 + 3O2 \rightarrow 2C6H5CO2H + 2H2O}\]

Answer: $\mathrm{percent\: yield=91.3\%}$

In a laboratory experiment, the reaction of 3.0 mol of H₂ with 2.0 mol of I₂ 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, (C₂H₅)₂O, 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.

2C₂H₅OH + H₂SO₄ ⟶ (C₂H₅)₂ + H₂SO₄·H₂O

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 C₂H₅OH (d = 0.7894 g/mL)?

Answer: Convert mass of ethanol to moles of ethanol; relate the moles of ethanol to the moles of ether produced using the stoichiometry of the balanced equation. Convert moles of ether to grams; divide the actual grams of ether (determined through the density) by the theoretical mass to determine the percent yield; 87.6%

Outline the steps needed to determine the limiting reactant when 30.0 g of propane, C₃H₈, is burned with 75.0 g of oxygen.

\[\mathrm{percent\: yield=\dfrac{0.8347\:\cancel{g}}{0.9525\:\cancel{g}}\times 100\%=87.6\%}\]

Determine the limiting reactant.

Outline the steps needed to determine the limiting reactant when 0.50 g of Cr and 0.75 g of H₃PO₄ react according to the following chemical equation?

\[\ce{2Cr + 2H3PO4 \rightarrow 2CrPO4 + 3H2}\]

Determine the limiting reactant.

Answer: The conversion needed is $\ce{mol\: Cr \rightarrow mol\: H2PO4}$. Then compare the amount of Cr to the amount of acid present. Cr is the limiting reactant.

Q4.4.14

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?

\[\ce{Li + N2 \rightarrow Li3N}\]

Answer: \[\ce{6Li} + \ce{N2} \rightarrow \: \ce{2Li3N}\]

\[1.50g\: \ce{Li} \times \dfrac{1\: mole\: \ce{Li}}{6.94g\: \ce{Li}} \times\dfrac{2\: mole\: \ce{Li3N}}{6\:mole\: \ce{Li}} = 0.0720\: moles\: \ce{Li3N}\]

\[1.50g\: \ce{N2} \times \dfrac{1\: mole\: \ce{N2}}{28.02g\: \ce{N2}} \times\dfrac{2\: mole\: \ce{Li3N}}{1\:mole\: \ce{N2}} = 0.107\: moles\: \ce{Li3N}\]

$\ce{Li}$ is the limiting reactant

Uranium can be isolated from its ores by dissolving it as UO₂(NO₃)₂, then separating it as solid UO₂(C₂O₄)·3H₂O. Addition of 0.4031 g of sodium oxalate, Na₂C₂O₄, to a solution containing 1.481 g of uranyl nitrate, UO₂(NO₂)₂, yields 1.073 g of solid UO₂(C₂O₄)·3H₂O.

\[\ce{Na2C2O4 + UO2(NO3)2 + 3H2O ⟶ UO2(C2O4)·3H2O + 2NaNO3}\]

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

Answer: Na₂C₂O₄ is the limiting reactant. percent yield = 86.6%

How many molecules of C₂H₄Cl₂ can be prepared from 15 C₂H₄ molecules and 8 Cl₂ 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?

Answer: Only four molecules can be made.

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

What is the limiting reactant when 0.200 mol of P₄ and 0.200 mol of O₂ react according to \[\ce{P4 + 5O2 \rightarrow P4O10}\]
Calculate the percent yield if 10.0 g of P₄O₁₀ 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/ $\mathrm{(1\: troy\: ounce=31.1\: g)}$

Answer: This amount cannot be weighted by ordinary balances and is worthless.

4.5: Quantitative Chemical Analysis

What volume of 0.0105-M HBr solution is be required to titrate 125 mL of a 0.0100-M Ca(OH)₂ solution?

\[\ce{Ca(OH)2}(aq)+\ce{2HBr}(aq) \rightarrow \ce{CaBr2}(aq)+\ce{2H2O}(l)\]

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?

