Final answer:
Option (A), To calculate the volume of a 3.73 mol sample of hydrogen gas at STP, we use the ideal gas law, which results in a volume of 84.2 liters, demonstrating that volume is independent of gas type at STP and useful for stoichiometry.
Step-by-step explanation:
Hydrogen-powered fuel cells are considered a clean source of energy because they produce water as the only byproduct when generating electricity. To calculate the volume that a 3.73 mol sample of hydrogen gas occupies at STP (standard temperature and pressure), we can use the ideal gas law, which is expressed as PV = nRT. Here, P is the pressure, V is the volume, n is the amount of substance in moles, R is the ideal gas constant, and T is the temperature in Kelvin.
At STP conditions, the temperature is 273.15 K and the pressure is 1 atm. The ideal gas constant in these units is 0.0821 L·atm/(mol·K). Using the ideal gas law and this standard information, we find that:
V = nRT/P = (3.73 mol)(0.0821 L·atm/(mol·K))(273.15 K)/1 atm = 84.2 L
This calculation shows that the volume occupied by 3.73 mol of hydrogen gas at STP is 84.2 liters. Since volume is independent of gas type at STP, this relationship is helpful in stoichiometry purposes. This example can help students understand the use of the ideal gas law in determining gas volumes.