Solving Gas Law Problems

The Ideal Gas Law can easily be reduced to Charles’, Boyle’s, or Avogadro’s Law.For example, suppose that n and T are held constant.The symbol “R” in this equation is a constant called “the gas constant” and its value can be computed by measuring the temperature, volume, and pressure of a known quantity of an ideal gas and substituting these values into the Ideal Gas Law solved for R.

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In the last section we saw that Charles’ Law relates the volume of a gas to its temperature; Boyle’s Law relates volume to pressure; and Avogadro’s Law relates volume to the number of moles of gas present, as well as a number of other relationships between P, V, n, and T.

In particular, we saw that volume is directly proportional to the temperature (in Kelvins!

Rather than remember all of the possible relationships between P, V, n, and T, and have to deal with a host of different “constants,” it would be nice to have a single relationship with a constant of proportionality that was really constant; that is, one whose value did not depend on what the other parameters’ values were.

The Ideal Gas Law | Using the Ideal Gas Law All of these relationships can be combined into a single law called the “Ideal Gas Law.” This law, which applies to gases whose behavior follows the assumptions of the kinetic molecular theory, relates pressure, volume, temperature, and number of moles of gas by the equation PV = n RT.

This means that most gases behave ideally to about two significant digits.

In practice, gases whose behavior deviates from the ideal gas law by more than about 1% are typically those with large, multi-atom molecules (say, ten atoms or more) or medium-sized molecules capable of hydrogen bonding.Note how the units cancel to give the units of the answer, liters.Checking to make sure that the units cancel properly to give the appropriate units for the answer (in this case, liters for a volume) is a good way to check that you’ve done the algebra correctly and a valuable habit to get into.In it, you will measure n, T, P, and V for a sample of hydrogen gas, then use these values to compute the value of the gas constant, R.The actual value of R will depend on the units that you use for P and V (n is always in moles and T in Kelvins).The two operations you will most often use are multiplying both sides of an equation by some quantity and dividing both sides of an equation by some quantity in order to solve it.At times you may also need to add or subtract quantities from both sides of an equation.Our answer will be in units of liters because those are the volume units for this value of the gas constant.Now, substituting the values of n, R, T, and P into the solved equation, we find that the volume is 8.6 liters.As you will see, the units in the constant will cancel units in P, V, n, and/or T so that the answer to any particular calculation will match the units you expect for the answer – provided, of course, that the problem has been solved correctly.While, strictly speaking, the Ideal Gas Law applies only to ideal gases, it works well enough for almost all gases if we use a less precise value for R: 0.082 Latm/Kmol.


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