The combined gas law combines
Boyle’s Law and Charles’ Law

Combined Gas Law


Boyle’s Law P
1
V
1
Charles’ Law
= P

V
1
T
1
=
V
T
2
2
Combined Gas Law
P
1
V
1
T
1
=
P
2
V
2
T
2
2
V
2

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.
P
2
V
2
T
2
P
V
1
T
1
1
=
=
=
=
=
=

Combined Gas Laws







Next, write down the information you know and want to know.
P
2
V
2
T
2
P
V
1
T
1
1
= 12 atm
=
=
=
=
=

Combined Gas Law







Next, write down the information you know and want to know.
P
2
V
2
T
2
P
V
1
T
1
1
= 12 atm
= 23 L
=
=
=
=

Combined Gas Law







Next, write down the information you know and want to know.
P
2
V
2
T
2
P
V
1
T
1
1
= 12 atm
= 23 L
= 200K
=
=
=

Combined Gas Law







Next, write down the information you know and want to know.
P
2
V
2
T
2
P
V
1
T
1
1
= 12 atm
= 23 L
= 200K
= 14 atm
=
=

Combined Gas Law







Next, write down the information you know and want to know.
P
2
V
2
T
2
P
V
1
T
1
1
= 12 atm
= 23 L
= 200K
= 14 atm
= x
=

Combined Gas Law







Next, write down the information you know and want to know.
P
2
V
2
T
2
P
V
1
T
1
1
= 12 atm
= 23 L
= 200 K
= 14 atm
= x
= 300 K

Combined Gas Law

Now plug in the information you have . . .
P
1
V
1
T
1
=
P
2
V
2
T
2
12atm(23L)
200K
=
14 atm (x)
300K

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