The combined gas law can be used to calculate the new volume of a gas if the pressure, volume, and temperature change. If gas initially has a pressure of 12 atm, volume of 23 L, and temperature of 200 K, and the pressure increases to 14 atm and temperature rises to 300 K, the combined gas law equation can be set up and solved to find that the new volume is 29.57 L.

1. Combined Gas Law
The combined gas law combines
Boyle’s Law and Charles’ Law

2. Combined Gas Law
 Boyle’s Law P1V1 = P2V2
 Charles’ Law
V1
=
V2
T1 T2
 Combined Gas Law
P1V1
=
P2V2
T1 T2

3. Combined Gas Law
 For example: If I initially have a gas
at a pressure of 12 atm, a volume of
23 L and a temperature of 200 K,
then I raise the pressure to 14 atm
and increase the temperature to 300
K, what is the new volume of the
gas?

4. Combined Gas Law
 Begin by converting to Kelvin. It is
not necessary in this problem.

5. Combined Gas Law
 Next, write down the information you
know and want to know.
 P1 =
 V1 =
 T1 =
 P2 =
 V2 =
 T2 =

6. Combined Gas Laws
 Next, write down the information you
know and want to know.
 P1 = 12 atm
 V1 =
 T1 =
 P2 =
 V2 =
 T2 =

7. Combined Gas Law
 Next, write down the information you
know and want to know.
 P1 = 12 atm
 V1 = 23 L
 T1 =
 P2 =
 V2 =
 T2 =

8. Combined Gas Law
 Next, write down the information you
know and want to know.
 P1 = 12 atm
 V1 = 23 L
 T1 = 200K
 P2 =
 V2 =
 T2 =

9. Combined Gas Law
 Next, write down the information you
know and want to know.
 P1 = 12 atm
 V1 = 23 L
 T1 = 200K
 P2 = 14 atm
 V2 =
 T2 =

10. Combined Gas Law
 Next, write down the information you
know and want to know.
 P1 = 12 atm
 V1 = 23 L
 T1 = 200K
 P2 = 14 atm
 V2 = x
 T2 =

11. Combined Gas Law
 Next, write down the information you
know and want to know.
 P1 = 12 atm
 V1 = 23 L
 T1 = 200 K
 P2 = 14 atm
 V2 = x
 T2 = 300 K

12. Combined Gas Law
 Now plug in the information you have . . .
P1V1
=
P2V2
T1 T2
12atm(23L)
=
14 atm (x)
200K 300K

13. Combined Gas Law
 Cross multiply to solve for x
12atm(23 L)(300K) = 200 K (14L)(x)
82800 = 2800x
x = 29.57 Liters