How do you calculate molar specific heat?

Question

I know how to calculate the specific heat, but not molar specific heat. What is molar specific heat and how do you calculate it?

Answer 1

Specific heat has the units of $\mathrm{J/(K\cdot kg)}$.

Molar specific heat is in units of $\mathrm{J/(K\cdot mol)}$, and is the amount of heat needed (in joules) to raise the temperature of $1$ mole of something, by $1$ kelvin (assuming no phase changes).

So, the conversion factor you need, from dimension analysis, will have unit $\pu{kg/mol}$.

$\pu{kg/mol}$ is the SI unit for molar mass.

Multiply the specific heat by the molar mass to get the molar specific heat.

For example, the molar mass of water is $\approx \pu{0.018 kg/mol}$.

The specific heat of water is $\approx 4186\ \mathrm{J/(K\cdot kg)}$.

So the molar specific heat of water is $4186\ \mathrm{J/(K\cdot kg)} \times \pu{0.018 kg/mol} \approx 75\ \mathrm{J/(K\cdot mol)}$