Question

The average kinetic energy of an ideal gas molecule in SI unit at $25°C$ will be

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

Answer 1

The correct option is D

$6.17\times {10}^{-21}J$

Step 1: Given data

The temperature of an ideal gas,

$$\begin{gathered} T=25°C \\ \Rightarrow T=25+273K \\ \Rightarrow T=298K \end{gathered}$$

Step 2: To find

The average kinetic energy of an ideal gas molecule in SI unit at $25°C$

Step 3: Formula and calculation

The formula for average kinetic energy, $K{E}_{avg}=\frac{3}{2}KT$
Where $K$ is the Boltzmann constant, $K=1.38\times {10}^{-23}J{K}^{-1}$

and $T$ is the temperature in Kelvin, $T=298K$

$$\begin{gathered} K{E}_{avg}=\frac{3}{2}KT \\ \Rightarrow K{E}_{avg}=\frac{3}{2}\times 1.38\times {10}^{-23}\times 298 \\ \Rightarrow K{E}_{avg}=6.17\times {10}^{-21}J \end{gathered}$$
The average kinetic energy of an ideal gas molecule in the SI unit at $25°C$ will be $6.17\times {10}^{-21}J$.

Option D is correct.