The specific heat of a monoatomic gas at constant pressure is 248.2 J `kg^(-1)K^(-1)` and at constant volume it is 149.0 J `kg^(-1) K^(-1)`. Find the mean molar mass of the gas.

Options

A. `83.8g"mol"^(-1)`
B. `84.0 g "mol"^(-1)`
C. `82 g"mol"^(-1)`
D. `80 g "mol"^(-1)`

Answer

A

Explanation

Molar heat capacity at constant pressure,
`C_(P)=248.2xxmJ.kg^(-1)`
where M is the molar mass of the gas
Similarly `C_(V)=149xxMJ.kg^(-1)`
`C_(P)-C_(V)=R`
`:.248.2xxM-149M=8.314`
`M=8.314/(248.2-149)=0.0838` kg/mol
Molar mass of the gas `=83.8` g/mol