Heat $\mathrm{Q}=\frac{3}{2}\mathrm{RT}$ is supplied to 4 moles of an ideal diatomic gas at temperature T, which remains constant. Number of moles of the gas dissolved into atoms is_________.

Let x moles of diatomic gas be associated. x moles of diatomic gas become 2x moles of a monatomic gas after dissociation. Internal energy of n moles of an ideal gas

$=\frac{3}{2}\mathrm{nRT}$ for monatomic gas

Internal energy of n moles of an ideal gas

$=\frac{5}{2}\mathrm{nRT}$(for diatomic gas)

So. [Internal energy of 2x moles of a monatomic gas + internal energy of (4 - x) moles of a diatomic gas = internal energy of 4 moles of a diatomic gas

$=\frac{3}{2}\mathrm{RT}$ (given)

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

On solving, x = 3 moles.