The total number of degrees of freedom associated with 2 ~cm ^3 of Nitrogen gas at normal temperature and pressure is: [Given Avogadro number as ' N ' ]

Step-by-step solution

At normal temperature and pressure (NTP), the molar volume of an ideal gas is 22400 cm ^3 . The number of moles n in 2 cm ^3 of Nitrogen gas is given by n = V V_ m = 2 22400 = 1 11200 moles. Nitrogen ( N₂ ) is a diatomic gas. The degrees of freedom f for a diatomic molecule at room temperature is 5 (3 translational and 2 rotational). The total number of molecules N_ total is n N , where N is the Avogadro number. Thus, N_ total = N 11200 . The total degrees of freedom is given by f N_ total = 5 N 11200 = N 2240 . An