A

Step 1: The mean kinetic energy (KE) of a gas molecule is given by the equation:
$$ KE = \frac{3}{2} kT $$
where \( k \) is Boltzmann's constant and \( T \) is the temperature in Kelvin.
Step 2: To convert the kinetic energy per molecule to kinetic energy per mole, we multiply by Avogadro's number \( N_A \):
$$ KE_{per \ mole} = N_A \cdot KE = N_A \cdot \frac{3}{2} kT $$
Step 3: Since \( R = N_A imes k \) (the gas constant), we substitute this into the equation:
$$ KE_{per \ mole} = \frac{3}{2} RT $$
The question states the mean kinetic energy per gm mole of gas at temperature T is equal to:
$$ KE = RT $$
This indicates that the question refers to the average kinetic energy associated with one degree of freedom for one mole of gas at temperature T.
Therefore, the average kinetic energy per gram mole of a gas at temperature T can be expressed as:
$$ KE = \frac{3}{2} RT $$
Hence the answer is represented as choice A.