For a static sample of gas, we can write each of the six gas laws as follows:
- PV = k1
- V / T = k2
- P / T = k3
- V / n = k4
- P / n = k5
- 1 / nT = 1 / k6
(The last law is written in reciprocal form). The subscripts on k indicate that six different values would be obtained.
When you multiply them all together, you get:
- P3V3 / n3T3 = k1k2k3k4k5 / k6
The cube root of k1k2k3k4k5 / k6 is the gas constant "R".
The units work out:
- k1 = atm-L
- k2 = L / K
- k3 = atm / K
- k4 = L / mol
- k5 = atm / mol
- 1 / k6 = 1 / mol-K
Each unit occurs three times and the cube root yields L-atm / mol-K, the classic units for R when used in a gas law context.
Resuming, we have:
PV / nT = R
or, more commonly:
PV = nRT
R is called the gas constant. Sometimes it is referred to as the universal gas constant. It can either be 0.08206L atm / mol K or 8.31J/mol K. For our chemistry 20 class with Mr. Shelley, we will use 8.31J/mol K.(Unless you want to learn the hard way like I did)