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With the increase in temperature of a gas, the fraction of molecules having velocities within a given range around the most probable velocity, would A) increase B) decrease C) remain unchanged D) initially increase and then decrease Correct answer is (B). Can you explain the answer.?
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With the increase in temperature of a gas, the fraction of molecules h...
Explanation:

Introduction:
The most probable velocity of gas molecules can be determined using the Maxwell-Boltzmann distribution, which describes the distribution of molecular velocities in a gas at a given temperature. This distribution shows that there is a range of velocities for gas molecules, with a peak at the most probable velocity.

Effect of temperature on molecular velocities:
When the temperature of a gas increases, the average kinetic energy of the gas molecules also increases. This leads to an increase in the velocity of the gas molecules. According to the Maxwell-Boltzmann distribution, an increase in temperature will cause the peak of the distribution curve to shift towards higher velocities.

Effect on the fraction of molecules within a given velocity range:
When the temperature of the gas increases, the fraction of molecules having velocities within a given range around the most probable velocity will decrease. This is because the distribution curve becomes broader and flatter at higher temperatures.

Explanation:
- Initially, at a lower temperature, the distribution curve is narrower and taller, with a well-defined peak at the most probable velocity. The fraction of molecules within a given velocity range around the most probable velocity is relatively high.
- As the temperature increases, the distribution curve becomes broader and flatter. The peak of the curve shifts towards higher velocities. This means that a larger fraction of molecules now have velocities outside the given range around the most probable velocity.
- Therefore, the fraction of molecules within the given velocity range decreases as the temperature increases. This is because the higher temperature leads to a larger spread of velocities among the gas molecules.

Conclusion:
In summary, as the temperature of a gas increases, the fraction of molecules having velocities within a given range around the most probable velocity decreases. This is due to the broader distribution of velocities at higher temperatures.
Community Answer
With the increase in temperature of a gas, the fraction of molecules h...
Because on increasing the temperature no of effective collision increases which in turn decreases the velocity of molecules
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For certain substances such as ammonium chloride, nitrogen peroxide, phosphorus pentachloride, etc. the measured densities are found to be less than those calculatedfrom their molecular formula. The observed densities decrease towards a limit as thetemperature is raised. This is due to the splitting of the molecules into simpler ones. The process is reversible and is called thermal dissociation.Examples :With increase in the number of molecules, the volume increases (pressure remaining constant) and, in consequence, the density decreases. As the temperature rises, more and more dissociation takes place, and when practically complete dissociation occursthe density reaches its lowest limit.The extent of issociation, ice., the fraction of the total number of molecules which suffers dissociation is called the degree of dissociation. Gas density measurements can be used to determine the degree of dissociation. Let us take by general case where one molecule of a substance A splits up into n molecule of B on heating; i.e.,t = 0 at = teq a x nx Total no. of moles Observed molecular weight or molar mass of the mixtureQ.If the total mass of the mixture in the above case is 300 gm, the moles at C(g) present are.

For certain substances such as ammonium chloride, nitrogen peroxide, phosphorus pentachloride, etc. the measured densities are found to be less than those calculatedfrom their molecular formula. The observed densities decrease towards a limit as thetemperature is raised. This is due to the splitting of the molecules into simpler ones. The process is reversible and is called thermal dissociation.Examples :With increase in the number of molecules, the volume increases (pressure remaining constant) and, in consequence, the density decreases. As the temperature rises, more and more dissociation takes place, and when practically complete dissociation occursthe density reaches its lowest limit.The extent of issociation, ice., the fraction of the total number of molecules which suffers dissociation is called the degree of dissociation. Gas density measurements can be used to determine the degree of dissociation. Let us take by general case where one molecule of a substance A splits up into n molecule of B on heating; i.e.,t = 0 at = teq a x nx Total no. of moles Observed molecular weight or molar mass of the mixtureQ.A sample of mixture of A(g), B(g) and C(g) under equilibrium has a mean molecular weight (observe d) is 80.The equilibrium is Find the degree of dissociation for A(g).

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With the increase in temperature of a gas, the fraction of molecules having velocities within a given range around the most probable velocity, would A) increase B) decrease C) remain unchanged D) initially increase and then decrease Correct answer is (B). Can you explain the answer.?
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