Question

The speed of sound in a mixture of 1 mole of He and 2 mole of oxygen at 27°C is ______.

Options

• 400 m/s

• 401 m/s

• 402 m/s

• 403 m/s

Answer 1

The speed of sound in a mixture of 1 mole of He and 2 mole of oxygen at 27°C is 401 m/s.

Explanation:

The molecular weight of the mixture,

`M_"mix" = (n_1M_1 + n_2M_2)/(n_1 + n_2) = (1 xx 4 + 2 xx 32)/(1 + 2)`

= `68/3 xx 10^-3` kg mol^-1

For helium, `C_{"v"_1} = 3/2 R`

For oxygen, `C_{"v"_2} = 5/2 R`

`(C_"v")_"mix" = (n_1C_{"v"_1} + n_2C_{"v"_2})/(n_1 + n_2) = (1 + (3R)/2 + 2 xx (5R)/2)/(1 + 2) = (13R)/6`

Now, `(C_p)_"mix" = (C_"v")_"mix" + R = (13R)/6 + R = 19/6R`

`r_"mix" = (C_p)_"mix"/(C_"v")_"mix" = 19/13`

Speed of sound in the mixture, v = `sqrt((r_"mix" xx RT)/M_"mix")`

= `sqrt(19/13 xx (8.31 xx 300)/(68/3 xx 10^-3))`

= 401 ms^-1