# Entropy of fusion; two methods, different result?

1. Mar 5, 2010

### standardflop

"Calculate the entropy of fusion of A at 25deg C given that its enthalpy of fusion is 32kJ/mol at its melting point 146deg C. Also given is Cp,m(liquid)= 28J/mol/K and Cp,m(s)= 19J/mol/K."

I thought of two approaches. Both should be valid (to my knowledge), but only the first gives the correct result. The first one:
Using Kirchhoffs Law,
$$\Delta H (T2) = \Delta H(T1) + \int_{T_1}^{T_2}\Delta Cp,m dT\approx \Delta H(T1)+\Delta Cp,m (T2-T1)$$
and then applying the definition
$$\Delta S(T2)= \frac{\Delta H(T2)}{T2}$$
(gives the correct result)

But my second idea apparantly failed:
Simply setting up the cyclic equality
$$\Delta S(s\to l,T2) = \Delta S(s,T2to T1)+\Delta S(s\to l,T1)+\Delta S(l,T1\to T2)$$

where the terms are of the form
$$\Delta S(i,T1\to T2) = Cp,m \ln (T2/T1)$$
Can someone tell me why this approach gives a different result, about 73J/mol/K compared with the first, and correct, result of approx. 100J/mol/K.?
Thank you in advance.