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# Worked example: Using the ideal gas law to calculate a change in volume

The ideal gas law can be used to describe a change in state for an ideal gas. In this video, we'll apply the ideal gas law to the initial and final states of a gas to see how changes in temperature and pressure affect the volume of the gas. Created by Sal Khan.

## Want to join the conversation?

• At , how does it make sense that volume increases as the temperature decreases? Didn't he say in the last video that as temperature decreases, so does volume?
• I believe it is because the differential in temperature change (296K to 229K) is countered by the much larger change in pressure (765Torr to 6.51Torr) and therefor you still get a large increase in volume even with one of the variables counteracting that increase. P1(765Torr) * T2(229K) is a much larger number than P2(6.51Torr) * T1(296K).
• At , why doesn't the # of moles change? Pressure and volume are changing in this question and isn't volume directly proportional to the # of moles (V=N)?

I have an additional question, so in this question-T2 (final temperature) is referring to the temperature inside the balloon?
• How do you suppose the number of moles could change though? The gas is inside the ballon, you should be assuming n is constant.

V=n isn’t true, they’re proportional yes, but not equal. The proportionality depends on the temperature and pressure like the ideal gas law shows.

The temperature refers to the gas molecules inside the ballon yes.
• I tried to answer the example before I continued to watch the solution, and what I did was I tried to find the value of n first by using the given initial values. After obtaining, I solved for the value of V2 by dividing P2 to nRT2 but when I watched the solution, my answer is different to Sal's answer. I would like to know what's the error in my procedure.
• That's another way to calculate the final volume which works. For your method to work you need to use 'R' and you have to make sure you use the correct version of 'R' to line up with the rest of the units in the problem. Pressure is in torr, volume is in liters, and temperature is in kelvin which means your value of the universal gas constant should have those same units. Which means you want to use 62.364 with units of L*torr*K^(-)*mol^(-). That was most likely your mistake, that you used the incorrect version of 'R'. Hope that helps.
• I'm stuck at the reasoning that the instructor initially used to formulate the equation.

If we're solving for Volume then wouldn't we divide P from both sides of the Ideal Gas Law?

PV=nRT ---> V = (nRT) / P

I understand the process of solving the equation once it has been constructed, but I'm lost as to the reasoning behind formulating it that way to begin with.

Hope someone can shed some light of this for me!

Best Regards,
Alex
(1 vote)
• So if we began with the ideal gas law and wanted to solve for volume, that would indeed be the equation we would use: V = (nRT)/P. However this use with just using this equation is that we don't just want to calculate volume at a single state, we want to calculate the volume at a new second state.

The problem with you equation is that it requires us to know the temperature, pressure, and moles of the gas to solve for the volume. However the problem gives no information about the number of moles, for either the initial or final state.

The idea with Sal's equation is that we rearrange the ideal gas law to that all the changing variables are on one side of the equation and the unchanging variables (the constants essentially) are on the other side. In this problem we don't know what the exact value of n is, but we know this it is unchanging is not gaining or losing gas so n is a constant in addition to R. So Sal's equation: PV/T = nR, has the changing variables on the left and the constants in the right. And this equation is true for both the initial and final states so we essentially have two versions of the same equation, just with different subscripts to denote the state. So if these two equations are equal to the same constant, then through the transitive property these two equations are equal to each other. Then through some algebra rearrangements we arrive at an equation that solves for the final volume.

Hope that helps.
• At weren't you supposed to multiply the 6.51 Torr by the 296 K?
• why did he count 5 places for the scientific notation superscript? I counted 6.
• How does the volume inside the balloon change when it gets to a higher / lower temperature?
(1 vote)
• As a clarification, the temperatures used in these gas problems apply to the temperature within the container such as a balloon. When we change the temperature, either as an increase or decrease, this causes a corresponding change in the kinetic energy of the gas particles. Kinetic energy is the energy of motion, so this will also change the gas molecules’ speeds. A different speed for the particles means they collide with the inside of the container with a different force, which we interpret as pressure. A different pressure therefore causes a change in volume as the gas particles push harder or weaker against the container’s surface (causing a contraction or expansion of the container).

Hope that helps.
• If the number of moles remains constant, what exactly is filling up the balloon to make it bigger?
(1 vote)
• The balloon is not gaining any additional air. The moles being constant means that the air inside the balloon is constant. The reason the balloon increases in volume is due to the change in atmospheric pressure.

The balloon has an internal pressure due to the gas inside pushing out against the inside of the balloon. It also has an external pressure due to the atmosphere’s air pushing against the outside of the balloon. Before the balloon is launched, both of these forces are equal and opposite resulting in its initial, stable volume. After it is launched, it ascends into the atmosphere where the atmospheric pressure gradually decreases. This is because as you move higher in the atmosphere, the amount of air particles decreases resulting in less collisions with surfaces (which is what pressure is). If the atmospheric pressure decreases, but the internal pressure of the balloon remains constant, then there is now a greater force pushing out compared to before it was launched. The internal pressure meeting less resistance from the atmospheric pressure causes the volume to increase.

Hope that helps.