Question

It takes 330 j of energy to raise the temperature of 14.6 g of benzene from 21.0 °c to 28.7 °c at constant pressure. What is the constant-pressure molar heat capacity of benzene?

Answer 1

The mathematical expression for heat capacity at constant pressure is given as:

$Q=n\times C_{p}\times \Delta T$   (1)

where, Q = heat capacity

$C_{p}$ =  molar heat capacity at constant pressure

$\Delta T$ = change in temperature

n = number of moles

Therefore, $\Delta T$ = $28.7^{o}C-21^{o}C$

= $7.7 ^{o}C$

Number of moles  =$\frac{given mass in g}{molar mass}$

= $\frac{14.6 g }{78.11 g/mol}$

= 0.186 mole

Put the values in formula (1)

$330 J=0.186 mole\times C_{p}\times (7.7 ^{o}C+ 273)$ (conversion of degree Celsius into kelvin)

$C_{p} = \frac{330 J}{0.186 mole\times 280.7 K}$

= $\frac{330 J}{52.2102 mole K}$

= 6.32 J /mol K

Hence, molar heat capacity of benzene at constant pressure  = $6.32 Jmol^{-1} K^{-1}$