1. 8.4 Temperature and Pressure (Gay-Lussac’s Law)
Gay-Lussac’s law: When the Kelvin temperature of a gas doubles at constant volume and amount of gas, the pressure also doubles.
Learning Goal Use the temperature–pressure relationship (Gay-Lussac’s law) to determine the final temperature or pressure when the volume and amount of gas are constant.

2. Gay-Lussac’s Law In Gay-Lussac’s law,
the pressure exerted by a gas is directly related to the Kelvin temperature of the gas.
volume and amount of gas are constant.

3. Study Check
Solve Gay-Lussac’s law for P2.

4. Solution
Solve Gay-Lussac’s law for P2. Multiply both sides by T2 and cancel: × × ×

5. Calculations Using 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 (constant volume and moles)? STEP 1 Organize the data in a table of initial and final conditions. Volume and moles remain constant.

6. Calculations Using Gay-Lussac’s Law
STEP 2 Rearrange to solve for unknown quantity P2. Solve Gay-Lussac’s law for P2: STEP 3 Substitute the values into the gas law equation and calculate. × × × ×

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

8. Solution
A gas has a pressure of 645 Torr at 128 °C. What is the temperature in Celsius if the pressure increases to 824 Torr (V and n remain constant)?
STEP 1 Organize the data in a table of initial and final conditions.
Volume and moles remain constant.

9. Solution
A gas has a pressure of 645 Torr at 128 °C. What is the temperature in Celsius if the pressure increases to 824 Torr (V and n remain constant)? STEP 2 Rearrange to solve for unknown quantity T2 Solve Gay-Lussac’s law for T2: STEP 3 Substitute the values into the gas law equation and calculate. × × -

10. Vapor Pressure and Boiling Point
When liquid molecules with sufficient kinetic energy break away from the surface of a liquid, they become a vapor.
In an open container, all the liquid will eventually evaporate.
In a closed container, the vapor accumulates and creates pressure called vapor pressure.
A liquid
exerts its own vapor pressure at a given temperature.
boils when its vapor pressure becomes equal to the external pressure.

11. Altitude and Boiling Point
At high altitudes,
atmospheric pressure is lower than 1 atm, 760 Torr.
the boiling point of water is lower than 100 °C.
In a closed container, such as a pressure cooker,
a pressure greater than 1 atm, 760 Torr, can be obtained.
water boils at a higher temperature than 100 °C.
Pressure and the boiling
point of water.

12. Vapor Pressure and Boiling Point

13. Study Check
Explain why water boils at a lower temperature in the mountains than at sea level.

14. Solution
Explain why water boils at a lower temperature in the mountains than at sea level.
Atmospheric pressure in the mountains is less than at sea level. The vapor pressure of the water reaches the atmospheric pressure at a lower temperature.