Final answer:
Using the ideal gas law, PV = nRT, and substituting the provided values, the calculation reveals that 25.2 moles of chlorine gas occupy a vessel of 31.0 L at 120.0 °C and 26.1 bar, which corresponds to answer choice (b).
Step-by-step explanation:
To calculate the number of moles of chlorine gas that would occupy a vessel of 31.0 L at 120.0 °C (393 K) and 26.1 bar, we can use the ideal gas law:
PV = nRT
where P is the pressure in bars, V is the volume in liters, n is the number of moles of the gas, R is the universal gas constant (0.08314 L·bar/mol·K), and T is the temperature in Kelvin.
Rearranging the equation to solve for n (number of moles), we get:
n = PV / RT
Substituting the given values into the equation:
n = (26.1 bar)(31.0 L) / ((0.08314 L·bar/mol·K)(393 K))
After performing the calculation:
n = 25.2 mol
Therefore, 25.2 moles of chlorine gas would occupy a vessel of 31.0 L at 120.0 °C and 26.1 bar, which corresponds to answer choice (b).