![]() ![]() The larger the size of the gas molecule, the larger b is. The correction we’ve introduced is a quantity called the molar volume of gas molecules, or simply the van der Waals b constant, after the Dutch thinker who developed this correction. So we have to correct by subtracting out the amount of space taken up by the molecules, which we do this way: ![]() When we go from molecules that are infinitely small to molecules that have real size, the volume of space available is going to be thrown off by that size, and thrown off more dramatically as the gas molecules get bigger. V in the ideal gas law works best, it turns out, when it represents the amount of space in the gas not taken up by gas molecules. The size of the molecule obviously impacts volume. So we can leave n and T alone when we correct for nonideality. Neither does the kinetic energy - the assumptions of ideality of a gas have to do with the size of molecules, not the mass. ![]() The number of molecules present - the count of moles - doesn’t change when the attraction or the size of molecules changes. We’ll take the more rational approach first. One of our first big theoretical hurdles is this: when we have conditions where the ideality of the gases isn’t something we can assume, when the molecules are big and when the molecules attract one another substantially, how do we handle the correction? Even if it's not a perfect computation, it's useful. We teach the ideal gas law not because it’s a perfect description of how gases behave at all conditions, but because it comes acceptably close to describing how gases behave at the conditions we’re most likely to experience, and it gives a passable first estimate even outside of those conditions. The ideal gas law clearly communicates that putting 1.000 kg of an elemental gas into a 40.0 L container is going to result in a very high pressure. Now, it comes close to working in real life under the conditions we care about the most relatively warm temperatures and relatively low pressures, conditions where the space between molecules is great and the molecules can zip past one another without substantial attraction or repulsion. The ideal gas law, of course, is one of the great general chemistry fibs. 31.25 moles of any gas, according to the ideal gas law, would apply a pressure of 19.1 atm on the walls of its container. There's nothing in that computation that's dependent on the gas being oxygen at all the only thing in the setup of that equation that did depend on the identity of the gas was determining that there was 31.25 mol of gas in 1.000 kg of oxygen. Now think about the ideal gas law computation we've just completed. We can then use that number of moles, the volume of the tank, and the temperature to find the pressure the gas is under: We can show that this mass of oxygen corresponds to 31.25 moles of gas (prove this to yourself!). Let's fill this gas container with 1.000 kg of oxygen gas. Let's maintain this tank at room temperature of 298 K. ![]() Let's take an oxygen tank of rigid walls, with a fixed volume of 40.0 L. \)Ĭonsider a simple application of the ideal gas law. ![]()
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