Heat Q=32RT 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=32nRT for monatomic gasInternal energy of n moles of an ideal gas=52nRT(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=32RT (given)⇒(2x)3RT2+(4−x)52RT−(4)52RT=32RTOn solving, x = 3 moles.