Oxygen is 16 times heavier than hydrogen. Equal volumes of hydrogen and oxygen mixed together and get thr mixture. What is ratio velocities of sound wave from mixture to the hydrogen ?

Question

Answer

Understanding Sound Velocity in Gases
When discussing the velocities of sound in gases, it is essential to consider their molecular weights and the relationship between the density of the gas and the speed of sound.
Sound Velocity Formula
The velocity of sound (v) in a gas can be expressed as:
v = √(γRT/M)
Where:
- γ (gamma) = ratio of specific heats
- R = universal gas constant
- T = absolute temperature
- M = molar mass of the gas
Mixing Hydrogen and Oxygen
- Hydrogen (H2) has a molar mass of approximately 2 g/mol (1 g/mol per hydrogen atom).
- Oxygen (O2) has a molar mass of approximately 32 g/mol (16 g/mol per oxygen atom).
When equal volumes of hydrogen and oxygen are mixed, the average molar mass (M_mixture) of the mixture can be calculated as follows:
- M_mixture = (M_H2 + M_O2) / 2 = (2 + 32) / 2 = 17 g/mol.
Comparative Analysis of Sound Velocities
- For hydrogen:
- M_H2 = 2 g/mol.
- v_H2 = √(γRT/2).
- For the mixture:
- M_mixture = 17 g/mol.
- v_mixture = √(γRT/17).
Calculating the Ratio of Velocities
To find the ratio of the velocity of sound in the mixture to that in hydrogen:
- v_mixture / v_H2 = √(2/17).
Conclusion
- The ratio of sound velocities indicates that sound travels faster in hydrogen than in the mixture due to its significantly lower molar mass.
- Hence, sound velocity in the mixture is lower than that in hydrogen, highlighting the influence of molecular weight on sound propagation in gases.

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