Question

The constant pressure molar heat capacity of cerium is given by the following expression. Cerium is a metal (ie solid).

C_p = (14.014 + 1.929 x 10^-2 T) J K^-1 mol^-1?

(a) Calculate the value of ?H for heating 1 moles of cerium from 25.0 C to 125.0 C (note since C_p is dependent on T, you have to integrate)

(b) Explain why C_p might depend on T.

Answer 1

(a) delta H = CpdT = (14.014 + 1.929x10-2 T)dT

Integrating the above function between the limits 298K - 398K gives,

= 298[14.014 T + 1.929x10-2 T2/2]398 ==> [14.014(100) + 9.645x10-3 (3982-2982)] = 1401.4 + 671.292 = 2072.69 J/mol

For 1 mole, delta H = 2.073 kJ.

(b) The heat capacity is an extrinsic property. As temperature is increased, the metal, Cerium expands and this reflects on the heat capacity. Therefore, the heat capacity is a temperature dependent quantity.