Enthalpy of Molecule and Temperature Changes with Integration

The enthalpy of a molecule, H, changes by dH when the temperature, T, changes by dT and the change is commonly given as a polynomial equation

dH = (a + bT + -cT²) dT

Calculate the change in the enthalpy, dH, of benzene (below Fig) when it is heated from 298 K to 398 K by integrating the polynomial given the following constants for benzene.

a = – 1.70 J mo1^-1 K^-1

b = 3.25 x 10^-1 J mol^-1 K^-2

c = 1.11 x 10^-4 J mo1^-1 K^-3

So,

Integrating from T₁ to T₂.

For clarity of presentation, below I have split the evaluation of the integrated equation over two lines

Δ H = 1.249 x 10⁴ J mol^-1

Δ H = 12.49 kJ mol^-1

As a final step the enthalpy change of the benzene upon heating has been quoted in the conventional units of kJ mol^-1.