1
$\begingroup$

My teacher told me that if we keep some weight on a piston containing 2 different gases, both gases will be at constant pressure, and hence the volume occupied by each gas will be proportional to number of moles of each gas according to the ideal gas law ($pV=nRT$)

My doubt is that won't the 2 gases exert different pressures and the sum of the two different pressures will be equal and opposite to the pressure exerted by the weight? Also, if the two gases exert different pressures, then how can we say that both gases are at constant pressure? Do gases at constant pressure exert equal pressure?

$\endgroup$
2
$\begingroup$

Without a clearer setup it's difficult to say whether someone misspoke, whether you misunderstood precisely what your teacher was saying, or whether your teacher was incorrect.

If the setup is that there is a single piston that contains two gases, and a weight is placed upon it, then:

  1. The volume of each of the gases in that piston is equal to the entire volume of the piston. The volume of any gas is the entire volume of its container. If the gases are ideal, then the volume of the piston will be the sum of the volumes of the piston if each of the gases were kept in it individually.
  2. The pressures of the two gases sum to the pressure exerted on the piston by the weight (and the outside atmosphere.) The pressures will be constant as long as the amount of gas present, the applied pressure, and the temperature are kept constant.

If the setup is that there are two pistons that each contain a gas, and an identical weight is placed upon each (or a single piston filled with two gases, one at a time) then:

  1. The volume of the two pistons will be proportional to the number of moles of ideal gas that it contains, as long as both are also at the same temperature (we're already assuming the same pressure due to the identical weight.)
  2. The pressures of the gases in the two pistons will be equal, because they are opposing the same weight + outside atmospheric pressure.

As to your other questions:
Gases at different pressures do indeed exert constant pressure, assuming things like constant temperature, constant volume, and constant number of moles of gas. The pressure of a gas is the result of huge numbers of gas particles striking the walls of their container every second. The rate at which those particles strike and rebound and the force with which they do so determines the pressure. Because there are sooooo many gas particles in any reasonable quantity of gas, the fluctuation in the rate and intensity of those collisions is nearly constant (to many, many decimal places.)

Gases at constant pressure do not necessarily exert equal pressures. If I pump up the front tire of a bicycle to twice the pressure as the back tire, each has a constant pressure, but they are different. If I put two moles of gas A and one mole of gas B into a sealed container, the pressure due to A will be twice that of the pressure due to B, but both will be constant, as will their sum, the total pressure of the container.

$\endgroup$
  • $\begingroup$ Thankyou for ypur reply.I didn't understand the line:"gases at different pressure do indeed exert constant pressure."What is the difference between the pressure exerted by gas and gas at any pressure? $\endgroup$ – Raksh23 Jan 11 '16 at 9:11
  • $\begingroup$ @Raksh23 I meant to say that although the partial pressures (the individual pressures of two or more gases in a mixture) are probably different, they are still constant. If I have 1 atm of mixed nitrogen and oxygen, with a 2:1 ratio of N2 to O2, the pressure of N2 will be 2/3 atm and the pressure of O2 will be 1/3 atm. Though they are different, those values will remain constant (unless other factors like temperature, volume, etc change.) I won't find that both the N2 and the O2 are suddenly producing 1/2 atm, for example. $\endgroup$ – Jason Patterson Jan 12 '16 at 2:46
1
$\begingroup$

Saying that the gases are at constant pressure means that the pressures do not vary with spatial position within the cylinder. Both gases occupy the entire volume, and, as you said, they exert unequal pressures. The pressure that a gas exerts within a mixture is called its partial pressure. The sum of the partial pressures of the gases add up to the total pressure, as you also said. The partial pressures are unequal, and the partial pressure of each gas is equal to the total pressure in the cylinder times the mole fraction of that gas. The total pressure supports the weight of the piston, so it is equal to the weight of the piston divided by its cross sectional area. I don't know what your teacher said, but your own understanding of what is happening is right on target.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.