Answer: 3.4 × 10⁻³ M H₂SO₄

What is the concentration of NaCl in a solution if titration of 15.00 mL of the solution with 0.2503 M AgNO₃ requires 20.22 mL of the AgNO₃ solution to reach the end point?\[\ce{AgNO3}(aq)+\ce{NaCl}(aq)\rightarrow \ce{AgCl}(s)+\ce{NaNO3}(aq)\]
In a common medical laboratory determination of the concentration of free chloride ion in blood serum, a serum sample is titrated with a Hg(NO₃)₂ solution.

\[\ce{2Cl-}(aq)+\ce{Hg(NO3)2}(aq)\rightarrow \ce{2NO3-}(aq)+\ce{HgCl2}(s)\]

What is the Cl⁻ concentration in a 0.25-mL sample of normal serum that requires 1.46 mL of 5.25 × 10⁻⁴ M Hg(NO₃)₂(aq) to reach the end point?

Answer: 9.6 × 10⁻³ M Cl⁻

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 HCI to reach the end point?
A sample of gallium bromide, GaBr₂, weighing 0.165 g was dissolved in water and treated with silver nitrate, AgNO₃, resulting in the precipitation of 0.299 g AgBr. Use these data to compute the %Ga (by mass) GaBr₂.

Answer: 22.4%

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 CO₂. 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 B₂O₃. What are the empirical and molecular formulas of the compound.

Answer: The empirical formula is BH₃. The molecular formula is B₂H₆.

Sodium bicarbonate (baking soda), NaHCO₃, can be purified by dissolving it in hot water (60 °C), filtering to remove insoluble impurities, cooling to 0 °C to precipitate solid NaHCO₃, and then filtering to remove the solid, leaving soluble impurities in solution. Any NaHCO₃ that remains in solution is not recovered. The solubility of NaHCO₃ 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 NaHCO₃ 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?

\[\ce{NaHCO3}(aq)+\ce{HCl}(aq)\rightarrow \ce{NaCl}(aq)+\ce{CO2}(g)+\ce{H2O}(l)\]

Answer: 49.6 mL

What volume of 0.08892 M HNO₃ is required to react completely with 0.2352 g of potassium hydrogen phosphate?

\[\ce{2HNO3}(aq)+\ce{K2HPO4}(aq)\rightarrow \ce{H2PO4}(aq)+\ce{2KNO3}(aq)\]

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?

\[\ce{C2O4H2}(aq)+\ce{2NaOH}(aq)\rightarrow \ce{Na2C2O4}(aq)+\ce{2H2O}(l)\]

Answer: 13.64 mL

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 H₂SO₄ concentration of 1.23 × 10⁻⁴ M.

\[\ce{H2SO4}(aq)+\ce{2KOH}(aq)\rightarrow \ce{K2SO4}(aq)+\ce{2H2O}(l)\]

Answer: 1.30 mL

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.

\[\ce{Ca(OH)2}(aq)+\ce{2HCl}(aq)\rightarrow \ce{CaCl2}(aq)+\ce{2H2O}(l)\]

What is the molarity?

Answer: 1.22 M

What mass of Ca(OH)₂ will react with 25.0 g of propionic acid to form the preservative calcium propionate 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 H₃PO₄?

\[\ce{H3PO4}(aq)+\ce{2KOH}(aq)\rightarrow \ce{K2HPO4}(aq)+\ce{2H2O}(l)\]

Answer: 34.99 mL KOH

Potassium acid phthalate, KHC₆H₄O₄, 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 KHC₆H₄O₄ reacts with 35.73 mL of a NaOH solution in a titration. What is the molar concentration of the NaOH?

\[\ce{KHC6H4O4}(aq)+\ce{NaOH}(aq)\rightarrow \ce{KNaC6H4O4}(aq)+\ce{H2O}(aq)\]

The reaction of WCl₆ 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?

Answer: The empirical formula is WCl₄.

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