Question

The most probable speed in a sample of gas refers to (1) The maximum speed of the molecules (2) The minimum speed of the molecules (3) The speed of the largest fraction of the molecules (4) None of the above

Short answer

Option (3) - The speed of the largest fraction of the molecules.

Step-by-step solution

Understand the Term 'Most Probable Speed'

The term 'most probable speed' in the context of a gas sample typically refers to the speed at which the largest number of gas molecules are moving. This is a key concept in the kinetic theory of gases.

Analyze Each Option

Look at each option and assess which one aligns with the definition of 'most probable speed'. Option (1) refers to the maximum speed, which is not typically representative of the largest number of molecules. Option (2) refers to the minimum speed, which is also not correct. Option (3) indicates the speed of the largest fraction of the molecules, which matches our definition. Option (4) suggests none of the previous options are correct.

Choose the Correct Option

Based on the analysis, option (3) - 'The speed of the largest fraction of the molecules', best fits the definition of 'most probable speed'.

Key concepts

kinetic theory of gases

The kinetic theory of gases is a fundamental concept in physics and chemistry. It explains the behavior of gas particles in terms of their motion and interactions. According to this theory, gas particles are in constant random motion.
As they move, they collide with each other and the walls of the container.
These collisions are elastic, meaning there is no net loss of total kinetic energy.
The kinetic theory of gases provides essential insights into properties like pressure, temperature, and volume.
The temperature of a gas is proportional to the average kinetic energy of its molecules.
Higher temperatures mean higher average speeds of the gas molecules.

molecular speed distribution

Molecular speed distribution describes how the speeds of molecules are spread out in a sample of gas.
Not all molecules move at the same speed; instead, there is a range of speeds.
Some molecules move very slowly, while others move extremely fast.
Between these extremes, most molecules will have speeds in a certain range.
The molecular speed distribution can be represented using a graph, with the speed on the x-axis and the number of molecules on the y-axis.
This graph shows that most gas molecules have speeds around a central value, while fewer molecules move very slowly or very quickly.
This central value is critical in understanding the behavior of gas and is closely related to the concept of the 'most probable speed.'

maxwell-boltzmann distribution

The Maxwell-Boltzmann distribution is a statistical tool used to describe the molecular speed distribution of gas particles.
It mathematically describes how the speeds of molecules are distributed in a gas sample.
This distribution provides a curve that shows the probability of finding a molecule with a given speed.
The peak of this curve corresponds to the most probable speed, where most gas molecules are found.
The distribution tells us that:

• The majority of molecules have speeds close to the most probable speed.
• There are fewer molecules at very high and very low speeds.

Using this distribution, we can derive important concepts like the average speed and root mean square speed.
The Maxwell-Boltzmann distribution depends on the temperature and mass of the gas molecules.
Higher temperatures shift the distribution curve to the right, meaning higher speeds.