Question

The enthalpy of 36 g of water vapor increases by 1830 J when its temperature increases from 150° C to 175°C. Assume that water vapor is an ideal gas. What is the molar specific heat at constant pressure in Sl units for water vapor?

Answer 1

The molar specific heat at constant pressure for water vapor, given an enthalpy change of 1830 J for a 25°C increase in temperature of 36 g of water vapor, is 36.6 J/mol°C.

Step-by-step explanation:

The student asked about the molar specific heat at constant pressure of water vapor when its temperature increases from 150°C to 175°C, given that the enthalpy change is 1830 J for 36 g of water vapor. Assuming water vapor behaves as an ideal gas, to calculate the molar specific heat at constant pressure (Cp), we use the formula ΔH = nCp ΔT, where ΔH is the enthalpy change, n is the number of moles of the gas, and ΔT is the temperature change. First, we determine the number of moles of water vapor by using its molar mass (18.0 g/mol).

For 36 g of water vapor, n = 36g / 18.0 g/mol = 2 moles. The temperature change, ΔT, is 175°C - 150°C = 25°C. Inserting these values into the equation and solving for Cp gives:

Cp = ΔH / (n ΔT) = 1830 J / (2 moles × 25°C) = 1830 J / (50 mol°C) = 36.6 J/mol°C. Therefore, the molar specific heat at constant pressure for water vapor is 36.6 J/mol°C.