HCl(g) HBr(g) HF(g)
Which of these gases has the fastest average speed? Which has the highest average kinetic energy?
To determine which of these gases has the fastest average speed, we can use the concept of the root mean square (RMS) speed. The RMS speed can be calculated using the following equation:
RMS speed = √(3RT / M)
Where:
RMS speed is the root mean square speed,
R is the ideal gas constant (8.314 J/(mol K)),
T is the temperature in Kelvin, and
M is the molar mass of the gas.
To compare the RMS speeds of HCl, HBr, and HF, we need to know the molar masses of these gases. The molar mass of HCl is approximately 36.461 g/mol, HBr is approximately 80.911 g/mol, and HF is approximately 20.01 g/mol.
Assuming the gases are at the same temperature, we can see that the gas with the lowest molar mass will have the highest RMS speed, as per the equation given above. Therefore, HF has the fastest average speed among HCl, HBr, and HF.
Now, let's discuss the gas with the highest average kinetic energy. The average kinetic energy of a gas can be calculated using the equation:
Average kinetic energy = (3/2)kT
Where:
Average kinetic energy is the average energy associated with the motion of gas particles,
k is the Boltzmann constant (1.38 × 10^-23 J/K),
and T is the temperature in Kelvin.
Since the average kinetic energy is directly proportional to temperature, all gases at the same temperature will have equal average kinetic energies. Therefore, HCl, HBr, and HF gases will have the same average kinetic energy if they are at the same temperature.