Question

If the universal gas constant is $8.3joulemo{l}^{-1}{K}^{-1}$ and the Avogadro's number is $6\times {10}^{23}$. The mean kinetic energy of oxygen molecules at ${327}^{\circ }C$ will be :

• A. $415\times {10}^{-23}joule$
• B. $2490\times {10}^{-22}joule$
• C. $1245\times {10}^{-23}joule$
• D. $830\times {10}^{-22}joule$

Answer 1

The correct option is C $1245\times {10}^{-23}joule$

The universal gas constant (R) is $8.3J/mol/K$ and the Avogadro's number $N_A$ is $6\times {10}^{23}$. Temperature (T) is ${327}^{o}C$ or $327+273$ K.
The mean kinetic energy of oxygen molecules at 327 degC will be $\frac{3RT}{2N_A}=\frac{3\times 8.3J/mol/K\times (327+273)K}{2\times 6\times {10}^{23}}=1245\times {10}^{-23}joule$