Question

The speed of sound in hydrogen at NTP is 1270 m/s. Then, the speed in a mixture of hydrogen and oxygen in the ratio 4:1 by volume will be:

317 m/s
635 m/s
830 m/s
950 m/s

Answer 1

Let the volume of oxygen be V
then the volume of Hydrogen be 4V
so, total volume of mixture of Hydrogen and oxygen = 4V + V = 5V

now, mass of mixture = mass of Hydrogen + mass of oxygen

volume of mixture × density of mixture = volume of Hydrogen × density of Hydrogen + volume of oxygen × density of oxygen

5V × D = 4V × d + V × 16d [ actually, density is directly proportional to molar mass of element , so, density of Hydrogen = 16 × density of oxygen ]
Where D is density of mixture , d is the density of Hydrogen.
so, D = 4d
means , density of mixture is 4 times of density of Hydrogen .

now, speed of sound in the mixture,
$\bold{V_{mix} = \sqrt \frac{\gamma P}{D}}$
γ is same for mixture because both the gas in the mixture { Hydrogen and oxygen } are diamagnetic .
so, speed of sound in the Hydrogen ,
$\bold{V_{H_2}= \sqrt\frac{\gamma P}{d}}$

$now, \bold{\frac{V_{mix}}{V_{H_2}}=\sqrt{\frac{d}{D}}}$
now, you should use D = 4d ,
$then, \bold{V_{mix}=\frac{V_{H_2}}{2}}$
$so, \bold{ V_{mix}=\frac{1270}{2}=635m/s}$

Answer 2

Answer:

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Explanation:

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