Hydrogen gas can be formed by the reaction of methane with water according to the equation: CH4(g) + H2O(g) ⇌ CO(g) + 3H2(g). In a particular reaction, 25.5 L of methane gas (measured at a pressure of 730 torr and a temperature of 298 K) is used. How many liters of hydrogen gas are produced at the same conditions?

• A. 25.5 L
• B. 51.0 L
• C. 76.5 L
• D. 102.0 L

Answer: (C)

Verified step by step guidance

1. Identify the balanced chemical equation for the reaction: CH4(g) + H2O(g) ⇌ CO(g) + 3H2(g). This indicates that 1 mole of CH4 produces 3 moles of H2.
2. Use the ideal gas law, PV = nRT, to calculate the number of moles of CH4. Convert the pressure from torr to atm by dividing by 760 (since 1 atm = 760 torr).
3. Calculate the number of moles of CH4 using the formula: n = PV / RT, where P is the pressure in atm, V is the volume in liters, R is the ideal gas constant (0.0821 L·atm/mol·K), and T is the temperature in Kelvin.
4. Determine the moles of H2 produced using the stoichiometry of the reaction. Since 1 mole of CH4 produces 3 moles of H2, multiply the moles of CH4 by 3 to find the moles of H2.
5. Convert the moles of H2 back to volume using the ideal gas law, assuming the same conditions of temperature and pressure. Use the formula V = nRT / P to find the volume of H2 produced.