The root mean square velocity of all molecules in a mixture containing CO 2 and N 2 in the mole ratio 1 : 7 is found to be x times the root mean square velocity of CO 2 molecules at the same tem

Question

The root mean square velocity of all molecules in a mixture containing CO 2 ​ and N 2 ​ in the mole ratio 1 : 7 is found to be x times the root mean square velocity of CO 2 ​ molecules at the same temperature. The value of x is :

TestHub · Accepted Answer

⟨ c 2 ⟩ = 8 1 × 44 3 k T ​ + 7 × 28 3 k T ​ ​ = 8 3 k T ​ ( 44 1 ​ + 4 1 ​ ) = 8 3 k T ​ × 44 12 ​ = 88 9 k T ​ (per unit mass basis). For CO 2 ​ : c 2 = 44 3 k T ​ = 88 6 k T ​ . So x 2 = 6 9 ​ = 2 3 ​ , x = 2 3 ​ ​ .

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