11th Chemistry vander walls equation for Quarterly Exam last night kku preparation pdf

Van der Waals Equation for Real Gases

This is a perfect guide for your last-night preparation for the 11th Chemistry quarterly exam. Understand this well, and you can confidently answer any question on this topic!

Why do we need the Van der Waals Equation?

The Ideal Gas Equation (PV = nRT) is simple and useful, but it's based on two assumptions that are not true for real gases [1]:

1. Gas molecules have no volume (they are point masses).
2. There are no forces of attraction or repulsion between gas molecules.

In reality, gas molecules do have a small but significant volume, and they do attract each other (intermolecular forces) [3, 16]. The van der Waals equation is a modified version of the ideal gas law that accounts for these two factors for real gases [1, 4].

The Van der Waals Equation

For 'n' moles of a real gas, the equation is:

(P + an²/V²)(V - nb) = nRT

Let's break down the two important corrections made to the Ideal Gas Law's pressure (P) and volume (V) terms [5, 12].

---

1. The Volume Correction (V - nb)

Ideal Gas Assumption: Molecules are so small that their volume is negligible. The entire volume of the container (V) is available for them to move.

Reality: Gas molecules are particles with a definite volume. Therefore, the actual volume available for the gas molecules to move is the volume of the container minus the volume occupied by the molecules themselves [8, 11].

• V is the total volume of the container.
• nb is the "excluded volume" per 'n' moles of gas. It corrects for the volume occupied by the gas molecules [5].
• The constant 'b' is the volume correction factor for one mole of a gas and is unique for each gas [5].

So, the corrected volume term is (V - nb).

2. The Pressure Correction (P + an²/V²)

Ideal Gas Assumption: There are no intermolecular forces of attraction.

Reality: Molecules in a real gas attract each other. A molecule in the center is pulled equally in all directions. However, a molecule about to hit the container wall is pulled back by other molecules, as shown below. This reduces the force of its impact on the wall [3, 16].

As a result, the observed pressure (P) of a real gas is less than the pressure it would have if it were an ideal gas.

To fix this, we add a correction term to the observed pressure:

• The correction term is an²/V² [12].
• This term accounts for the force of attraction between molecules. The attraction depends on the concentration of molecules (n/V), so the total effect is proportional to (n/V)² [3].
• The constant 'a' is a measure of the magnitude of the attractive forces between molecules and is unique for each gas [5].

So, the corrected pressure term is (P + an²/V²).

Summary of Van der Waals Constants

Constant	What it Represents	Units
a	Magnitude of intermolecular attractive forces [5]. A larger 'a' means stronger attraction.	atm L² mol⁻² [5]
b	Effective volume occupied by one mole of gas molecules (excluded volume) [5, 11]. A larger 'b' means larger molecules.	L mol⁻¹ [5]

Key Takeaways for Full Marks

• The van der Waals equation corrects the ideal gas law for real gases by accounting for intermolecular forces and molecular volume [1].
• Pressure Correction (P + an²/V²): The observed pressure is lower than ideal pressure due to attractive forces, so a term is added [3].
• Volume Correction (V - nb): The available volume is less than the container volume due to the size of molecules, so a term is subtracted [11].
• Remember the equation and be ready to explain what each correction term (`an²/V²` and `nb`) and each constant (`a` and `b`) signifies.