Does the pressure exerted by a gas depend on its molar mass?
Yes, the pressure exerted by a gas does depend on its molar mass. This relationship can be understood by considering the ideal gas law, which states that the pressure exerted by a gas is directly proportional to its molar mass.
The ideal gas law is represented by the equation:
PV = nRT
where P is the pressure of the gas, V is the volume it occupies, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
Rearranging the ideal gas law, we can isolate the pressure term:
P = (nRT) / V
Now, if we compare two different gases, with the same volume, temperature, and number of moles, the only difference between them would be their molar mass. Let's say we have a gas with molar mass M1 and another gas with molar mass M2.
The number of moles, n, remains constant for both gases, as well as the volume, V, and temperature, T. Substituting these values into the equation:
P1 = (nRT) / V
P2 = (nRT) / V
Since n, R, V, and T are all the same for both gases, we can see that the pressure is directly proportional to the molar mass of the gas. Therefore, a gas with a higher molar mass will exert a higher pressure compared to a gas with a lower molar mass, assuming other variables are constant.
It's important to note that this relationship holds true when comparing gases at the same temperature and volume.