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according to kinetics theory of gases,the ratio of root mean square velocity of molecular oxygen and hydrogen at 300k is
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Understanding Root Mean Square Velocity
The root mean square (RMS) velocity is a measure of the speed of particles in a gas. It is derived from the kinetic theory of gases, which relates the temperature of a gas to the average kinetic energy of its molecules.
RMS Velocity Formula
The RMS velocity (v_rms) can be expressed as:
- v_rms = sqrt(3RT/M)
Where:
- R = Universal gas constant
- T = Absolute temperature in Kelvin
- M = Molar mass of the gas
Molecular Weights of Oxygen and Hydrogen
- Molar mass of Oxygen (O2) = 32 g/mol
- Molar mass of Hydrogen (H2) = 2 g/mol
Calculating the Ratio of RMS Velocities
To find the ratio of RMS velocities of O2 and H2 at 300 K:
- For Oxygen:
- v_rms(O2) = sqrt(3 * R * 300 / 32)
- For Hydrogen:
- v_rms(H2) = sqrt(3 * R * 300 / 2)
The ratio can be simplified as:
- v_rms(O2) / v_rms(H2) = sqrt(M_H2 / M_O2)
Substituting the molar masses:
- v_rms(O2) / v_rms(H2) = sqrt(2 / 32) = sqrt(1/16) = 1/4
Conclusion
Thus, the ratio of the root mean square velocity of molecular oxygen to that of hydrogen at 300 K is 1:4. This means hydrogen molecules move four times faster than oxygen molecules at the same temperature, highlighting the influence of molecular mass on gas velocity.
The root mean square (RMS) velocity is a measure of the speed of particles in a gas. It is derived from the kinetic theory of gases, which relates the temperature of a gas to the average kinetic energy of its molecules.
RMS Velocity Formula
The RMS velocity (v_rms) can be expressed as:
- v_rms = sqrt(3RT/M)
Where:
- R = Universal gas constant
- T = Absolute temperature in Kelvin
- M = Molar mass of the gas
Molecular Weights of Oxygen and Hydrogen
- Molar mass of Oxygen (O2) = 32 g/mol
- Molar mass of Hydrogen (H2) = 2 g/mol
Calculating the Ratio of RMS Velocities
To find the ratio of RMS velocities of O2 and H2 at 300 K:
- For Oxygen:
- v_rms(O2) = sqrt(3 * R * 300 / 32)
- For Hydrogen:
- v_rms(H2) = sqrt(3 * R * 300 / 2)
The ratio can be simplified as:
- v_rms(O2) / v_rms(H2) = sqrt(M_H2 / M_O2)
Substituting the molar masses:
- v_rms(O2) / v_rms(H2) = sqrt(2 / 32) = sqrt(1/16) = 1/4
Conclusion
Thus, the ratio of the root mean square velocity of molecular oxygen to that of hydrogen at 300 K is 1:4. This means hydrogen molecules move four times faster than oxygen molecules at the same temperature, highlighting the influence of molecular mass on gas velocity.
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according to kinetics theory of gases,the ratio of root mean square velocity of molecular oxygen and hydrogen at 300k is Related: Introduction to Chemical Kinetics - Chemical Kinetics?
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