Combined Gas Law
A cylinder container contains a gas with a volume of 30 L, a pressure of 110 kPa, and a temperature of 420 K. Find the temperature of the gas which has a volume of 40 L and a pressure of 120 kPa.
Even though the Combined Gas Law is a more detailed formula, do not get intimidated. Like Boyle's Law and Charles' Law, we first need to identify all of our values. Again, we need to look at the formula to do this.
Formula:
P1 x V1/T1 = P2 x V2/T2
For this Combined Gas Law Problem, we are going to use the simplified formula to find our missing variable, which happens to be T2 in this case. We will be using
T2 = P2 x V2 x T1/ P1 x V1
Our list will look like this:
P1 = __
V1 = __
T1 = __
P2 = __
V2 = __
T2 = __
Now, let's fill in the blanks with what we know.
P1 = 110 kPa
V1 = 30 L
T1 = 420 K
P2 = 120 kPa
V2 = 40 L
T2 = ?
Now, let's plug our values into the formula: T2 = P2 x V2 x T1/ P1 x V1
T2 = (120 kPa)(40L)(420 K)/ (110 kPa) x (30 L)
T2 = (2016000 kPa/L/K) / 3300 kPa/L
Divide 2016000 by 3300 and cancel the units
T2 = 610.9 K
The answer is 610.91 K due to significant figures and the fact that temperature will always be expressed in Kelvin. In this problem, using the formula specific for the T2 variable was much easier. Though using variable specific formulas for Boyle's Law and Charles' Law are acceptable and will provide you with the right answer, they are very easy to work with in their original form. You should honestly only need to use the variable specific formulas for the Combined Gas Law, but it is up to personal preference.
