Question 8

Step 1: Enthalpy ($H$) is a state function for an ideal gas, which means the total change in enthalpy ($\Delta H$) depends only on the initial and final states of the system, specifically the temperature change.

Step 2: Identify the initial and final temperatures from the graph: Initial state $X$: $T_X = 335\text{ K}$ Final state $Z$: $T_Z = 415\text{ K}$

Step 3: Calculate the molar heat capacity at constant pressure ($C_{P, m}$) using the relation for an ideal gas: $C_{P, m} = C_{V, m} + R$ $C_{P, m} = 12 + 8.3 = 20.3\text{ J K}^{-1}\text{ mol}^{-1}$

Step 4: Calculate the total change in enthalpy using the formula $\Delta H = n C_{P, m} \Delta T$: $\Delta T = T_Z - T_X = 415 - 335 = 80\text{ K}$ $\Delta H = 5 \times 20.3 \times 80$ $\Delta H = 400 \times 20.3$ $\Delta H = 8120\text{ J}$

Final Answer: 8120