Oxygen (assume it to be ideal gas) is filled in a closed container of constant volume. If the temperature of the gas is increased by a significant amount, some of the molecules dissociate into atoms.

Question

Oxygen (assume it to be ideal gas) is filled in a closed container of constant volume. If the temperature of the gas is increased by a significant amount, some of the molecules dissociate into atoms. If the specific heat changes by 8% , what fraction of initial amount of oxygen has been dissociated ? (Do not consider vibrational degree of freedom)

TestHub · Accepted Answer

​ M C f ​ = m 1 ​ c 1 ​ + m 2 ​ c 2 ​ M C f ​ = ( 1 − x ) m c 1 ​ + 2 x × 2 m ​ c 2 ​ = ( 1 − x ) × 2 5 R ​ + 2 x × 2 3 R ​ = ( 5 + x ) 2 R ​ ⇒ C f ​ = m ( 5 + x ) R /2 ​ ; C i ​ = 2 m 5 R ​ ∴ c Δ c ​ = 0.08 ⇒ 5 x ​ = 0.08 ⇒ x = 0.4 ​

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