AT WHAT TEMPERATURE , TRANSLATIONAL KINETIC ENERGY OF 14 G OF NITROGEN WILL BE SAME AS THAT OF 32 GM OF OXYGEN AT 300 K?

1. Translational kinetic energy of a gas = $\frac{3}{2}nRT$
   
                      Where n=number of moles and T=temperature

2. Translational kinetic energy for O₂ = $$\begin{gathered} \frac{3}{2}\times \frac{given mass}{molar mass}\times R\times T \\ =\frac{3}{2}\times \frac{32g}{32g/mol}\times R \times 300 K \\ = 450 R \end{gathered}$$

    Translational kinetic energy for N₂ = $$\begin{gathered} \frac{3}{2}\times \frac{14g}{14g/mol}\times R\times T \\ = \frac{3}{2} RT \end{gathered}$$

3. As the translational kinetic energies for both are same :

         $$\begin{gathered} 450 R = \frac{3}{2} R \times T \\ T = 300K \end{gathered}$$