how is the rms speed of n2 molecules in
a gas sample change by mixing with a sample of an at the same temperature
Your post needs clarification. .....by mixing with a sample of an ??? at the same temperature.
When two gas samples are mixed together at the same temperature, the rms (root mean square) speed of the molecules of the resulting gas mixture remains consistent. To understand why, let's break down the concept step by step.
1. Determine the rms speed of a gas molecule:
The rms speed of a gas molecule is given by the equation:
vrms = √(3kT/m)
where:
- vrms is the rms speed,
- k is the Boltzmann constant,
- T is the absolute temperature, and
- m is the molar mass of the gas molecule.
2. Consider a gas sample of N2:
For N2 molecules, the molar mass (m) is the sum of the atomic masses of two nitrogen atoms, which is approximately 28 g/mol.
3. Mixing two gas samples at the same temperature:
When two gas samples are mixed, the individual gas molecules continue to move randomly and independently. The temperature remains the same before and after mixing the gases.
4. The Law of Conservation of Energy:
According to the Law of Conservation of Energy, the total energy of the system remains constant. In the case of two gas samples mixed together at the same temperature, the total kinetic energy of the gas molecules does not change.
5. Relationship between temperature and kinetic energy:
The kinetic energy of gas molecules is directly proportional to the temperature. As the temperature remains constant after mixing the two gas samples, the kinetic energy of the molecules in the resulting gas mixture remains unchanged.
6. Conservation of rms speed:
Since the total kinetic energy and temperature do not change after mixing, the rms speed of the gas molecules also remains the same. This implies that the average speed and distribution of velocities of the molecules within the mixture are preserved.
In conclusion, when two gas samples are mixed at the same temperature, the rms speed of the N2 molecules in the resulting gas mixture remains unchanged. This is because the conservation of energy and the constant temperature ensure that the kinetic energy and, hence, the rms speed of the gas molecules are not altered.