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Select the correct option(s) for an ideal gas
  • a)
    Most probable speed increases with increase in temperature
  • b)
    Fraction of particles moving with most probable speed increases with increase in temperature
  • c)
    Fraction of particles moving with most probable speed are more for Cl2 than H2 under similar condition of T, P & V.
  • d)
    Most probable speed is more for Cl2 than H2 at same temperature
Correct answer is option 'A,C'. Can you explain this answer?
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Select the correct option(s) for an ideal gasa)Most probable speed inc...
(A) Most probable speed increases with an increase in temperature.
M2RT​​

(B) The fraction of particles moving with most probable speed decreases with an increase in temperature.
With an increase in the temperature, the most probable velocity increases and the fraction of molecules decreases.

(C) The fraction of particles moving with most probable speed is more for Cl2​ than H2​ under a similar condition of T, P & V.
The most probable speed is inversely proportional to the molar mass. Higher is the molar mass, lower will be the most probable speed and higher will be the fraction of molecules moving at most probable speed.

(D) Most probable speed is lower for chlorine than for hydrogen at the same temperature.
The most probable speed is inversely proportional to the molar mass. Higher is the molar mass, lower will be the most probable speed.
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Select the correct option(s) for an ideal gasa)Most probable speed inc...
Explanation:

a) Most probable speed increases with an increase in temperature:


  • According to the Maxwell-Boltzmann distribution, the most probable speed of gas particles is directly proportional to the square root of the temperature.

  • As the temperature increases, the kinetic energy of the gas particles also increases.

  • Since kinetic energy is directly proportional to the square of the velocity, an increase in temperature leads to an increase in the most probable speed of gas particles.

  • Therefore, option 'a' is correct.



b) Fraction of particles moving with the most probable speed increases with an increase in temperature:


  • The fraction of particles moving with the most probable speed is determined by the shape of the Maxwell-Boltzmann distribution curve.

  • At lower temperatures, the curve is broad and more particles have speeds below the most probable speed.

  • As the temperature increases, the curve becomes narrower and taller, indicating that more particles have speeds closer to the most probable speed.

  • Therefore, option 'b' is incorrect.



c) Fraction of particles moving with the most probable speed is more for Cl2 than H2 under similar conditions of T, P, V:


  • The fraction of particles moving with the most probable speed depends on the molar mass of the gas.

  • According to Graham's law of effusion, the rate of effusion of a gas is inversely proportional to the square root of its molar mass.

  • Since Cl2 has a higher molar mass than H2, it will have a lower rate of effusion and a higher fraction of particles moving with the most probable speed.

  • Therefore, option 'c' is correct.



d) Most probable speed is more for Cl2 than H2 at the same temperature:


  • The most probable speed depends on the temperature and is independent of the molar mass of the gas.

  • Therefore, option 'd' is incorrect.


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Select the correct option(s) for an ideal gasa)Most probable speed increases with increase in temperatureb)Fraction of particles moving with most probable speed increases with increase in temperaturec)Fraction of particles moving with most probable speed are more for Cl2 than H2 under similar condition of T, P & V.d)Most probable speed is more for Cl2 than H2 at same temperatureCorrect answer is option 'A,C'. Can you explain this answer?
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