Combined Gas Law: Relationships Between Pressure, Volume, and Temperature

Gases

Combined Gas Law

The Combined Gas Law is a fundamental equation in chemistry that relates the pressure, volume, and temperature of a fixed amount of gas. It is derived from Boyle's Law, Charles' Law, and Gay-Lussac's Law, which each describe the relationship between two of these variables while keeping the third constant.

• Boyle's Law: Pressure is inversely proportional to volume (at constant temperature).

• Charles' Law: Volume is directly proportional to temperature (at constant pressure).

• Gay-Lussac's Law: Pressure is directly proportional to temperature (at constant volume).

The Combined Gas Law equation is:

$\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$

Where:

• $P_1$ and $P_2$ are the initial and final pressures

• $V_1$ and $V_2$ are the initial and final volumes

• $T_1$ and $T_2$ are the initial and final temperatures (in Kelvin)

Example Problem

Example: A sample of gas initially has a volume of 900.0 mL at 520 K and 1.80 atm. What is the pressure of the gas if the volume decreases to 350 mL while the temperature increases to 770 K?

• Given: $V_1 = 900.0$ mL, $T_1 = 520$ K, $P_1 = 1.80$ atm, $V_2 = 350$ mL, $T_2 = 770$ K

• Find: $P_2$

• Solution: Rearranging the combined gas law equation to solve for $P_2$:

$P_2 = \frac{P_1 V_1 T_2}{T_1 V_2}$

Plug in the values to calculate $P_2$.

Practice Problems

• Practice 1: A 5.01 gas has a pressure of 1.7 atm when the temperature is 60.0°C. What will be the temperature of the gas mixture if the volume and pressure are decreased to 2.45 L and 0.810 atm respectively?

• Practice 2: A sealed container with a movable piston contains a gas with a pressure of 1300 torr, a volume of 800 mL, and a temperature of 315°C. What would the volume be if the new pressure is 0.82 atm, while the temperature decreased to 25°C?

Key Points

• The combined gas law allows prediction of how a change in one variable (pressure, volume, or temperature) affects the others for a fixed amount of gas.

• Always convert temperatures to Kelvin before using the equation.

• Units for pressure and volume must be consistent throughout the calculation.

Additional info:

• The combined gas law is a special case of the ideal gas law when the amount of gas (number of moles) is constant.

• It is commonly used in laboratory and real-world applications to predict the behavior of gases under changing conditions.