Question

Question #d4f18

Answer 1

In addition to Boyle's, Charles', and Gay-Lussac's Laws, there are also the Combined Gas Law, and the Ideal Gas Law.

Video examples of gas law problems available from Noel Pauller

Combined Gas Law:

`(P_1V_1)/(T_1) = (P_2V_2)/(T_2)`

Example: The original volume of a gas was 300.0 L at 0.250 atm and 400.0 K. What is the new volume of the gas at 2.00 atm and 200.0 K?
`P_1 = 0.250 "atm"`
`V_1 = 300.0 "L"`
`T_1 = 400.0 "K"`
`P_2 = 2.00 "atm"`
`V_2 = ?`
`T_2 = 200.0 "K"`

Solution: Rearrange the equation for the Combined Gas Law to isolate `V_2`, then solve for `V_2`.

`V_2 = (P_1V_1T_2)/(P_2T_1) = (0.250 "atm"*300.0 "L"*200.0 "K")/(2.00 "atm"*400.0 "K") = 18.75 "L"`

The Ideal Gas Law:

`PV = nRT` (n is moles and R is the gas constant)

Example: At what temperature will 0.575 mole of a gas occupy 5.00 liters at 2.25 atm?
`P = 2.25 "atm"`
`V = 5.00 "L"`
`n = 0.575 "mol"`
`R` = `"0.08205736 L atm K"^(-1) "mol"^(-1)"` (http://en.wikipedia.org/wiki/Gas_constant)
`T = ?`

Solution: Rearrange the equation for the Ideal Gas Law to isolate `T`, then solve for `T`.

`T = (PV)/(nR) = (2.25 atm * 5.00 L)/(0.575 mol * 0.08205736 "L atm K"^(-1) mol"^(-1)) = 238K` (3 sig figs)