Question

The enthalpy of fusion for benzene (C6H6, 78.0 g/mol) is 127.40 kJ/kg, and its melting point is 5.5°C. What is the entropy change when 1 mole of benzene melts at 5.5°C? (Show all unit conversions and write out all equations)

Answer 1

Answer:

35.662 J/K is the entropy change when 1 mole of benzene melts at 5.5°C

Explanation:

The enthalpy of fusion for benzene = $\Delta H_{fus}= 127.40 kJ/kg$

Molar mass of benzene = 78.0 g/mol

Or can be written as 1 mole of benzene = 78.0 g

1 g of benzene  = $\frac{1}{78.0 } mol$

$\Delta H_{fus}$= 127.40 kJ/kg=127.40 kJ/1000 g (1kg = 1000 g)

$=\frac{127.40 kJ}{1000 g}=\frac{127.40 kJ}{1000\times \frac{1}{78.0} mol}$

= 9.9372 kJ/mol = 9937.2 J /mol

The entropy change when 1 mole of benzene melts at 5.5°C:

$\Delta S_{fus}=\frac{\Delta H_{fus}}{T}$

T = 5.5°C = 278.65 K

$\Delta S_{fus}=\frac{9937.2 J /mol}{278.65 K}=35.662 J/K$