Question

The specific heat at constant volume for the monoatomic argon is $0.075 \,kcal / kg - K$, whereas its gram molecular specific heat is $C_{V}=2.98\, cal / mol K$. 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

Answer: (A)

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