Question

In a gaseous sample containing 4 mol of ClF at 514 K and 1 bar, how many moles of molecules are in the first excited vibrational state? Treat the gas as non-interacting with capital theta subscript v i b end subscript = 1132 K.

Answer 1

Relative population of two different energy states is given by Boltzman population distribution :

since,

suppose the system is at temperature equals to 300 K, then

= 0.023

i.e.  relative population between first excited state and ground state is 0.023.

assuming that initially all the molecules were in the ground state, then 2.3 % of the molecules will be in first excited state.

i.e. 0.023 * 4

= 0.09 mol of ClF

= 0.09 moles of ClF is in first excited state.