Gas Laws

Types of Gas Laws

Boyle's Law: Relationship Between Pressure and Volume

In 1662, Robert Boyle discovered how the volume of a gas changes with pressure.

Boyle's Law states that at constant temperature, the volume of a fixed mass of gas is inversely proportional to its pressure.

Mathematically, this is expressed as:

P \times V = \text{constant} \quad \text{(at constant temperature)}

Where:

$P$ = pressure of the gas
$V$ = volume of the gas

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Example: If you decrease the volume of a gas, its pressure increases, as long as the temperature remains constant.

For example, if a gas with a volume of 500 cm³ has a pressure of 100 kPa, reducing its volume to 250 cm³ will double its pressure to 200 kPa.

Charles's Law: Relationship Between Volume and Temperature

Charles's Law explains how gases expand when heated.

It states that at constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature (measured in Kelvin).

Mathematically:

V \propto T \quad \text{or} \quad \frac{V}{T} = \text{constant} \quad \text{(at constant pressure)}

Where:

$V$ = volume of the gas
$T$ = temperature in Kelvin

Converting Celsius to Kelvin:

To convert a temperature from degrees Celsius to Kelvin, add 273 to the Celsius temperature.

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Example Calculation:

27^\circ C + 273 = 300 \, K

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Example Problem: If a gas occupies 1 L at 300 K, heating it to 600 K will cause its volume to double, assuming constant pressure.

Combined Gas Law: Boyle's and Charles's Laws Together

The Combined Gas Law combines Boyle's and Charles's laws into one relationship that accounts for changes in pressure, volume, and temperature simultaneously. It is given by:

\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}

Where:

$P_1, V_1, T_1$ = initial pressure, volume, and temperature
$P_2, V_2, T_2$ = final pressure, volume, and temperature

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Example: A sample of nitrogen gas has a volume of 200 cm³ at 27°C (300 K) and a pressure of 90,000 Pa. What would its volume be at standard temperature and pressure (s.t.p: 0°C or 273 K, 100,000 Pa)?

Using the combined gas law:

\frac{90,000 \times 200}{300} = \frac{100,000 \times V_2}{273}

Solving for $V_2$ , the volume at s.t.p. is 164 cm³.

Gay-Lussac's Law of Combining Volumes

In 1808, Joseph Gay-Lussac observed that gases react in simple whole-number ratios by volume when measured under the same conditions of temperature and pressure.

This is known as Gay-Lussac's Law of combining volumes.

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Example: When hydrogen and oxygen react to form water vapour, 2 volumes of hydrogen react with 1 volume of oxygen to produce 2 volumes of water vapour ( $2H₂ + O₂ → 2H₂O$ ).

Avogadro's Law: Relationship Between Volume and Molecules

In 1811, Amedeo Avogadro proposed Avogadro's Law, which states that equal volumes of gases, under the same conditions of temperature and pressure, contain equal numbers of molecules.

This means that 1 mole of any gas occupies the same volume at the same temperature and pressure. At s.t.p., 1 mole of any gas occupies 22.4 L.

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Example: If you have 2 moles of nitrogen gas (N₂) at s.t.p., its volume would be:

2 \, \text{moles} \times 22.4 \, \text{L/mole} = 44.8 \, \text{L}

Ideal Gas Equation

The ideal gas equation combines all the gas laws into one equation that describes the behaviour of an ideal gas:

PV = nRT

Where:

$P$ = pressure (in Pa)
$V$ = volume (in m³)
$n$ = number of moles of gas
$R$ = universal gas constant (8.31 J K⁻¹ mol⁻¹)
$T$ = temperature (in Kelvin)

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Example: 0.5 g of a gas occupies 200 cm³ at 27°C (300 K) and a pressure of 100 kPa (100,000 Pa). Calculate the number of moles and the relative molecular mass of the gas.

Step 1: Convert units

Volume:

200 \, \text{cm³} = 2 \times 10^{-4} \, \text{m³}

Temperature:

27°C + 273 = 300 \, K

Pressure:

100 \, \text{kPa} = 100,000 \, \text{Pa}

Step 2: Use the ideal gas equation to find the number of moles

(100,000 \times 2 \times 10^{-4}) = n \times 8.31 \times 300

Solving for $n$ , the number of moles is 0.008 moles.

Step 3: Find the relative molecular mass:

Since 0.008 moles of gas weighs 0.5 g, 1 mole weighs:

\frac{0.5}{0.008} = 62.5 \, \text{g/mol}

Thus, the relative molecular mass of the gas is 62.5 g/mol.

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Summary

Gas laws describe how gases behave under different conditions of pressure, temperature, and volume. Boyle's Law explains how volume decreases as pressure increases. Charles's Law relates temperature to volume. Avogadro's Law reveals that the volume of a gas is directly proportional to the number of gas molecules. The ideal gas equation combines all these relationships and is key to solving gas-related problems in chemistry.

Gas Laws Simplified Revision Notes for Leaving Cert Chemistry

Gas Laws

Types of Gas Laws

Boyle's Law: Relationship Between Pressure and Volume

Charles's Law: Relationship Between Volume and Temperature

Converting Celsius to Kelvin:

Combined Gas Law: Boyle's and Charles's Laws Together

Gay-Lussac's Law of Combining Volumes

Avogadro's Law: Relationship Between Volume and Molecules

Ideal Gas Equation

Summary

500K+ Students Use These Powerful Tools to Master Gas Laws For their Leaving Cert Exams.

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