Gas Stoichiometry and Ideal Gas Law Problem-Solving Guidance

Q1. 8.00 g of hydrogen gas (H2) are combined with excess oxygen gas (O2) to produce water vapor at 1 atm and 273 K. How many liters of water vapor are produced?

Background

Topic: Gas Stoichiometry at STP

This question tests your ability to use stoichiometry and the concept of molar volume at standard temperature and pressure (STP) to determine the volume of a gas produced in a chemical reaction.

Key Terms and Formulas

• STP (Standard Temperature and Pressure): 273 K and 1.00 atm

• Molar volume at STP: 1 mol of any gas occupies 22.4 L

• Balanced equation: $2\,\mathrm{H}_2(g) + \mathrm{O}_2(g) \rightarrow 2\,\mathrm{H}_2\mathrm{O}(g)$

• Molar mass of H2: 2.02 g/mol

Step-by-Step Guidance

1. Calculate the number of moles of H2 used: $n_{\mathrm{H}_2} = \frac{8.00\,\mathrm{g}}{2.02\,\mathrm{g/mol}}$

2. Use the stoichiometry of the reaction to find the moles of H2O produced. According to the balanced equation, 2 mol H2 produces 2 mol H2O, so the mole ratio is 1:1.

3. Since the reaction occurs at STP, use the molar volume to convert moles of H2O to liters: $V_{\mathrm{H}_2\mathrm{O}} = n_{\mathrm{H}_2\mathrm{O}} \times 22.4\,\mathrm{L/mol}$

Try solving on your own before revealing the answer!

Q2. Calculate the volume of NH3 (in liters) needed at 20°C and 25.0 atm to react with 150 kg of H2SO4 according to: 2 NH3 (g) + H2SO4 → (NH4)2SO4 (aq)

Background

Topic: Gas Stoichiometry Using the Ideal Gas Law

This question tests your ability to use stoichiometry and the ideal gas law to determine the volume of a gas required for a reaction under non-STP conditions.

Key Terms and Formulas

• Ideal Gas Law: $PV = nRT$

• Balanced equation: $2\,\mathrm{NH}_3(g) + \mathrm{H}_2\mathrm{SO}_4(aq) \rightarrow (\mathrm{NH}_4)_2\mathrm{SO}_4(aq)$

• Molar mass of H2SO4: 98.09 g/mol

• R (gas constant): 0.0821 L·atm/(mol·K)

Step-by-Step Guidance

1. Convert 150 kg of H2SO4 to grams: $150\,\mathrm{kg} \times 1000 = 150,000\,\mathrm{g}$

2. Calculate the number of moles of H2SO4: $n_{\mathrm{H}_2\mathrm{SO}_4} = \frac{150,000\,\mathrm{g}}{98.09\,\mathrm{g/mol}}$

3. Use the stoichiometry of the reaction to find the moles of NH3 needed. According to the balanced equation, 1 mol H2SO4 reacts with 2 mol NH3.

4. Use the ideal gas law to solve for the volume of NH3: $V = \frac{nRT}{P}$, where $n$ is the moles of NH3, $T$ is 293 K (20°C), and $P$ is 25.0 atm.

Try solving on your own before revealing the answer!