Question

The specific heat at constant volume for the monoatomic argon is $0.075$ $kcal/kg-K$, whereas its gram molecular specific heat is $C_V=2.98cal/molK$. The mass of the carbon atom is :

• 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

The correct option is A $6.60\times {10}^{-23}g$

Molar specific heat $=$ Molecular weight $\times$ gram specific heat

$C_V=M\times c_V$

$2.98cal/mol-K=M\times 0.075kcal/kg-K$

$=\frac{M\times 0.075\times {10}^3}{{10}^3}cal/g-K$

$\therefore$ 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 $=\frac{39.7}{6.023\times {10}^{23}}$

$=6.60\times {10}^{-23}g$