Gas Laws

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Core Concept

The gas laws describe how gases respond to changes in pressure, volume, and temperature. These relationships are crucial for predicting and understanding gas behavior under different conditions.

Practice Tips

  • Convert Temperature to Kelvin: Always use Kelvin for temperature when working with gas laws.

  • Be Consistent with Units: Make sure pressure and volume units match, especially if converting between units like atm, kPa, or mmHg.

  • Direct vs. Inverse Relationships:

    • Boyle’s Law (pressure and volume) is an inverse relationship: as one increases, the other decreases.

    • Charles’s, Gay-Lussac’s, and Avogadro’s Laws all show direct relationships: as one variable increases, so does the other.

  • Know When to Use Each Law: Determine which variables are held constant and which are changing to decide which gas law to apply.

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Key Terms

  • Pressure (P): The force that gas particles exert on the walls of their container; typically measured in units like atmospheres (atm), kilopascals (kPa), or millimeters of mercury (mmHg).

  • Volume (V): The amount of space a gas occupies, usually measured in liters (L) or milliliters (mL).

  • Temperature (T): A measure of the average kinetic energy of gas particles; always use the Kelvin scale in gas law calculations.

  • Moles (n): The amount of gas, measured in moles (mol).

Merged Gas Laws Table (Transposed)
Boyle’s Law Charles’s Law Gay-Lussac’s Law Avogadro’s Law Combined Gas Law
Relationship Pressure-Volume Volume-Temperature Pressure-Temperature Volume-Mole Pressure-Volume-Temperature
Type Inverse Direct Direct Direct Mixed
Equation \( P_1 V_1 = P_2 V_2 \) \( \frac{V_1}{T_1} = \frac{V_2}{T_2} \) \( \frac{P_1}{T_1} = \frac{P_2}{T_2} \) \( \frac{V_1}{n_1} = \frac{V_2}{n_2} \) \( \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \)
Explanation At constant temperature, the volume of a gas is inversely proportional to its pressure. At constant pressure, the volume of a gas is directly proportional to its temperature (Kelvin). At constant volume, the pressure of a gas is directly proportional to its temperature (Kelvin). At constant temperature and pressure, the volume of a gas is directly proportional to the moles of gas. Combines Boyle’s, Charles’s, and Gay-Lussac’s laws to relate changes in (P), (V), and (T) when the amount of gas is constant.
Graph Hyperbolic curve for (P) vs. (V) Straight line for (V) vs. (T) (K) Straight line for (P) vs. (T) (K) Straight line for (V) vs. (n) N/A
Example Problem If you have a gas at 1.5 atm pressure and a volume of 2.0 L, what will the volume be if the pressure increases to 3.0 atm at constant temperature? A gas occupies 3.0 L at 273 K. What will the volume be at 546 K if pressure is constant? A gas at 1.0 atm and 300 K is heated to 600 K at constant volume. What is the final pressure? If 2.0 mol of a gas occupies 10.0 L, what volume will 5.0 mol of gas occupy at the same temperature and pressure? A gas has an initial volume of 5.0 L at 1.0 atm and 300 K. What will the volume be if the pressure is increased to 2.0 atm and the temperature raised to 400 K?
Solution Use \( P_1 V_1 = P_2 V_2 \):
\( (1.5 \,\text{atm})(2.0 \,\text{L}) = (3.0 \,\text{atm})(V_2) \)
\( V_2 = \frac{(1.5)(2.0)}{3.0} = 1.0 \,\text{L} \) 		Use \( \frac{V_1}{T_1} = \frac{V_2}{T_2} \):
\( \frac{3.0 \,\text{L}}{273 \,\text{K}} = \frac{V_2}{546 \,\text{K}} \)
\( V_2 = \frac{3.0 \times 546}{273} = 6.0 \,\text{L} \) 		Use \( \frac{P_1}{T_1} = \frac{P_2}{T_2} \):
\( \frac{1.0 \,\text{atm}}{300 \,\text{K}} = \frac{P_2}{600 \,\text{K}} \)
\( P_2 = \frac{(1.0)(600)}{300} = 2.0 \,\text{atm} \) 		Use \( \frac{V_1}{n_1} = \frac{V_2}{n_2} \):
\( \frac{10.0 \,\text{L}}{2.0 \,\text{mol}} = \frac{V_2}{5.0 \,\text{mol}} \)
\( V_2 = \frac{(10.0)(5.0)}{2.0} = 25.0 \,\text{L} \) 		Use \( \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \):
\( \frac{(1.0)(5.0)}{300} = \frac{(2.0)(V_2)}{400} \)
\( V_2 = \frac{(1.0)(5.0)(400)}{(2.0)(300)} = 3.33 \,\text{L} \)

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