Question

It takes 585 J of energy to raise the temperature of 125.6 g mercury from 20.08C to 53.58C. Calculate the specific heat capacity and the molar heat capacity of mercury.

Answer 1

The specific heat capacity is the amount of energy (in form of heat) that must be added to the unit of mass in order to rise its temperature by 1 degree:

$c = \frac{Q}{m∆T} = \frac{585\text{ J}}{125.6\text{ g}·(53.58-20.08)\text{ K}} = 0.139$ J g^-1 K^-1.

The molar heat capacity , in its turn, is the amount of energy (in form of heat) that must be added to 1 mole of the substance in order to rise its temperature by 1 degree.

The number of the moles of mercury in 125.6 g is (molar mass of mercury is 200.59 g/mol):

$n = \frac{m}{M} = \frac{125.6\text{ g}}{200.59\text{ g/mol}} = 0.626$ mol.

Then, the molar heat capacity of mercury is:

$c_m = \frac{Q}{n∆T} = \frac{585\text{ J}}{0.626 \text{ mol}·(53.58-20.08)\text{ K}} = 27.89$ J mol^-1 K^-1.

Answer: the specific heat capacity and the molar heat capacity of mercury are 0.139 J g^-1 K^-1 and 27.89 J mol^-1 K^-1, respectively.

Note: remember that the difference temperature in celsius and in kelvin have the same numeric value due to the conversion rule (+273.15 to convert from celsius to kelvin).