# Combined Gas Law

```Combined Gas Law
The combined gas law combines
Boyle’s Law and Charles’ Law
Combined Gas Law
Boyle’s Law P1V1 = P2V2
 Charles’ Law
V1
V2
=
T1
T2
 Combined Gas Law
P1V1 P2V2
=
T1
T2

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?
Combined Gas Law
 Begin
by converting to Kelvin. It is
not necessary in this problem.
Combined Gas Law
Next, write down the information you
know and want to know.
 P1 =
 V1 =
 T1 =
 P2 =
 V2 =
 T2 =

Combined Gas Laws
Next, write down the information you
know and want to know.
 P1 = 12 atm
 V1 =
 T1 =
 P2 =
 V2 =
 T2 =

Combined Gas Law
Next, write down the information you
know and want to know.
 P1 = 12 atm
 V1 = 23 L
 T1 =
 P2 =
 V2 =
 T2 =

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 =

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 =

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 =

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

Combined Gas Law
Now plug in the information you have . . .
P1V1 P2V2
=
T1
T2

12atm(23L) 14 atm (x)
=
200K
300K
Combined Gas Law

Cross multiply to solve for x
12atm(23 L)(300K) = 200 K (14L)(x)
82800 = 2800x
x = 29.57 Liters
```
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