Exercises

Exercise 1. Consider the following equation:

2 LiOH (s) + CO₂ (g) → Li₂CO₃ (s) + H₂O (l)

Calculate the volume of CO₂ at 23.0°C and 783 mmHg that can be absorbed by 355 g of LiOH.

First determine the number of moles of COsub>2.

\(\displaystyle 355\;g\;LiOH\frac{mol\;LiOH}{23.95\;g\;LiOH}\times\frac{1\;mol\;CO_2}{2\;mol\;LiOH}\;=\;7.41\;mol\;CO_2\)
 
Next, use the ideal gas law to solve for the volume of CO₂.

P = 1.03 atm
n = 7.41 mole
T = 296.15 K

PV = nRT and \(\displaystyle V\;=\;\frac{nRT}{P}\)
 
\(\displaystyle V=\;\frac{7.41\;mol\;\times 0.0821\frac{L⋅atm}{mol⋅K}\times\;296.15\;K}{1.03\;atm}\;=\;\mathbf{175\;L\;CO_2}\)

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Exercise 2. Chlorine, Cl₂, gas can be formed by the following reaction:

2 NaCl (s) + 2 H₂SO₄ (l) + MnO₂ (s) → Na₂SO₄ (s) + MnSO₄ (s) + 2 H₂O (g) + Cl₂ (g)

A volume of 0.602 L of gas is collected over water at 28.0°C and a pressure of 758 mmHg. Calculate the number of grams of NaCl that was reacted.

Calculate the number of moles of Cl₂ gas using the ideal gas law, PV = nRT. First we need to subtract the pressure of the water vapor from the total pressure. Look up the vapor pressure of water at 28.0°C. It is 28.3 mmHg at 28°C.

P = 758 mmHg – 28.3 mmHg = 729.7 mmHg = \(729.7\;mmHg\)

Next find the number of moles of Cl₂ gas using the ideal gas law and solving for n.

\(\displaystyle n\;=\frac{PV}{RT}\;=\;\frac{0.960\;atm\;0.602\;L}{0.0821\;\frac{L⋅atm}{mol⋅K}\;\times301\;K}\;=\;0.0234\;mol\)

Next, use the balanced equation to determine the mass of NaCl.

\(\displaystyle 0.0234\;mol\;Cl_2\times\;\frac{2\;mol\;NaCl}{1\;mol\;Cl_2}\times\;\frac{58.44\;g\;NaCl}{1\;mol\;NaCl}\;=\;\mathbf{2.73\;g\;NaCl}\)

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Exercise 3. Consider the following equation:

2 NH₃ (g) + CO₂ (g) → NH₂CONH₂ (aq) + H₂O (l)

What volume of ammonia is required to produce 525 g of urea (NH₂CONH₂) at 22°C and 1.52 atm?

First determine the number of moles of ammonia that react with 525 g of urea.

\(\displaystyle 525\;g\;urea\times\frac{1\;mol\;urea}{60.056\;g\;urea}\times\;\frac{2\;mol\;NH_3}{1\;mol\;urea}\;=\;17.5\;mol\;NH_3\)
 
Next determine the volume of gas using the ideal gas law and solving for V.

\(\displaystyle V=\;\frac{17.5\;mol\;\times 0.0821\frac{L⋅atm}{mol⋅K}\times\;295\;K}{1.52\;atm}\;=\;\mathbf{279\;L\;NH_3}\)

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Exercise 4. A volume of 26.5 mL HCl reacts with 56.5 mL of sodium carbonate according to the following reaction.

2 HCl (aq) + Na₂CO₃ (aq) → CO₂ (g) + H₂O (l) + 2 NaCl (aq)

If 145 mL of CO₂ is formed at 28.0°C and 745 mmHg, what is the molarity of HCl?

First, use the ideal gas laws to find the number of moles of CO₂ produced, PV = nRT. Solve for n.

\(\displaystyle n\;=\;\frac{PV}{RT}\)
 
P = \(745\;mmHg\times\frac{1\;atm}{760\;mmHg}\;=\;0.980\;atm\)
V = 0.145 L
T = 273 + 28.0°C = 301 K

\(\displaystyle n\;=\;\frac{0.980\;atm\times\;0.145\;L}{0.0821\;\frac{L⋅atm}{mol⋅K}\times\;301\;K}\;=\;5.75\times\;10^{-3}\;mol\)
 
Determine the moles of HCl.

\(\displaystyle 5.75\times\;10^{-3}\;mol\;CO_2\times\;\frac{2\;mol\;HCl}{1\;mol\;HCl}\;=\;0.0115\;mol\;HCl\)
 
Next divide the moles of HCl by the volume of HCL.

\(\displaystyle \frac{0.0115\;mol\;HCl}{0.0265\;L}\;=\;\mathbf{0.434\;M}\)

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Exercise 5. Consider the following reaction.

HC₃H₃O₃ (aq) → C₂H₄O (aq) + CO₂ (g)

How many grams of pyruvic acid were reacted, HC₃H₃O₃, if the sample gives 22.5 mL CO₂ gas at 348 mmHg at 31.0°C?

First, find the moles of CO₂ gas using the ideal gas law.

\(\displaystyle n\;=\;\frac{PV}{RT}\;=\;\frac{0.458\;atm\times\;0.0225\;L}{0.0821\frac{L⋅atm}{mol⋅K}\times\;304\;K}\;=\;4.13\times\;10^{-4}\;mol\;CO_2\)
 
Now determine the number of grams of pyruvic acid using the balanced chemical equation.

\(\displaystyle 4.13\times 10^{-4}\;mol\;CO_2\times\frac{1\;mol\;HC_3H_3O_3}{1\;mol\;CO_2}\times\frac{88.06\;g\;HC_3H_3O_3}{1\;mol\;HC_3H_3O_3}\;=\;\mathbf{0.0364\;g}\)

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Exercise 6. A 3.45 g sample of baking soda, NaHCO₃, was heated and decomposed to solid sodium carbonate, carbon dioxide, and water vapor. What volume, in L, of carbon dioxide gas at 76.5°C and 758 mmHg was produced? (Hint: Write a balanced equation)

First write a balanced chemical equation.

2 NaHCO₃ (s) → Na₂CO₃ (s) + 2 CO₂ (g) + H₂O (g)

Next, determine the number of moles of CO₂ produced using the balanced equation.

\(\displaystyle 3.45\;g\;NaHCO_3\times\frac{1\;mol\;NaHCO_3}{84.007\;g\;NaHCO_3}\times\frac{2\;mol\;CO_2}{2\;mol\;NaHCO_3}\;=\;0.0411\;mol\;CO_2\)
 
Next, use the ideal gas law to determine the volume of carbon dioxide.

\(\displaystyle V\;=\;\frac{nRT}{P}\;=\;\frac{0.0411\;mol\;\times 0.0821\frac{L⋅atm}{mol⋅K}\times 349.65\;K}{0.997\;atm}\;=\;\mathbf{1.18\;L}\)

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