The Combined Gas Law and Avogadros Principle

The gas laws may be combined into a single law, called the combined gas law, that relates two sets of conditions of pressure, volume, and temperature by the following equation. 

With this equation, you can find the value of any one of the variables if you know the other five. 

solve the combined gas law equation for the quantity to be determined, the new volume, V2. 

Finally, determine whether the answer makes sense. The temperature increases, which should cause the gas to expand. The decrease in pressure should cause the volume to expand further. Therefore, the final volume should be somewhat larger than the starting volume. 

A balloon is inflated with 2.42 L of helium at a temperature of 2TC. Later, the volume of the balloon has changed to 2.37 L at a temperature of 19°C and a pressure of 99.7 kPa. What was the pressure when the balloon was inflated  

Boyle s, Charles s, and Gay-Lussac s laws can be combined into a single law. This combined gas law states the relationship among pressure, volume, and temperature of a fixed amount of gas. All three variables have the same relationship to each other as they have in the other gas laws Pressure is inversely proportional to volume and directly proportional to temperature, and volume is directly proportional to temperature. The equation for the combined gas law can be expressed as 

As with the other gas laws, this equation allows you to use known values for the variables under one set of conditions to find a value for a missing variable under another set of conditions. Whenever five of the six values from the two sets of conditions are known, the sixth can be calculated using this expression for the combined gas law. 

This combined law lets you work out problems involving more variables that change, and it also provides a way for you to remember the other three laws without memorizing each equation. If you can write out the combined gas law equation, equations for the other laws can be derived from it by remembering which variable is held constant in each case. 

For example, if temperature remains constant as pressure and volume vary, then Tj = T2. After simphlying the combined gas law under these conditions, you are left with 

You should recognize this equation as the equation for Boyle s law. See whether you can derive Charles s and Gay-Lussac s laws from the combined gas law. 

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