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Assertion: The molality and molarity of ...

Assertion: The molality and molarity of very dilute aqueous solutions differ very little.
Reason: The density of water is about `1.0 g cm^(-3)` at room temperature.

A

Statement-I is true, Statement-II is true , Statement-II is correct explanation for Statement-I

B

Statement-I is true, Statement-II is true , Statement-II is `NOT` a correct explanation for statement-I

C

Statement-I is true, Statement-II is false

D

Statement-I is false, Statement-II is true

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze the assertion and the reason provided. ### Step-by-Step Solution: 1. **Understanding Molarity and Molality**: - **Molarity (M)** is defined as the number of moles of solute per liter of solution. The formula is: \[ \text{Molarity (M)} = \frac{\text{Number of moles of solute}}{\text{Volume of solution in liters}} \] - **Molality (m)** is defined as the number of moles of solute per kilogram of solvent. The formula is: \[ \text{Molality (m)} = \frac{\text{Number of moles of solute}}{\text{Mass of solvent in kg}} \] 2. **Density of Water**: - The density of water is approximately \(1.0 \, \text{g/cm}^3\) or \(1000 \, \text{kg/m}^3\). This means that 1 liter of water has a mass of about 1 kg. 3. **Relating Molarity and Molality for Dilute Solutions**: - For very dilute solutions, the volume of the solvent (water) is nearly equal to the volume of the solution. Therefore, when we have a solution where the solute concentration is very low, the mass of the solvent (in kg) is approximately equal to the volume of the solution (in liters). - Hence, for very dilute solutions: \[ \text{Molarity} \approx \text{Molality} \] 4. **Conclusion**: - Since the assertion states that the molality and molarity of very dilute aqueous solutions differ very little, and the reason provided states that the density of water is about \(1.0 \, \text{g/cm}^3\) at room temperature, both the assertion and reason are correct. - Therefore, the answer is that both the assertion and the reason are true, and the reason correctly explains the assertion. ### Final Answer: Both the assertion and reason are correct. The molality and molarity of very dilute aqueous solutions differ very little due to the density of water being approximately \(1.0 \, \text{g/cm}^3\).
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