Question

The average kinetic energy of an ideal gas per molecule in $SI$ unit at ${25}^{o}C$ will be

• A. $6.17\times {10}^{-21}kJ$
• B. $6.17\times {10}^{-21}J$
• C. $6.17\times {10}^{-20}J$
• D. $7.16\times {10}^{-20}J$

Answer 1

The correct option is B $6.17\times {10}^{-21}J$

The average kinetic energy of an ideal gas per molecule in $SI$ unit at ${25}^{o}C$ will be $6.17\times {10}^{-21}\text{J/molecule}$.
Average kinetic energy $\overline{KE}=\frac{3}{2}kT=\frac{3}{2}\frac{R}{N}T$

$\overline{KE}=\frac{3}{2}\times \frac{\text{8.313 J/mol/K}}{6.023\times {10}^{23}\text{molecules/mol}}\times \text{298 K}$

$\overline{KE}=6.17\times {10}^{-21}\text{J/molecule}$