How Do I Solve for Variables in the Combined Gas Law Equation?

[stasik50]

So, I have an equation.

* = multiplication
i = initial
v = final
/ = Division
P = Pressure
V = Volume
T = Temperature

Pi*Vi / Ti = Pf*Vf / Tf

I'm not sure how to use this equation. I know that we are trying to find either Pressure Final, Volume Final, or Temperature Final. I'm not sure which one of these we are trying to find.

So can someone please show me how to use this equation (providing the numbers). I have a quiz tomorrow, and I don't know how to do this. I will be forever grateful!

 

[sArGe99]

This is derived from the ideal gas equation PV = nRT
PV/T = nR which is a constant for a given system.
This gives (Pi Vi) / Ti = (Pf Vf) / Tf

Suppose you know the initial values of temp. pressure and volume and any final values of any two of these state variables. You can then use this equation to find the third variable.

 

[stasik50]

So how would I switch around the variables to find Pressure or Volume?

 

[stasik50]

Oh, and how would you solve this equation?

 

[sArGe99]

The question will have to specify at least 5 variables, so that we can find the sixth in this equation. Maybe multiple data will given so that we can solve from it. Like, two different data and two variables, which CAN be solved.

 

[stasik50]

But let's say we already have the 5 variables, can you please tell me how we would solve the sixth one? I'm not sure how to do that.

Thank you for all the help you've given me already.

 

[Feldoh]

You have: $$\frac{P_i V_i}{T_i} = \frac{P_f V_f}{T_f}$$

Say you want to solve for P_f, just isolate that variable.

$$\frac{P_i V_i}{T_i} * \frac{T_f}{V_f}= \frac{P_f V_f}{T_f} * \frac{T_f}{V_f}$$

Which after canceling some of the terms out of both sides we get:

$$\frac{P_i V_i T_f}{T_i V_f} = P_f$$