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Avogadro's Law

There is even more we can do with good old P V = n R T. The first part of this section introduced you to Avogadro's Law. One mole of any gas takes up a volume of 22.4 liters at standard temperature and pressure (STP). If we go back to the comparison of two formulas of the Ideal Gas Law, we have:

P1 V1 = n1 R T1
P2 V2 = n2 R T2

The R's are the same, so they can be cancelled. At standard temperature, T1 = T2 = 273K, and the T's can be cancelled. At standard pressure, P1 = P2 = 1 atmosphere, and the P's can be cancelled. When all the canceling has been done,

V1 = n1
V2   n2

If the volume is proportional to the number of mols of a gas, there is a constant, k, that we can use in the formula, V = k n, to express the proportionality of V and n. What is that proportionality constant? At standard temperature and pressure, the pressure is one atmosphere and the temperature is 273K. The Universal Gas Constant is still 0.0821 Liter - atmospheres per mol - degree. Let's set n at one to find out what k is.

P V = n R T and V = n R T/P

V = (1 mol) (0.0821 L - A/ mol - K) (237 K) / (1 A)

Cancel the mols, the A's (for Atmosphere) and the K's. Do the math.

V = 22.4 Liters

We have seen this number before in Avogadro's Law, and this is where it comes from. When n is one mol and V is 22.4 Liters, k is 22.4 Liters/mol.

1 mol of any gas at STP = 22.4 liters

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