Question

velocity of sound in hydrogen at ntp is v . what will be the velocity of the sound in a mixture of hydrogen and oxygen in the 4:1 atNTP is

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, $\bold{V_{mix}=\frac{V_{H_2}}{2}}$
​​
$\bold{ V_{mix}=\frac{1270}{2}=635m/s}$

Answer 2

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,

γ is same for mixture because both the gas in the mixture { Hydrogen and oxygen } are diamagnetic .

so, speed of sound in the Hydrogen ,