Partial Pressure Ratios Using Mole Fraction Method

❓ Question

At sea level, dry air composition:

• N₂ = 70%
• O₂ = 27%
• Ar = 3%

Total pressure = 1.15 atm

Find:

1️⃣ $P_{N_2} : P_{O_2}$
2️⃣ $P_{O_2} : P_{Ar}$

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🖼 Question Image

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✍️ Short Concept

From Dalton’s Law:

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

So:

$$\frac{P_1}{P_2} = \frac{x_1}{x_2} = \frac{n_1}{n_2}$$

👉 Ratio of partial pressures = ratio of moles

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🔷 Step 1 — Assume Convenient Mass 💯

Assume:

$$100 \, g \text{ air}$$

So:

• N₂ = 70 g
• O₂ = 27 g
• Ar = 3 g

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🔷 Step 2 — Convert to Moles

$$n_{N_2} = \frac{70}{28} = 2.5$$
$$n_{O_2} = \frac{27}{32} \approx 0.843$$
$$n_{Ar} = \frac{3}{40} = 0.075$$

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🔷 Step 3 — Ratio of Partial Pressures

Using:

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

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(i) $P_{N_2} : P_{O_2}$

$$= \frac{2.5}{0.843} \approx 2.96 : 1$$

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(ii) $P_{O_2} : P_{Ar}$

$$= \frac{0.843}{0.075} \approx 11.25 : 1$$

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✅ Final Answer

$$\boxed{P_{N_2} : P_{O_2} \approx 2.96 : 1}$$
$$\boxed{P_{O_2} : P_{Ar} \approx 11.25 : 1}$$

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⭐ Golden JEE Insight

👉 Total pressure does NOT matter for ratios

👉 Directly use:

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

No need to calculate actual pressures!