Gas laws are also used in stoichiometry calculations. The problems are similar to previous stoichiometry problems. For example, we can determine the volume of hydrogen gas that is produced from the reaction of 56.7 g of zinc. The reaction was run at 20°C under a pressure of 1.0 atm. First, make sure you have a balanced chemical equation.

Zn (s) + 2 HCl (aq) → ZnCl₂ (aq) + H₂ (g)

Find the number of moles of H₂ produced and then use the ideal gas law to determine the volume of H₂.

\(\displaystyle 56.7\;g\;Zn\;\times\frac{1\;mol\;Zn}{65.38\;g\;Zn}\times\frac{1\;mol\;H_2}{1\;mol\;Zn}\;=\;0.867\;mol\;H_2\)
 
Next, use the ideal gas law to solve for V. The temperature is 20°C + 273 = 293 K

\(\displaystyle V\;=\;\frac{nRT}{P}\;=\;\frac{0.867\;mol\times\;0.0821\frac{L⋅atm}{mol⋅K}\times\;293\;K}{1.0\;atm}\;=\;\mathbf{20.9\;L}\)
 
According to Avogadro’s law, we know that equal volumes of gas at the same pressure and temperature contain the same number of moles of gas. When these conditions are constant for a chemical reaction, the volumes of gas will combine according to the stoichiometric coefficients in the balanced chemical equation. We can consider volumes rather than moles when performing calculations. Consider the following balanced equation where the reactants and products are gases.

N₂ (g) + 3 H₂ (g) → 2 NH₃

According to the equation, 1 mole of N₂ reacts with 3 moles of H₂ to produce 2 moles of NH₃. The equation also states that 1 L of N₂ reacts with 3 L of H₂ to produce 2 L of NH₃. If 0.550 L of H₂ was reacted, how many moles of NH₃ is produced?

\(\displaystyle 0.550\;L\;H_2\;\times\frac{3\;L\;H_2}{2\;L\;NH_3}\;=\;\mathbf{0.825\;L\;NH_3}\)

 

Worksheet: Gases and Stoichiometry Part 1
Worksheet: Gases and Stoichiometry Part 2

Watch the following video before attempting exercises

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.

Check Solution to Exercise 1

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.

Check Solution to Exercise 2

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?

Check Solution to Exercise 3

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?

Check Solution to Exercise 4

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?

Check Solution to Exercise 5

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)

Check Solution to Exercise 6

 
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