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

Let x moles of diatomic gas become 2x moles of a monoatomic gas after dissociation. Internal energy of n moles of an ideal gas :

$\begin{array}{l}{U}_{mono}=\frac{3}{2}\mathrm{nRT} \left[\text{ for monoatomic gas }\right]\\ U_{diatomic}=\frac{5}{2}\mathrm{nRT} \left[ \text{ for diatomic gas }\right]\end{array}$

So, (Internal energy of 2x moles of a monoatomic gas + internal energy of (4 - x) moles of a diatomic gas) - internal energy of 4 moles of a diatomic gas

$\begin{array}{l}=\frac{3}{2}\mathrm{RT}\text{ (given) }\\ \Rightarrow \left(2\mathrm{x}\right)\left(\frac{3\mathrm{RT}}{2}\right)+(4-\mathrm{x})\left(\frac{5}{2}\mathrm{RT}\right)-\left(4\right)\left(\frac{5}{2}\mathrm{RT}\right)=\frac{3}{2}\mathrm{RT}\end{array}$

On solving, x = 3 moles.