Final answer:
To find the total volume of a gas mixture, we sum the moles of each component, and use the ideal gas law PV = nRT. For a sample with 5.55 moles of N2 and 1.74 moles of O2, at 10.15 atm and 325 K, the total volume is approximately 19.737 L.
Step-by-step explanation:
To calculate the total volume of a gas mixture using the ideal gas law, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin. First, determine the total number of moles of gas. In this case, the sample of air has 5.55 moles of N2 and 1.74 moles of O2, so the total moles n is the sum of these two, which equals 7.29 moles.
Given that the temperature T is 325 K and the pressure P is 10.15 atm, we can rearrange the ideal gas law to solve for volume: V = nRT/P. The ideal gas constant R in the correct units (L atm / (mol K)) is 0.0821. Plugging in the known values gives us V = (7.29 moles)(0.0821 L atm / (mol K))(325 K) / (10.15 atm), which calculates to a total volume of approximately 19.737 L for the sample of air.