First slide

Rms speed

Question

The speed of sound in hydrogen at STP is v. The speed of sound in a mixture containing 3 moles of hydrogen and 2 moles of oxygen at STP will be

Easy

A

$\frac{v}{2}$
B

$\frac{v}{\sqrt{5}}$
C

$\sqrt{7} v$
D

$\frac{v}{\sqrt{7}}$

Solution

Let the density of hydrogen be $ρ' = 2 ρ,$ then the density of oxygen will be $32 ρ$ . The density of the mixture will be
$ρ " = \frac{3}{5} \times 2 ρ + \frac{2}{5} \times 32 ρ = 14 ρ$
Since the pressure is the same, we have
$\frac{v "}{v} = \sqrt{\frac{ρ'}{ρ "}} = \sqrt{\frac{2 ρ}{14 ρ}} = \frac{1}{\sqrt{7}}$

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