# Avogadro's Law

This is part of Year 11 HSC Chemistry course under the topic of *Gas Laws*.

### HSC Chemistry Syllabus

**Conduct investigations and solve problems to determine the relationship between the Ideal Gas Law and:****Avogadro's Law**

**Avogadro's Law Explained**

**Gas Laws**

Avogadro's law is one of the four individual gas laws which were combined to describe the ideal gas law.

The gas laws describe the behaviour of gases under ideal circumstances and assume their properties that ideal gases:

- Have a low density since the spaces between the particles of gas are large
- Are free flowing/forming meaning that they fill the volumes of their containers and can leak through cracks
- Are compressible and expandable
- Are diffusive meaning that they travel from areas of higher concentration to areas of lower concentration.

Avogadro's law focuses on the directly proportional relationship between volume and amount when the pressure and temperature of gas is kept constant.

###
**Avogadro'****s Law**

Avogadro's Law is named after Amadeo Avogadros, an 17th-century scientist who was the first to distinguish between atoms and molecules.

Avogadro's law states that the volume that is occupied by a gas is directly proportional to the amount of gas that is present when the pressure and temperature of gas are kept constant. Mathematically the relationship described by Avogadro's Law can be expressed as

$$V \propto n$$

and thus

$$\frac{V_1}{n_1} = \frac{V_2}{n_2}$$

Where:

- `V_1` and `n_1` represent the initial volume and number of moles of gas
- `V_2` and `n_2` represent the volume and number of moles of gas after a change has been imparted on the gas system.

In the context of Avogadro's Law, amount refers to the quantity of the particles of gas in a system while volume refers to the space that is occupied by those gas particles.

An implication of Avogadro's law is that same quantities or number of moles of gases would occupy equal volume at the same pressure and temperature. For example, 1 mole of hydrogen gas and 1 mole of oxygen gas would both occupy 24.79 L at RTP (298.15 K and 100 kPa).

Since the volume of a gas is directly proportional to its number of moles, the molar ratio between different quantities of gases can be inferred by comparing their volumes. For example, the ratio of volumes of 1 mole of hydrogen gas and 2 moles of oxygen gas would be also in a ratio of 1 : 2.

**Units of Measurement:**

**Amount**- number of particles/molecules
- number of moles (divided by Avogadro's number)

**Volume**- Millilitre (mL)
- 1 litre (L) = 1000 mL
- 1 cubic metre (m
^{3}) = 1000 L

**Deriving and understanding Avogadro's Law**

The ideal gas law is given by the formula:

$$PV = nRT$$

Where:

- P is pressure (in kPa)
- V is volume (in L)
- n is the number of moles of gas
- R is the universal gas constant = 8.314 J mol
^{–1}K^{–1} - T is temperature (in Kelvin)

The equation can be rearranged into

$$V = \frac{nRT}{P}$$

When pressure and temperature are kept constant, the expression `\frac{RT}{P}` is equivalent to a constant `k`. Thus the following mathematical equation can also be obtained:

$$V = k \times n$$

The relationship described by Avogadro's Law is demonstrated in the graph below.

**Real-World Examples & Practical Applications**

**Balloon Pump**: In the example demonstrated, there are initially 6 units of gas that exist inside of the balloon. When the pump is pushed, gas enters into the balloon and the balloon expands in size. Once all of the gas has travelled into the balloon, the volume has increased by exactly twice the amount. What is also observed as predicted by Avogadro's law is that the amount of gas inside of the balloon has also increased by twice the amount to 12 units of gas.