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Question

The speed of sound in hydrogen gas at STP is vo. The speed of sound in a mixture containing 3 parts of hydrogen gas and 2 parts of oxygen gas at STP will be

A
vo3
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B
vo5
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C
vo6
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D
vo7
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Solution

The correct option is D vo7
At a given pressure and temperature, the density of gas is directly proportional to its molecular weight.
PM=ρRT
ρM
ρ1ρ2=M1M2=232=116
ρ2=16ρ1 ...............(1)
Here,
ρ1 density of hydrogen,
ρ2 density of oxygen

Now, density of mixture,
ρmix=ρ1 V1 +ρ2 V2V1+V2
ρmix=ρ1V1+16ρ1×2V13V1+2V13=35ρ1 V15V1
[ given V1V2=32 and from (1)]
ρmix=7 ρ1 ..........(2)
Speed of sound,
v=γPρ
At constant pressure,
v1ρ
So,
vH2vmix=ρmixρH2
vmix=vH2×ρH2ρmix
vmix=vo×ρ17ρ1
vmix=vo7

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