In this example, we have conditions changing for a sample of gas, and we use the combined gas
law to determine the effects. Our problem reads: "A sample of air in a balloon has a volume of
2.50 liters at 22.0 degrees Celsius. At what temperature in degrees Celsius will the air have a
volume of 2.00 liters, assuming constant pressure?"
We can start with the combined gas law: P is pressure, V is volume, n is the number of moles of
gas, and T is the absolute temperature in Kelvin. Any variable for a sample of gas that does not
change can be crossed out of the equation. In the problem, we're explicitly told that pressure does
not change, so we will remove it from the equation. We can also assume that the number of
moles of gas does not change because we're not told they change.
This leaves us with the equation V1/T1 = V2/T2, which is Charles's law. In this problem, we
want to know about temperature, so we can solve for T2, which will be the temperature at which
the sample of air has a volume of 2.00 liters. Since T2 is in the denominator, we can first cross-
multiply. Then we can divide both sides by V1 to get T2 = (V2 * T1) / V1.
Substituting in our values from the problem, V2 is 2.00 liters, and V1 and T1 are the initial
volume and temperature, which are 2.50 liters and 22.0 degrees Celsius. However, we cannot use
degrees Celsius in this equation. The temperature must be in Kelvin. So, to convert to Kelvin, we
add 273 to the temperature in degrees Celsius.
Completing the calculation, we get 236 Kelvin, and our units for temperature in this equation are
always Kelvin. But the problem asks for the temperature in degrees Celsius, so we need to
convert back to degrees Celsius by subtracting 273. 236 Kelvin minus 273 is -37 degrees
Celsius.
