ChemistryChapter 2: Matter
2.4.3 Avogadro's Law
**Avogadro's Law:** It states that for a gas at **constant temperature and pressure**, the
Explanation level
Introduction
Boyle's Law relates pressure and volume. Charles's Law relates temperature and volume. But there is one more important variable in gases: the amount of gas, measured in moles.
Avogadro's Law describes the relationship between the volume of a gas and the number of moles of gas, while the temperature and pressure stay the same.
Definition
Avogadro's Law: It states that for a gas at constant temperature and pressure, the volume of the gas is directly proportional to the number of moles of gas.
In simple words: If you increase the amount of gas (more moles), the volume increases. If you decrease the amount of gas (fewer moles), the volume decreases — as long as temperature and pressure stay the same.
Main Idea
- Direct relationship: When moles go up, volume goes up.
- When moles go down, volume goes down.
- The ratio of volume to moles is constant (at constant temperature and pressure).
Core Concept
The relationship can be written mathematically as:
V ∝ n
This means:
V = kn
Rearranging:
Vn = k
Vn = constant
Where:
- V = volume of the gas
- n = number of moles of gas
- k = a constant (at constant temperature and pressure)
Key point: If the number of moles is doubled, the volume is doubled. If the number of moles is halved, the volume is halved.
Mathematical Form
The mathematical statement of Avogadro's Law is:
V ∝ n
V = kn
Vn = k
Vn = constant
For two different sets of conditions (at the same temperature and pressure):
V1n1 = V2n2
Where:
- V1 = initial volume
- n1 = initial number of moles
- V2 = final volume
- n2 = final number of moles
Units:
- Volume is usually measured in dm³, cm³, or m³.
- Amount of gas is measured in moles (mol).
Kinetic Particle Theory Interpretation
Effect of Number of Particles (Moles) on Volume
What happens when the number of gas particles (moles) increases:
- When the number of gas particles increases, there are more particles colliding with the walls of the container.
- To keep the pressure constant, the volume of the container must increase to accommodate the additional particles.
- This maintains the same number of collisions per unit area.
What happens when the number of particles decreases:
- If the number of particles decreases, the volume must decrease to maintain constant pressure.
Simple explanation: Imagine a room with a certain number of people. If you add more people, the room needs to be bigger to keep the same "crowdedness" (pressure). If you remove people, the room can be smaller. The same idea applies to gas particles.
Constant Temperature and Pressure
- The temperature ensures the kinetic energy of each particle remains the same.
- The pressure remains constant by adjusting the volume according to the number of particles.
Key point: At constant temperature and pressure, the volume adjusts so that the pressure stays the same, even though the number of particles has changed.
Molar Volume at RTP
A very important consequence of Avogadro's Law is the molar volume of a gas at Room Temperature and Pressure (RTP).
At RTP (25°C and 1 atm):
- One mole of any gas occupies a volume of 24 dm³.
Examples:
- 24 dm³ of H2 gas at RTP = 2 g = 1 mole
- 24 dm³ of NH3 gas at RTP = 17 g = 1 mole
- 24 dm³ of any gas at RTP = 1 mole
Key point: The molar volume is the same for all gases at the same temperature and pressure. This is a direct consequence of Avogadro's Law.
Formula / Mathematical Form
V ∝ n
V = kn
Vn = k
Vn = constant
V1n1 = V2n2
At RTP: 1\ mole of any gas = 24\ dm3
Solved Example
Example: A container holds 2.0\ moles of a gas occupying a volume of 48\ dm3 at RTP. If the number of moles is increased to 3.0\ moles at the same temperature and pressure, what will be the new volume?
Given: n1 = 2.0\ mol V1 = 48\ dm3 n2 = 3.0\ mol
Required: V2 = ?
Formula: V1n1 = V2n2
Substitution: 482.0 = V23.0
Calculation: 24 = V23.0 V2 = 24 × 3.0 V2 = 72\ dm3
Final Answer: The new volume is 72\ dm3.
Check: Moles increased from 2.0 to 3.0 (ratio 3:2). Volume increased from 48 to 72 (same ratio). ✓
Important Points
- - Avogadro's Law applies at constant temperature and pressure.
- - Volume is directly proportional to the number of moles.
- - Vn = constant.
- - The formula for two sets of conditions is V1n1 = V2n2.
- - When moles increase, volume increases (more particles, need more space).
- - When moles decrease, volume decreases (fewer particles, need less space).
- - At constant temperature and pressure, the volume adjusts to keep the pressure the same.
- - At RTP (25°C and 1 atm), 1 mole of any gas occupies 24 dm³.
Remember
- - Avogadro's Law → volume and moles are directly related.
- - Vn = constant.
- - V1n1 = V2n2.
- - Moles ↑ → Volume ↑.
- - Moles ↓ → Volume ↓.
- - Temperature and pressure must be constant.
- - At RTP, 1 mole of any gas = **24 dm³**.
- - Molar volume is the same for all gases at the same T and P.
Common Mistakes
| Mistake | Correction |
|---|---|
| Thinking volume and moles are inversely proportional | They are directly proportional |
| Forgetting that temperature and pressure must be constant | Avogadro's Law only applies at constant temperature and pressure |
| Using the wrong formula | Use V1n1 = V2n2, not V1 n1 = V2 n2 |
| Confusing moles with mass | Moles = amount of substance; mass = grams |
| Thinking molar volume depends on the type of gas | At the same T and P, all gases have the same molar volume |
| Forgetting to convert to moles when given mass | Use n = massmolar mass |
| Mixing up units of volume | Keep units consistent on both sides |
Quick Revision
Avogadro's Law states that for a gas at constant temperature and pressure, the volume of the gas is directly proportional to the number of moles of gas.
- Mathematically:
- V ∝ n
- V = kn
- Vn = k
- Vn = constant
- V1n1 = V2n2
Kinetic Particle Theory Interpretation:
- Effect of Number of Particles (Moles) on Volume: When the number of gas particles (moles) increases, there are more particles colliding with the walls of the container. To keep the pressure constant, the volume of the container must increase to accommodate the additional particles and maintain the same number of collisions per unit area. Conversely, if the number of particles decreases, the volume must decrease to maintain constant pressure.
- Constant Temperature and Pressure: The temperature ensures the kinetic energy of each particle remains the same, and the pressure remains constant by adjusting the volume according to the number of particles.
- Molar Volume at RTP:
- At RTP (25°C and 1 atm), 1 mole of any gas occupies 24 dm³.
60-Second Revision
- Avogadro's Law: V ∝ n at constant temperature and pressure.
- Vn = constant
- V1n1 = V2n2
- Moles ↑ → Volume ↑
- Moles ↓ → Volume ↓
- At RTP, 1 mole of any gas = **24 dm³**.
- More particles → more collisions → need more volume.
- ⚠️ Warning: Avogadro's Law only applies when temperature and pressure are constant.
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Review the key facts, formulas and checks before you move on.2.4.3 Avogadro's Law
Sticky Notes · Quick Revision
Key Point 1
- Avogadro's Law → V ∝ n
Key Point 2
- Vn = constant
Key Point 3
- V1n1 = V2n2
Key Point 4
- Moles ↑ → Volume ↑
Key Point 5
- Moles ↓ → Volume ↓
Key Point 6
- Constant temperature and pressure.
Key Point 7
- At RTP, 1 mole of any gas = **24 dm³**.
Key Point 8
- More particles → more collisions → need more volume.
Key Point 9
- Molar volume is the same for all gases at same T and P.
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