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# The Laws of Gases Help (page 3)

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By McGraw-Hill Professional
Updated on Aug 29, 2011

#### Examples

If you have an atmosphere of mixed gases on an alien planet, composed of oxygen ( p = 0.3 atm), argon ( p = 0.1 atm), nitrogen ( p = 0.8), and neon ( p = 0.01), what is the total pressure of the atmospheric gases?

P total = P 1 (0.3) + P 2 (0.1) + P 3 (0.8) + P 4 (0.01)

P total = 1.21 atm

The total pressure of the alien atmosphere is greater than that of any of the single gases alone.

## Combined Gas Law

Considering all the gas laws, then, you can figure out nearly every temperature, volume, and pressure of a gas if you know the other constants. This can be thought of as the combined gas law .

The combined gas law is made up of the general rules for temperature, volume, and pressure described in Boyle’s, Charles’, and Gay-Lussac’s laws.

It is written as:

P 1 V 1 / T 1 = P 2 V 2 / T 2

When you know five of the six values, you can figure out the missing value. If the volumes don’t change, then you can write the combined gas law as:

V 2 = V 1 × P 1 / P 2 × T 2 / T 1

V 2 = V

1 = P 1 / P 2 × T 2 / T 1 , or P 2 / P 1 = T 2 / T 1 (which is Gay-Lussac’s law)

#### Examples

If a bicycle tire has a volume of 0.5 m 3 at 20°C and 1 atm (760 torr), figure out the volume when taken into the mountains where the pressure is 720 torr and temperature is 14°C.

V 1 = 0.5 m 3 , T 1 = 20°C, T 2 = 14°C, P 1 = 760 tor, P 2 = 720 torr

V 2 = x

T 1 = 20 + 273 = 293 K, T 2 = 14 + 273 = 287 K

V 2 = 0.5 m 3 × 760 torr/720 torr × 287°C/293°C

0.5 m 3 × 1.056 torr × 0.980°C

V 2 = 0.52 m 3

As the temperature and pressure decrease, the tire volume is less compressed and feels mushy. To get the same riding feel on the tires, you might want to pump up the tires a bit.

Practice problems for these concepts can be found at – Chemistry and Gases Practice Test

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