Gas Laws - Notes
Properties of Gases
• Recall that gases have unique properties when compared to solids and liquids.
• What are some of these unique properties?
– Gases exert pressure
– Can change volume of gas (compressible)
– Gas occupies the volume of the container
• The volume of a solid or liquid depends primarily on the number of particles (moles)
present.
• The volume of a gas depends on the number of particles present, but can also be
changed by altering the pressure or temperature.
• Because the particles are very far apart in a gas (except at very high pressure), it
can be assumed that the volume of the gas particles is negligible, and there are no
intermolecular forces acting between them.
• If these assumptions are true, we refer to it as an ideal gas, and regardless of the
identity of the gas, it will obey the gas laws.
Gay-Lussac’s Law: Pressure and Temperature
• Pressure is defined as the force exerted over a certain area.
• In a gas, pressure arises from the collisions between gas particles and the walls of the
container.
• Pressure is usually expressed in kilopascals (kPa) or atmospheres (atm).
• Pressure at sea level is around 1 atm (101.3 kPa).
• Conversion: Celsius to Kelvin → add 273.15
• Gay-Lussac’s Law (1809): The pressure exerted by a gas is directly proportional to
temperature, if volume is held constant.
1
Boyle’s Law: Pressure and Volume
• In 1662, Robert Boyle discovered that the volume of a given amount of gas varies
inversely with pressure when temperature is kept constant.
P ↑
1
V
or P1 V1 = P2 V2
Questions:
• What will happen to the volume of the syringe if you press the plunger on a sealed
syringe filled with air?
→ Decrease in volume
• Thus, what will happen to the pressure of the gas inside the syringe?
→ Increase in pressure
• Explain why a balloon inside a sealed syringe will deflate when the plunger is depressed.
→ This is due to the pressure increasing around the balloon, decreasing the volume of
the syringe. The increase in pressure of gas surrounding the balloon results in a decrease
of volume.
Charles’ Law: Temperature and Volume
• Jacques Charles discovered that the volume and temperature of a gas are directly
proportional if pressure is kept constant.
V ↑T
or
V1
V2
=
T1
T2
Questions:
• What happens to the density of a gas when heated?
D=M
↓ T =↓ V ↔↗ D
V
• Hence, explain how a hot air balloon works.
→ Air inside the balloon is heated, which increases the volume and decreases the density,
so the balloon rises.
2
Avogadro’s Law: Volume and Moles
• Avogadro’s law states that equal volumes of di!erent gases at the same temperature and pressure contain the same number of particles.
V1
V2
=
n1
n2
Question: What conditions must exist for equal gas volumes to contain equal numbers
of molecules?
→ Pressure and Temperature constant
V ↑ n or
Avogadro’s Law of Combining Volumes
• “The ratios of the volumes of gases involved in a chemical reaction can be expressed
by small, whole numbers.”
• Example:
2H2 (g) + O2 (g) → 2H2 O(g)
• 2 L of hydrogen reacts with 1 L of oxygen to form 2 L of water vapour.
• 10 mL of hydrogen reacts with 5 mL of oxygen to form 10 mL of water vapour.
• Question: What volume of oxygen gas will react with 50 mL of hydrogen gas?
Concept Check 1.1
(a) A container of gas at 300 K and 150 kPa is heated up to 450 K, with the volume held
constant.
Calculate the pressure after heating, and state the law used.
P1
P2
=
T1
T2
(b) A 50.0 mL syringe containing nitrogen is compressed from 100 kPa to 430 kPa.
Calculate the new volume of the syringe and state the law used.
P1 V 1 = P2 V 2
3
The Ideal Gas Law
P V = nRT
Where:
• P = pressure in kilopascals (kPa)
• V = volume in litres (L)
• n = moles of gas particles
• R = 8.314 J mol-1 K-1
• T = temperature in Kelvin (K)
Molar Volume
• Ideal gas law can determine the volume of 1 mole of gas at specific conditions.
• Standard conditions:
– STP: 0°C (273.15 K), 100 kPa
– RTP: 25°C (298.15 K), 100 kPa
Molar Volume Table:
Conditions Temperature and Pressure
STP
0°C (273.15 K), 100 kPa
RTP
25°C (298.15 K), 100 kPa
Simplified formula:
n=
Molar Volume (L mol-1 )
22.71
24.79
V
MV
Example Problem
0.038 g of zinc is dropped into excess nitric acid. Calculate the volume of hydrogen gas
produced at 25°C and 100 kPa.
Steps:
1. Write the balanced equation for the reaction.
2. Calculate the known moles of reactant.
3. Use the mole ratio to determine the moles of unknown substance.
4. Convert to the desired quantity.
4
Revision of Gas Laws
1. Gases can be compressed because:
(a) They are able to di!use and solids cannot.
(b) There is space between their particles.
(c) Many gases are less dense than air.
(d) The particle theory tells us that gas pressure acts in all directions.
2. When a gas is cooled its particles:
(a) Become smaller.
(b) Move more slowly.
(c) Drop down out of the air.
(d) Di!use through other nearby gases.
3. Absolute zero temperature is:
(a) The temperature on the Moon.
(b) Zero Celsius.
(c) Zero Kelvin.
(d) The main cause of decompression sickness.
4. Based on the equation: 2H2 (g) + O2 (g) → 2H2 O(g),
5 litres of oxygen can support the combustion of:
(a) 2 litres
(b) 5 litres
(c) 10 litres
(d) 2 ↘ 24.79 litres
5. A container is filled with a sample of oxygen gas. The pressure doubles while the
volume stays the same. The absolute temperature will:
(a) Double.
(b) Halve.
(c) Stay the same.
(d) Increase and then decrease.
5
6. Three identical flasks are filled with O2 , N2 , and Ar. Which is true?
(a) Each flask has the same number of gas molecules.
(b) There are twice as many oxygen and nitrogen molecules as argon molecules.
(c) The density of the gas in each flask is the same.
(d) The molar mass of the gas in each flask is the same.
7. Gases can vary in temperature, pressure, volume, and number of moles. Which are
inversely proportional?
(a) P and T
(b) V and T
(c) V and P
(d) n and P
8. The pressure of gas in a diver’s lungs changes from 100 kPa to 150 kPa. Initially 6 L
of gas was present. The new volume is:
(a) 3 L
(b) 4 L
(c) 6 L
(d) 9 L
9. A gas at 300 K and 250 kPa is cooled to 270 K. The new pressure is closest to:
(a) 300 kPa
(b) 270 kPa
(c) 225 kPa
(d) 220 kPa
10. The calculation of quantities in chemical equations is called:
(a) Stoichiometry
(b) Analysis
(c) Calorimetry
(d) The universal gas law
6
11. Charles’s law can be expressed as:
(a) P V = nRT
(b) VT = constant
(c) PTV = constant
(d) P V = constant
12. An ideal gas is one in which:
(a) The gas particles have no volume.
(b) There are no forces between particles.
(c) Collisions between particles are elastic.
(d) All of the above.
13. Volume occupied by 2.0 moles of helium at 400 K and 100 kPa is:
(a) 665.0 L
(b) 66.5 L
(c) 21.1 L
(d) 8.0 L
14. The graph of Volume (V) vs. Temperature (T) represents:
(a) Charles’s law
(b) Boyle’s law
(c) Gay-Lussac’s law
(d) Avogadro’s law
15. Under what conditions do real gases behave most like ideal gases?
(a) High temperature and low pressure
(b) Low temperature and high pressure
(c) Low temperature and low pressure
(d) High temperature and high pressure
Inquiry Question:
How does the ideal gas law relate to all other gas laws?
7