A vessel contains a non-linear triatomic gas. If 50 % of gas dissociate into individual atom, then find new value of degree of freedom by ignoring the vibrational mode and any further dissociation.

(1) 2.15

(2) 3.75

(3) 5.25

(4) 6.35

Ans. is given 3.75 but mine is coming 4.5. Pls give detailed explanation with the solution...

Let us assume 1 mole of triatomic gas is there. Therefore, 3*Na (avogadro number of particles) is present initiallySo 0.5 moles has 1.5 Na atomsNow one part of 0.5 moles remains undisssociated. Therefore degree of dissociation is 0.5 *6 =3The other 0.5 moles has 1.5 Na which breaks into 3 atoms. So total number of atoms is 0.5 NaNow degree of freedom for monoatomic gas is 3So degree of freedom for 0.5 Na monoatomic particles is 1.51.5 *0.5(number of moles) gives 0.75So total is 3.75