Gas Laws: Avogadro's Law

Introduction

Avogadro's Law: At a constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of the gas.

Historical Context:

• 1811: Amedeo Avogadro introduced his hypothesis that equal volumes of gases, at identical conditions, contain an equal number of molecules.
• 1860 Karlsruhe Congress: Avogadro's hypothesis gained recognition through advanced experimental techniques.

Mathematical Representation

• Formula: The relationship between volume and moles is given by $V \propto n$ or $V = k \times n$.
  • $V$ is the volume of the gas, $n$ is the number of moles, and $k$ is the proportionality constant.

Example Calculation:

• For 2 moles of gas at STP with $k = 22.4 \text{ L/mol}$, the volume is calculated as $V = 22.4 \times 2 = 44.8 \text{ L}$.

Experimental Validation

Significance: Experiments substantiate Avogadro's Law in practical scenarios.

Historical Experiments:

• Joseph Louis Gay-Lussac's Experiments: Explored fixed volume ratios in chemical reactions, which influenced Avogadro's hypothesis.

Methodology:

• Setup: Employ a gas syringe under controlled parameters.
• Process: Observe gas volumes under stable conditions.

EXPECTED OUTCOMES: Observations should confirm the volume-mole proportionality.

Graphical Analysis

• Graph Construction:
  • Represent volume (V) on the y-axis and moles (n) on the x-axis.

• Interpretation: A linear graph signifies direct proportionality, consistent with Avogadro's Law.

Integration with Other Laws

Avogadro's Law is part of the Ideal Gas Law: $PV = nRT$, corresponding with:

Common Misconceptions

• Misbelief in Molar Volume Variation:

  • Reality: At STP, molar volume remains constant for different gases.

• Confusion with Mass:

  • Greater molar mass does not imply a larger volume at STP.

Practice Problems

• Problem: Calculate the volume of 4 moles at STP.

  • Solution: $V = 22.4 \text{ L/mol} \times 4 \text{ mol} = 89.6 \text{ L}$

• Problem: At non-STP conditions, with 5 moles and a volume of 120 L, determine $k$.

  • Solution: $k = \frac{V}{n} = \frac{120 \text{ L}}{5 \text{ mol}} = 24 \text{ L/mol}$

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By mastering Avogadro's Law, students can better grasp gas behaviour, essential for both examinations and practical applications in science and industry.