Final answer:
The molar heat capacity of benzene at constant pressure, when it takes 330 J to raise the temperature of 24.6 g of benzene from 21 °C to 28.7 °C, is approximately 139 J/mol·K.
Step-by-step explanation:
The student asked how to calculate the molar heat capacity of benzene at constant pressure, given that it takes 330 J of energy to raise the temperature of 24.6 g of benzene from 21 ℃ to 28.7 ℃. The molar mass of benzene is 78.11 g/mole. To find the molar heat capacity (Cp), we use the formula: Cp = (q) / (m × ΔT × M), where q is the heat supplied, m is the mass of the substance, ΔT is the change in temperature, and M is the molar mass. First, we convert the mass of benzene to moles: 24.6 g / (78.11 g/mole) = 0.315 mol. Then we calculate ΔT, which is 28.7 ℃ - 21 ℃ = 7.7 ℃. Plugging these values into the formula, we get Cp = 330 J / (0.315 mol × 7.7 ℃) = approximately 139 J/mol·K.