1. Temperature and Pressure (Gay-Lussac’s Law)
Chapter 7 Gases
7.5
Temperature and Pressure (Gay-Lussac’s Law)

2. Gay-Lussac’s Law: P and T
In Gay-Lussac’s law,
the pressure exerted by a gas is directly related to the Kelvin temperature
V and n are constant
P1 = P2
T T2

3. Learning Check
Solve Gay-Lussac’s law for P2.
P1 = P2
T T2

4. Solution Solve Gay-Lussac’s law for P2. P1 = P2 T1 T2
Multiply both sides by T2 and cancel:
P1 x T2 = P2 x T2
T T2
P2 = P1 x T2 T1

5. Calculation with Gay-Lussac’s Law
A gas has a pressure at 2.0 atm at 18 °C. What is the
new pressure when the temperature is 62 °C? (V and n
constant)
STEP 1 Set up a data table:
Conditions Conditions Know Predict
P1 = 2.0 atm P2 = ? P increases
T1 = 18 °C T2 = 62 °C T increases
= 291 K = 335 K

6. Calculation with Gay-Lussac’s Law (continued)
STEP 2 Solve Gay-Lussac’s Law for P2:
P1 = P2
T T2
P2 = P1 x T2 T1
STEP 3 Substitute values to solve for unknown:
P2 = atm x 335 K = atm
291 K
Temperature ratio
increases pressure

7. Learning Check A gas has a pressure of 645 mmHg at 128 °C. What is
the temperature in Celsius if the pressure increases to
824 mmHg (n and V remain constant)?

8. Solution A gas has a pressure of 645 mmHg at 128 °C. What is
the temperature in Celsius if the pressure increases to
1.50 atm (n and V remain constant)?
P2 = atm x mmHg = mmHg
1 atm
STEP 1 Set up a data table:
Conditions Conditions Know Predict
P1 = 645 mmHg P2 = mmHg P increases
T1 = 128 °C T2 = K – T increases
= 401 K = ? °C

9. Solution (continued) STEP 2 Solve Gay-Lussac’s Law for T2: P1 = P2
T T2
T2 = T1 x P2 P1
STEP 3 Substitute values to solve for unknown:
T2 = 401 K x mmHg = 709 K – 273 = 436 °C
645 mmHg Pressure ratio
increases temperature

10. Vapor Pressure The vapor pressure of water
is the pressure above water at equilibrium in a closed container
at the boiling point is equal to the external (atmospheric) pressure

11. Vapor Pressure and Boiling Point
is the pressure of gas molecules above the surface of a liquid
at the boiling point, becomes equal to the external pressure

12. Boiling Point of Water The boiling point of water
depends on the vapor pressure
is lower at higher altitudes
is increased by using an autoclave to increase external pressure

13. Learning Check
In which pair of temperatures for water will boiling occur? Atmospheric pressure Vapor Pressure A. 760 mmHg 760 mmHg B. 960 mmHg 760 mmHg C. 520 mmHg 620 mmHg

14. Solution
In which pair of temperatures for water will boiling occur? Atmospheric Vapor Boiling Pressure Pressure Occurs? A. 760 mmHg 760 mmHg yes B. 960 mmHg 760 mmHg no C. 520 mmHg 620 mmHg yes