A sample of nitrogen gas occupies 2.50 L at 300 K and 1.00 atm. If the gas is completely vaporized from liquid nitrogen at its boiling point (77 K), and the pressure remains constant, which of the following equations would you use to determine the heat of vaporization (ΔH_vap) of nitrogen using the Ideal Gas Law and the given data?

• A. ΔH_vap = nRT ln(V_2/V_1)
• B. ΔH_vap = nRT
• C. ΔH_vap = nRT ln(P_2/P_1)
• D. ΔH_vap = nRT ln(T_2/T_1)

Answer: (B)

Verified step by step guidance

1. Identify the physical process: nitrogen is vaporized at its boiling point, meaning the phase change occurs at constant temperature (T = 77 K) and constant pressure (P = 1.00 atm).
2. Recall that the heat of vaporization (ΔH_vap) is related to the change in vapor pressure or volume during phase change, and can be connected to thermodynamic equations involving the Ideal Gas Law.
3. Recognize that the Clausius-Clapeyron equation relates the heat of vaporization to the change in vapor pressure with temperature: \(\Delta H_{vap} = -R T^2 \left(\frac{d \ln P}{d T}\right)\), but since temperature is constant here, this form is not directly applicable.
4. Since the problem involves volume change at constant pressure and temperature, use the Ideal Gas Law \(PV = nRT\) to relate volume and temperature changes, and consider the equation \(\Delta H_{vap} = nRT \ln\left(\frac{V_2}{V_1}\right)\) which connects heat of vaporization to volume change at constant pressure and temperature.
5. Therefore, the correct equation to determine \(\Delta H_{vap}\) from the given data is \(\Delta H_{vap} = nRT \ln\left(\frac{V_2}{V_1}\right)\), where \(V_1\) and \(V_2\) are the initial and final volumes of nitrogen gas.