Heat Q=32RT, is supplied to moles of an ideal diatomic gas at temperature 7, which remains constant. How many moles of the gas are dissolved into atoms?

Let x moles of diatomic gas be associated, x moles of diatomic gas become 2x moles of a monoatomic gas after dissociation. Internal energy of n moles of an ideal gas=32nRT for monoatomic gas =52nRT for diatomic gas 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=32RT (given) (2x)3RT2+(4−x)52RT−(4)52RT=32RTOn solving, x = 3 moles.