A free variable is a symbol in a math expression where substitution may take place.
The Ideal Gas Law is
PV=nRT
R is a known value–said better, once we choose our units the other variables, R takes a single value based on our choices.
This leaves the other four variables open and we can put any values in them that we want, so we call them free variables.
Each time we assign a value to a variable, we change that free variable to a bound variable. When we get down to the point where only two free variables remain, we can assign one more value to a free variable and then the other one automatically becomes whatever value we get from the calculation.
Rob Sterling 