Understanding Gas Laws in Year 11 Chemistry

Gay-Lussac's Law

At constant volume, the pressure of a gas is directly proportional to its temperature in Kelvin.

Boyle's Law

The pressure of a gas is inversely proportional to its volume at constant temperature.

Charles' Law

The volume of a gas is directly proportional to its absolute temperature at constant pressure.

Avogadro's Law

The volume of a gas is directly proportional to the number of moles of gas at constant temperature and pressure.

Ideal Gas Law

PV = nRT, where P is pressure, V is volume, n is amount of gas in moles, R is the gas constant, and T is absolute temperature.

Ideal Gas

A theoretical gas composed of particles that have no volume, experience no intermolecular forces, move in random motion, and undergo perfectly elastic collisions.

Pressure

The force exerted by gas particles colliding with the walls of their container.

Temperature Dependence

The behavior of gases, such as volume and pressure, changes with temperature; gases expand when heated and contract when cooled.

Compressibility and Expandability

Gases can be compressed or expanded due to their low densities and large spacing between molecules.

Diffusivity

The ability of different gases to mix easily due to the large gaps between gas molecules.

Standard Temperature and Pressure (STP)

Defined as a temperature of 0°C (273 K) and a pressure of 100 kPa (or 1 atm).

Unit Conversion for Pressure

1 kilopascal (kPa) = 1000 Pa; 1 atmosphere (atm) = 101325 Pa; 1 atmosphere (atm) = 101.325 kPa.

Unit Conversion for Volume

1 L = 1000 mL; 1 L = 1000 cm³ = 0.001 m³.

Unit Conversion for Temperature

0 °C = 273.15 K; 25 °C = 298.15 K.

Example 1 Calculation

For 0.500 mol of nitrogen gas at 350 K and pressure of 150 kPa, V = (0.500 mol x 8.314 J/mol·K x 350 K)/ 150 kPa = 9.70 L.

Example 2 Scenario

A 2.5 L container holds 0.45 moles of nitrogen gas at 315 K; pressure needs to be calculated.

Properties of Gas

Gases have unique physical properties such as low density, freely forming shapes, and the ability to diffuse.

Combustion of Methane

CH4(g) + 2O2(g) → CO2(g) + 2H2O(g) is a chemical reaction involving gases.

Vinegar and Baking Soda Reaction

CH3COOH(aq) + NaHCO3(s) → CH3COONa(aq) + CO2(g) + H2O(l) is a chemical reaction involving gases.

Gas Laws Definition

The gas laws describe the relationship between pressure, volume, temperature, and amount of ideal gases.

Gas Constant (R)

R = 8.314 J / mol·K, used in the Ideal Gas Law.

PV = nRT

Ideal gas law equation relating pressure (P), volume (V), number of moles (n), ideal gas constant (R), and temperature (T).

P1/T1 = P2/T2

Formula used in Gay-Lussac's Law to relate initial and final pressures and temperatures.

V = nRT/P

Formula to calculate the volume of a gas given the number of moles, temperature, and pressure.

P = nRT/V

Formula to calculate the pressure of a gas given the number of moles, temperature, and volume.

Example 1 (Gay-Lussac's Law)

If the pressure of gas is 125 kPa at 300 K, the new pressure at 900 K is calculated to be 375 kPa.

Example 2 (Gay-Lussac's Law)

If a gas is heated from 19°C to 80°C with an initial pressure of 2000 Pa, the final pressure is 2420 kPa.

Example 3 (Volume Calculation)

The volume of 1.30 mol of Argon gas at STP is calculated to be 29.51 L.

Example 1 (Boyle's Law)

If the pressure applied to 20.0 ml oxygen increases from 74 kPa to 100 kPa, the new volume is 14.8 mL.

Example 2 (Boyle's Law)

Final pressure of 1.0 L of nitrogen gas at 100 kPa after being released to an evacuated 4.0 L container is calculated.

Example 3 (Boyle's Law)

Final volume of 70 ml nitrogen at STP when the pressure is doubled is calculated.

Practice Question 1

What is the volume of 2.40 mol of Argon gas at 180 kPa and 25°C?

Practice Question 2

Calculate the number of moles of nitrogen gas in a 2.60 L container at 5 atm and 60°C.

Practice Question 3

A sample of an ideal gas occupies a volume of 550 mL at 25°C with a pressure of 1.20 atm. What is the number of moles?

Practice Question 4

How many grams of carbon dioxide should be placed in a 250 mL container at -24°C to produce a pressure of 95 kPa?

Answer to Practice Question 1

33.05 L (2 d.p).

Answer to Practice Question 2

0.48 mol (2 d.p).

Answer to Practice Question 3

0.0269 mol.

Answer to Practice Question 4

0.01147 mol -> 0.505 g.

Practice Question 5

A container of gas is initially at 0.500 atm at 25°C. What will the pressure be at 125°C?

Practice Question 6

If a gas is cooled from 323.0 K to 273.15 K and volume is kept constant, what final pressure would result if the original pressure was 280 kPa?

Practice Question 7

The temperature of a sample of gas in a steel tank at 30.0 kPa is increased from -100.0˚C to 25.0 ˚C. What is the final pressure inside the tank?

Answer to Practice Question 5

67.65 kPa.

Answer to Practice Question 6

237 kPa.

Answer to Practice Question 7

51.7 kPa.

Final volume of ammonia

3.5 L when the pressure is halved.

Final pressure of air in syringe

202.65 kPa when compressed to half its original volume.

Absolute zero

The coldest possible temperature where molecular motion stops, defined as -273.15°C or 0 K.

Volume at 80°C for hydrogen gas

1.8 L (1 d.p) at 80°C, assuming constant pressure.

Volume of nitrogen dioxide at 0°C

The volume occupied by nitrogen dioxide when cooled to 0°C from 100°C and 100 kPa.

Volume of helium gas at 60°C

The volume of a balloon containing 2.0 L of helium gas at 20°C when the temperature rises to 60°C, assuming constant pressure.

New volume of gas at 400 K

The new volume of a gas that has a volume of 0.750 L at 300 K when heated to 400 K.

Final volume of gas heated from 25°C to 150°C

The final volume calculated assuming constant pressure after converting temperatures to Kelvin.

Final volume of nitrogen at 0°C

The final volume of nitrogen gas in litres when cooled from 37°C to 0°C.

Volume decrease of nitrogen gas

The amount by which the volume of nitrogen gas decreased when cooled from 37°C to 0°C.

Moles of gas escaped from balloon

The number of moles of gas that escaped when the volume of a balloon decreased from 4.60 L to 3.60 L.

Volume of Argon gas

The volume that 4.80 mol of Argon would occupy under the same conditions as 2.50 mol occupying 7.50 L.

Molar volume of gas

The volume of 1 mole of the substance at given temperature and pressure.

Volume occupied by sulfur dioxide

1.24 L occupied by 3g of sulfur dioxide at 25°C and 100 kPa.

Volume occupied at STP by 88g carbon dioxide

The volume occupied at STP by 88g of carbon dioxide.

Volume occupied at STP by 42g nitrogen

The volume occupied at STP by 42g of nitrogen.

Volume occupied at STP by 18.3g hydrogen chloride

The volume occupied at STP by 18.3g of hydrogen chloride.

Mass of methane at room temperature and pressure

The mass of 1.24 L of methane at room temperature and pressure of 100 kPa.

Mass of carbon dioxide at room temperature and pressure

The mass of 2.48 L of carbon dioxide at room temperature and pressure of 100 kPa.

Mass of acetylene at room temperature and pressure

The mass of 49.6 L of acetylene at room temperature and pressure of 100 kPa.