91Ó°ÊÓ

Specific heat capacity at constant volume,

$c_v=0.075cal/g∘C$

The expression for the specific heat capacity is at constant volume is given by,

$C_V=\frac{f}{2}R$

Here c_v is specific heat capacity at constant volume, f is the degree of freedom, R is the gas constant.

The expression for the specific heat capacity is at constant volume is also given by,c_v=c_vM

Here c_v is specific heat capacity at constant volume, M is the total mass.

Since
$C_V=\frac{f}{2}R$

Argon is a monoatomic gas, and for a monoatomic gas,f=3

$$\begin{gathered} c_v=\frac{3}{2}R \\ =\frac{3}{2}\left(8.31\frac{J}{mol}K\right) \end{gathered}$$

Now convert joules to calories:

$$\begin{gathered} c_v=\frac{3}{2}R \\ =\frac{3}{2}\left(8.31\frac{J}{mol}K\right)\left(\frac{1cal}{4.186J}\right) \\ =2.98\frac{cal}{mol.K} \end{gathered}$$

c_v is related to C_V as,

C_v=c_vM

Here M is the total mass, which is given by

M=mN_A,

Here m is the mass of the single atom and N_A is Avogadro number.

Mass of an argon atom$\begin{array}{l}m=\frac{M}{N_A}\\ =\frac{{\displaystyle \frac{C_v}{c_v}}}{N_A}\\ =\frac{{\displaystyle \frac{2.98}{0.075}}}{6.02×{10}^{23}}\end{array}$

Now convert the above mass of argon atom into the

Therefore the mass of an argon atom is $m=6.6×10-26kg$.

Molar mass of argon:

$$\begin{gathered} M=\frac{C_V}{c_v} \\ =\frac{2.98}{0.075} \\ =39.7g/mol \end{gathered}$$

Therefore the molar mass of argon is 39.7g/mol .