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# Kinetic molecular theory and the gas laws

The kinetic molecular theory (KMT) can be used to explain the macroscopic behavior of ideal gases. In this video, we'll see how the KMT accounts for the properties of gases as described by the various gas laws (Boyle's law, Gay-Lussac's law, Charles's law, Avogadro's law, and Dalton's law of partial pressures). Created by Sal Khan.

## Want to join the conversation?

• A few questions about pressure:
1. Is pressure = force / total surface area of the container?
2. Force is a vector quantity, so if we want the total force, shouldn't force to the right cancel with forces to the left?
(Sorry if this is more focusing on physics)
Thanx!:)
• Pressure is force per unit of area. We're looking at each individual square of area (of whichever unit) and seeing how much force is being applied to each of those squares. If it's a gas then we assume the pressure is being exerted equally on the entire surface.

Force is a vector but all of these forces are directed outward against the surface of the container so they're not opposing each other and therefore not canceling each other out.

Hope that helps.
• do the molecules of a gas exert an attractive force between each other
• Good question! This is where things start getting interesting. You are right in saying that there is an attractive force between gas molecules, but for ideal gasses we ignore them and assume they don't impact anything (that's why they're "ideal"). Of course, sometimes, this causes problems. Deviations from the ideal gas law like these are covered in the next unit.
• At Sal explains that Pressure is proportional to Temperature because as the temperature increases, the velocity of the particles hitting the wall also speeds up, thereby increasing the pressure on the container. However, since the temperature is proportional to (mv^2)/2, wouldn't the velocity of the particles have a square root relationship to temperature. Thus shouldn't the pressure of the container also have a squared rooted relationship to temperature?
• Pressure is directly proportional to temperature, or P α T. And temperature is directly proportional to kinetic energy where kinetic energy has the formula K.E. = (1/2)mv^(2). So we can say that temperature is directly proportional to the square of the particle's velocity, or T α v^(2). So therefore we can say that pressure is also directly proportional to the square of the particle's velocity through the transitive property, or P α v^(2).

For some reason you're taking the square root of the temperature-velocity relationship, essentially getting sqrt(T) α v, and then saying that now the square root of temperature is directly proportional to pressure, or sqrt(T) α P. Which doesn't follow since there is no way to link the square root of temperature with pressure, except through velocity. We can do the same operation with the pressure-velocity relationship and say that sqrt(P) α v, and only know we can relate pressure and temperature together through the transitive property using velocity. This yields sqrt(P) α sqrt(T), where the square roots can be removed by squaring both sides yielding P α T. Which is just the original proportionality relationship. So, no pressure and temperature don't have a square root relationship.

Hope that helps.
• This might be too unrelated, but I have a clear memory of leaving inflated balloons in a room, and after a month or so they are shrivelled up and tiny.

I understand that if there are temperature drops in the room, the balloon's volume will decrease, but surely this would only be a bit.

Assuming the temperature in the room stays roughly the same, why do balloons (or balls, or anything that's inflated for that matter) eventually deflate?

Is it because they are not 100% airtight? Or some other unrelated physics law...
Thanks
(1 vote)
• Temperature does affect gas volume in a balloon according to Charles’s Law. As temperature decreases, volume decreases too (assuming the pressure and moles of gas remain constant). Likewise, as temperature increases, volume increases too (same assumptions). Mathematically this is represented as: V α T, which means volume of gas is directly proportional to the temperature of the gas.

So temperature would affect a balloon’s volume, but it would be a different pattern then what you’re observing. The temperature throughout the day changes as it transitions from day to night, from hot to cold. So if the volume changes were solely due to temperature, you would observe a periodic change in the balloon’s volume. If would shrink during the night when the temperature is at its minimum, and inflate during the day when the temperature is at its maximum. But if the volume is steadily decreasing regardless of the time of day, then another effect is causing the volume change.

For balloons or any other rubber balls filled with air (tires too), they lose gas particles inside them over time. Technically this is Avogadro’s Law which says that moles of a gas and its volume are directly proportional: n α V. So if there are less moles of gas in the balloon, then the volume will decrease. And unlike the temperature cause, this will be permanent since gas will not reenter the balloon and inflate it again.

The gas particles escaping isn’t so much due to the tied end or the place where you filled the balloon up though. If you make a tight seal, you’ll still see the balloon deflate. Most of the gas particles actually escape by passing through the rubber. Interestingly the gas particles do this primarily by dissolving into the rubber, migrating through the rubber, and ‘evaporating’ into the outside air. Even though the balloon’s rubber is a solid, you can have gas particles dissolve into it and bind to the rubber polymer. It’ll alternatively bind and unbind as it makes its way through the rubber until finally reaching the outside. If you’re interested there’s an old paper called the “Permeability of Rubber to Gases” by Edwards and Pickering published back in 1919 which talks about this and how well different types of gases dissolve in rubber.

So a balloon shrivels up after a while because the gas gradually escapes.

Hope that helps.