If the speed of sound in a mixture of 2 moles of Helium and 2 moles of Hydrogen at temperature `(972)/(5)` K is n `xx 100 ms^(-1)`, then the value of n is
(Take , R = `(25)/(3) J mol^(-1) K^(-1)`)

Options

A. 9
B. 10
C. 100
D. 90

Answer

A

Explanation

Given, T = `(972)/(5) K, R = (25)/(3) J mol^(-1) K^(-1)`
Molecular mass of the mixture
= `(n_(He) M_(He) + n_(H) M_(H))/(n_(He) + n_(H))`
`therefore n_(He) = 2 "moles", n_(H) = 2 " moles" `
` M_(He) = 4r M_(H) = 2 `
`therefore` Molecular mass of the mixtures,
`M = (2 xx 4 + 2 xx 2 )/(2 + 2) `
= `(8 + 4)/(4) ` = 3 gm/mole
`therefore` Degree of freedom of mixture
f = `(2 xx 3 + 2 xx 5 )/(2 + 2) = 4 `
`therefore " " f_("mix") = 1 + (2)/(f) = 1.5`
`therefore` Speed of sound = `sqrt( (f_("mix") RT)/(M))`
= `sqrt( (1.5 xx (25)/(3) xx (972)/(5) )/(3 xx 10^(-3))) `
= 900 = n `xx ` 100 m/s
Hence, n = 9