Heat $Q=\frac{3}{2}RT$ is supplied to 4 moles of an ideal diatomic gas kept in closed container at temperature T . how many moles of the gas are disassociated into atoms if temperature of gas is constant?

Let x mole of the gas be dissociated, x moles of atomic becomes 2x moles of a  monatomic  gas after dissociation.
Internal energy of n moles of an ideal gas =  $\frac{3}{2}nRT$ for monatomic gas 

and U = $\frac{5}{2}nRT$  for  diatomic gas 

so, (internal energy of 2x moles of monoatomic gas + internal energy of (4 –x) moles of a diatomic gas) – internal energy of 4 moles of a diatomic gas = $\frac{3}{2}nRT\left(\text{given}\right)$

 $\left(2x\right)\left(\frac{3RT}{2}\right)+(4-x)\left(\frac{5RT}{2}\right)-\left(4\right)\left(\frac{5RT}{2}\right)=\frac{3}{2}RT$  

on solving x = 3 moles