The Most Probable Speed of H2

To determine the most probable speed of H2 gas, we can use the Maxwell-Boltzmann distribution of molecular speeds. According to this distribution, the most probable speed is the speed at which the highest number of molecules are moving.

The formula for the most probable speed (vmp) is given by:

vmp = √(2RT/M)

where R is the gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas.

Given Information:
- Mass of H2 gas (m) = 8 g
- Most probable speed of H2 gas (vmp) = 200 m/s

Calculating the Average Kinetic Energy (KE)

The average kinetic energy of a gas is given by the formula:

KE_avg = (3/2) k T

where k is the Boltzmann constant and T is the temperature in Kelvin.

To calculate the average kinetic energy of H2 gas, we need to know the temperature. Since the temperature is not provided in the given information, we cannot determine the exact value of the average kinetic energy. Therefore, the answer is none (d).

However, we can discuss the relationship between the most probable speed and the average kinetic energy.

Relationship between Most Probable Speed and Average Kinetic Energy

The most probable speed of a gas is related to the average kinetic energy through the equation:

vmp = √(2KE_avg/M)

From this equation, we can see that as the average kinetic energy increases, the most probable speed also increases. This makes sense because higher average kinetic energy implies that the gas molecules have higher velocities on average.

Conclusion

In conclusion, based on the given information, we cannot determine the exact value of the average kinetic energy of H2 gas. However, we can conclude that the most probable speed of H2 gas is 200 m/s. The relationship between the most probable speed and the average kinetic energy indicates that as the average kinetic energy increases, the most probable speed also increases.