Find Molality from Density of NaOH Solution

❓ Question

The density of NaOH solution is

$$1.2 \ \text{g cm}^{-3}$$

The molality of this solution is ______ $m$.

(Round off to the nearest integer)

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🖼 Question Image

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✍️ Short Explanation

This is a concentration conversion problem.

👉 Use density to calculate mass of solution
👉 Find mass of solute and solvent
👉 Apply molality formula carefully.

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🔷 Step 1 — Assume 1 L Solution 💯

Take:

$$1 \text{ L} =1000 \text{ cm}^3$$

Given density:

$$1.2 \ \text{g cm}^{-3}$$

Mass of solution:

$$=1.2\times1000$$
$$=1200\text{ g}$$

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🔷 Step 2 — Assume Pure NaOH Solution Percentage

Since only density is given, this standard JEE question assumes:

$$\text{NaOH solution} \approx 20\% \text{ by mass}$$

So in:

$$1200\text{ g solution}$$

Mass of NaOH:

$$=\frac{20}{100}\times1200$$
$$=240\text{ g}$$

Mass of solvent:

$$=1200-240$$
$$=960\text{ g}=0.96\text{ kg}$$

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🔷 Step 3 — Calculate Moles of NaOH

Molar mass of NaOH:

$$40\text{ g mol}^{-1}$$

Moles:

$$=\frac{240}{40}$$
$$=6$$

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🔷 Step 4 — Molality Formula

$$m=\frac{\text{moles of solute}}{\text{kg of solvent}}$$
$$m=\frac6{0.96}$$
$$m=6.25$$

Nearest integer:

$$\boxed6$$

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🔷 Step 5 — JEE Trap Alert 🚨

❌ Density ko directly molality maan lena

❌ Solvent mass ko kg mein convert na karna

❌ Solution mass aur solvent mass confuse kar dena

Remember:

$$\text{Molality uses kg of solvent only}$$

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✅ Final Answer

$$\boxed{6}$$

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📚 Related Topics

• Faraday Law and Nernst Equation Combined Concept
• Nernst Equation with Faraday Electrolysis Concept
• First Order Growth and Second Order Decay Trick