One mole of a monoatomic gas is mixed with three moles of a diatomic gas. The molecular specific heat of mixture at constant volume is α 2 4 R J mol K - 1 ; then the value of α will be _____ . (Assume that the given diatomic gas has no vibrational mode.)

Step-by-step solution

Molecular specific heat at constant volume in terms of degrees of freedom is given by C V = f 2 R Molecular specific heat of mixture at constant volume is C V / mix = n 1 C V 1 + n 2 C V 2 n 1 + n 2 = 1 × 3 R 2 + 3 × 5 R 2 1 + 3 = 9 R 4 = α 2 4 R ⇒ α = 3