Introduction:
The fraction of molecules of a gas with 1% of the most probable speed at STP (Standard Temperature and Pressure) can be calculated using the Maxwell-Boltzmann distribution. This distribution describes the distribution of speeds of gas molecules in a sample at a given temperature.

Maxwell-Boltzmann Distribution:
The Maxwell-Boltzmann distribution is a probability distribution that describes the speeds of gas molecules in a sample. It states that the number of molecules with a particular speed is proportional to e^(-mv^2/2kT), where m is the mass of the gas molecule, v is the speed, k is the Boltzmann constant, and T is the temperature in Kelvin.

Fraction of Molecules with 1% of Most Probable Speed:
To calculate the fraction of molecules with 1% of the most probable speed, we need to find the speed that corresponds to the most probable speed and then calculate the fraction of molecules with a speed that is 1% of this value.

1. Find the Most Probable Speed:
The most probable speed, vmp, is given by the expression vmp = √(2kT/m), where T is the temperature in Kelvin and m is the mass of the gas molecule.

2. Calculate 1% of the Most Probable Speed:
To find 1% of the most probable speed, multiply the most probable speed by 0.01: v1% = 0.01 * vmp.

3. Calculate the Fraction:
To calculate the fraction of molecules with a speed of 1% of the most probable speed, we need to integrate the Maxwell-Boltzmann distribution from v1% to infinity and then divide by the total number of molecules.

Is the Value the Same for All Gases at All Temperatures?
No, the value of the fraction of molecules with 1% of the most probable speed is not the same for all gases at all temperatures. It depends on the mass of the gas molecule and the temperature.

1. Mass of the Gas Molecule:
The fraction of molecules with a given speed depends on the mass of the gas molecule. Heavier gas molecules will have a lower fraction of molecules with a speed of 1% of the most probable speed compared to lighter gas molecules. This is because the most probable speed is inversely proportional to the square root of the mass.

2. Temperature:
The fraction of molecules with a given speed also depends on the temperature. As the temperature increases, the fraction of molecules with a speed of 1% of the most probable speed also increases. This is because the most probable speed is directly proportional to the square root of the temperature.

Therefore, the fraction of molecules with 1% of the most probable speed will vary for different gases at different temperatures due to differences in their molecular masses and the temperature of the system.