### Combined Gas Law Definition

The combined gas law combines the three gas laws: Boyle's Law, Charles' Law, and Gay-Lussac's Law. It states the ratio of the product of pressure and volume and the absolute temperature of a gas is equal to a constant. When Avogadro's law is added to the combined gas law, the ideal gas law results. Unlike the named gas laws, the combined gas law doesn't have an official discoverer.

It is simply a combination of the other gas laws that works when everything except temperature, pressure, and volume are held constant.

There are a couple of common equations for writing the combined gas law. The classic law relates Boyle's law and Charles' law to state:

PV/T = k

where

P = pressure

V = volume

T = absolute temperature (Kelvin)

k = constant

The constant k is a true constant if the number of moles of the gas doesn't change, otherwise it varies.

Another common formula for the combined gas law relates "before and after" conditions of a gas:

P_{1}V_{1} / T_{1} = P_{2}V_{2} / T_{2}

### Combined Gas Law Example

Find the volume of a gas at STP when 2.00 liters is collected at 745.0 mm Hg and 25.0 °C.

To solve the problem, you first need to identify which formula to use. In this case, the question asks about conditions at STP, so you know you're dealing with a "before and after" problem. Next, you need to now what STP is.

If you haven't memorized this already (and you probably should, since it appears a lot), STP refers to "standard temperature and pressure", which is 273 K and 760.0 mm Hg.

Because the law works using absolute temperature, you need to convert 25.0 °C to the Kelvin scale. This gives you 298 K.

At this point, you can just plug the values into the formula and solve for the unknown, but a common mistake when you're new to this type of problem is confusing which numbers go together.

It's good practice to identify the variables. In this problem:

P_{1} = 745.0 mm Hg

V_{1} = 2.00 L

T_{1} = 298 K

P_{2} = 760.0 mm Hg

V_{2} = x (the unknown you're solving for)

T_{2} = 273 K

Next, take the formula and set it up to solve for your "x", which is V_{2} in this problem.

P_{1}V_{1} / T_{1} = P_{2}V_{2} / T_{2}

Cross-multiply to clear the fractions:

P_{1}V_{1}T_{2} = P_{2}V_{2}T_{1}

Divide to isolate V_{2:}

V_{2} = (P_{1}V_{1}T_{2}) / (P_{2}T_{1})

Plug in the numbers:

V_{2} = (745.0 mm Hg · 2.00 L · 273 K) / (760 mm Hg · 298 K)

V_{2} = 1.796 L

Report the value using the correct number of significant figures:

V_{2} = 1.80 L

### Uses of the Combined Gas Law

The combined gas law has practical applications when dealing with gases at ordinary temperatures and pressures. Like other gas laws based in ideal behavior, it becomes less accurate at high temperatures and pressures. The law is used in thermodynamics and fluid mechanics. For example, it can be used to calculate pressure, volume, or temperature for the gas in refrigerators or in clouds to forecast weather.