Dalton Law Mole Fraction Trick for Gas Mixtures

 

❓ Concept Question

In gas mixtures, why can’t we directly use mass percentage to find partial pressure ratios?

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🖼 Concept Image

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✍️ Short Concept

From Dalton’s Law:

$$P_i \propto x_i$$

👉 Partial pressure depends on mole fraction, NOT mass fraction.

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🔷 Step 1 — Golden Rule 💯

$$P_i = x_i \cdot P_{total}$$

So:

$$\frac{P_1}{P_2} = \frac{x_1}{x_2}$$

👉 Mole fraction decides pressure.

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🔷 Step 2 — Mass % ≠ Mole %

Given:

• N₂ = 70%
• O₂ = 27%
• Ar = 3%

⚠️ These are mass percentages, not mole percentages.

👉 Different gases = different molar masses

So direct ratio lena WRONG.

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🔷 Step 3 — Convert Mass to Moles

Use:

$$\text{Moles} = \frac{\text{mass}}{\text{molar mass}}$$

👉 Lighter gas → more moles
👉 Heavier gas → fewer moles

This changes the actual ratio.

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🔷 Step 4 — Pressure Ratio Shortcut

Since:

$$P_i = x_i \cdot P_{total}$$

Taking ratio:

$$\frac{P_1}{P_2} = \frac{n_1}{n_2}$$

👉 Total pressure cancels

👉 Only mole ratio matters.

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🔷 Step 5 — JEE Trap Alert

❌ Direct 70:27 use kar dena

❌ Molar mass ignore kar dena

Correct flow:

\text{Mass %} \rightarrow \text{Moles} \rightarrow \text{Ratio}

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✅ Final Takeaway

$$\boxed{\text{Partial pressure depends on mole fraction, not mass fraction}}$$

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⭐ Golden JEE Insight

Always remember:

👉 Same mass ≠ same number of particles

👉 Physics of gases = number of molecules matters