1. Gay-Lussac’s and Combined Gas Laws
Unit: Gas Laws
Gay-Lussac’s and Combined Gas Laws

2. After today you will be able to…
Explain the effect on gas properties using Gay-Lussac’s Law and the Combined Gas Law
Calculate an unknown pressure, temperature, or volume by solving algebraically

3. Gay-Lussac’s Law: Pressure and Temperature
Joseph Gay-Lussac discovered the relationship between temperature and pressure.
His name is on the gas law that describes this relationship.

4. “For a given volume of a gas, as the temperature of an enclosed gas increases, the pressure of a gas is directly proportional.”

5. Gay-Lussac’s Law: Pressure and Temperature
We can simplify this relationship by the formula: Where, P1, P2 = pressure in any unit (atm, kPa, or mmHg), BUT they must match! T1, T2 = temperature is always in Kelvin! (Recall, just add °C)
P1 P2
T1 T2 =

6. Gay-Lussac’s Law: Example
A gas has a pressure of 103kPa at 25°C. What will the pressure be when the temperature reaches 928°C? P1= T1= P2= T2=
103kPa
P1 P2
T1 T2 =
25°C +273= 298K ?
928°C+273= 1201K
(103kPa)
(P2) =
(298K)
(1201K) P2 =
420kPa

7. The Combined Gas Law
The combined gas law is a single expression that combines Boyle’s, Charles’s, and Gay-Lussac’s Laws.
This gas law describes the relationship between temperature, pressure, and volume of a gas.
It allows you to do calculations where only the amount of gas is constant.
RB + JC + JG-L = BFFs!

8. P1V1 P2V2 T1 T2 = The Combined Gas Law
Helpful hint: You are able to get which law you need by covering the variable that is not mentioned in the problem! There is no need to memorize 4 individual laws, just memorize the Combined Gas Law and you can derive all of the others!
If there is no mention of pressure in the problem, cover P up and you are left with the relationship between T and V. (aka Charles’s Law!)
If there is no mention of volume in the problem, cover V up and you are left with the relationship between T and P. (aka Gay-Lussac’s Law!)
For example, if there is no mention of temperature in the problem, cover T up and you are left with the relationship between P and V. (aka Boyle’s Law!)
P1V1 P2V2
T T2 =

9. The Combined Gas Law P1 V1 P2 V2 = T1 T2 P2 467mmHg = P1= V1= T1= P2=
A gas occupies 3.78L at 529mmHg and 17.2°C. At what pressure would the volume of the gas be 4.54L if the temperature is increased to 34.8°C?
P1=
V1=
T1=
P2=
V2=
T2=
P1 V1 P2 V2
T T2 =
529mmHg
3.78L
17.2°C + 273= 290.2K
(529mmHg)
(3.78L)
(P2)
(4.54L) ? =
(290.2K)
(307.8K)
4.54L
467mmHg
34.8°C + 273= 307.8K P2 =

10. Questions?