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 + -cT ^{2}) 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 T_{1} to T_{2}.

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

**Δ H = 1.249 x 10 ^{4} 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}.