Question

The specific heat at constant volume for the monatomic argon is $0.075kcal/kg-K$, whereas its gram molecular specific heat is $C_v=2.98cal/mol/K$. The mass of the argon atom is (Avogadro's number $=6.02\times 10^{23}molecules/mol$ )

• A. $6.60\times 10^{-23}g$
• B. $3.30\times 10^{-23}g$
• C. $2.20\times 10^{-23}g$
• D. $13.20\times 10^{-23}g$

Answer 1

Answer: (A)

Molar specific heat $=$ molecular weight $\times$ gram specific heat
$C_v=M\times c_v$
$2.98cal/mol-K=M\times 0.075kcal/kg-K$
$=M\times \frac{0.075\times 10^3}{10^3}cal/g-K$
$\therefore$ Molecular weight of argon
$M=\frac{2.98}{0.075}=39.7g$
i.e., mass of $6.023\times 10^{23}$ atom $=39.7g$
Therefore, mass of single atom
$=\frac{39.7}{6.023\times 10^{23}}=6.60\times 10^{-23}g$