Problem Solving

Although many texts approach the gas laws as separate conditions, with separate equations such as P₁V₁  = P₂V₂ for students to memorize and use; these concepts can also be taught in terms of only one equation, PV = nRT.

Because some students may not have an adequate background in algebra, presenting the gas laws logically will help them understand these concepts. For instance, if the two variables are pressure and volume (the text may call this Boyle’s law) we know that they vary inversely. As one increases, the other decreases. Therefore we can determine logically the direction of the change. It is useful to start by setting up a data table:

Example: What will the final pressure of a gas sample be if it is initially at 2.0 atm and the volume is changed from 42 L to 124 L at constant temperature?

Remember that T must always be in kelvins (or other absolute temperature     scale). Students should predict whether the pressure will increase or decrease (if volume increases, pressure will decrease) and set up the relationship accordingly.

 
            2.0 atm (42 L / 124 L) = ? atm

The fraction must be less than one to realize a decrease in pressure.

If the two variables are pressure and temperature (Gay-Lussac’s law), they are directly proportional. As one increases the other increases.

If the two variables are volume and temperature (Charles’ law), they are also directly proportional.

If there are more than two or more variables, each set or pair should be treated individually, either in two steps (using two tables) or in a combined equation.

 

Example: What is the volume of a gas sample at 0.95 atm and 25 °C, if its volume is 26 L at 1.2 atm and 14 °C?

First, use the relationship between P and V. Since the pressure decreases , the volume will increase.

26 L (1.2 atm/0.95 atm) = 33 L

If the temperature increases, the volume will also increase. Use the new volume found above:

33 L (298 K/287 K) = 34 L

If the table shows that only one set of conditions is involved, then PV=nRT should be directly used.

 

Example: How many moles of a gas will occupy 2.7 L at 36 °C and a pressure of 0.95 atm?

Note that all units used must match those in the constant (R).

If students lack the algebra background to complete such one-condition problems, suggest that they set up such problems using the molar volume of gas at standard temperature and pressure. This will allow them to treat it the same way as previous problems.