Problem 4 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

\(8 \mathrm{~g}\) of \(\mathrm{NaOH}\) is dissolved in \(18 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O} .\) Mole fraction of \(\mathrm{NaOH}\) in solution and molality (in \(\mathrm{mol} \mathrm{kg}^{-1}\) ) of the solution respectively are: (a) \(0.2,22.20\) (b) \(0.2,11.11\) (c) \(0.167,11.11\) (d) \(0.167,22.20\)

Step-by-Step Solution

Answer

Option (c): 0.167, 11.11

Step 1: Calculate Moles of NaOH and H2O

First, we'll calculate the moles of each component in the solution. The molar mass of NaOH is approximately 40 g/mol, so the moles of NaOH is calculated as follows:\[\text{Moles of NaOH} = \frac{8 \text{ g}}{40 \text{ g/mol}} = 0.2 \text{ mol}\]For H₂O, the molar mass is approximately 18 g/mol, so the moles of H₂O is:\[\text{Moles of H}_2\text{O} = \frac{18 \text{ g}}{18 \text{ g/mol}} = 1 \text{ mol}\]

Step 2: Calculate Mole Fraction of NaOH

The mole fraction is calculated using the formula:\[\text{Mole fraction of NaOH} = \frac{\text{Moles of NaOH}}{\text{Moles of NaOH} + \text{Moles of H}_2\text{O}}\]Substituting the values we found:\[\text{Mole fraction of NaOH} = \frac{0.2}{0.2 + 1} = \frac{0.2}{1.2} \approx 0.167\]

Step 3: Calculate Molality of the Solution

Molality is defined as the number of moles of solute per kilogram of solvent.Since the solvent is water with a mass of 18 g, we convert it to kilograms:\[\text{Mass of solvent (H}_2\text{O)} = \frac{18 \text{ g}}{1000} = 0.018 \text{ kg}\]Now, calculate the molality:\[\text{Molality} = \frac{\text{Moles of NaOH}}{\text{kg of H}_2\text{O}} = \frac{0.2}{0.018} \approx 11.11 \text{ mol/kg}\]

Step 4: Compare with Given Options

Now we compare our calculated results with the given options: - Mole fraction of NaOH is approximately 0.167 - Molality of the solution is approximately 11.11 mol/kg This matches option (c): (0.167, 11.11).

Key Concepts

Understanding Mole Fraction

In chemical calculations, mole fraction is a way to express the concentration of a component in a mixture. It's the ratio of the moles of a specific substance to the total moles of all substances present. This is particularly useful because it remains constant regardless of temperature and pressure changes, which affect volumes and concentrations expressed in molarity or molality. To calculate the mole fraction, use the formula:

• Mole fraction of a component = \( \frac{\text{Moles of the component}}{\text{Total moles in the solution}} \)

In our example, we calculated the moles of NaOH and H₂O. The mole fraction of NaOH was found by dividing the moles of NaOH, 0.2, by the total moles of both NaOH and H₂O, 1.2. This calculation provides the mole fraction of NaOH, which is approximately 0.167.This simple ratio shows how much of a specific substance is present in a sample relative to the whole. Knowing this can help in predicting how the components will interact.

Molality and Its Importance

Molality is another unit of concentration that describes the number of moles of solute present per kilogram of solvent. Unlike molarity, molality does not change with temperature since it involves mass rather than volume. This makes molality especially useful in scenarios where the temperature may fluctuate.Calculating molality involves two key components:

• The moles of the solute (in this case, NaOH)
• The mass of the solvent (here, water) in kilograms

For our solution, we calculated the molality as follows:The mass of the water is converted to kilograms: \( 18 \text{ g} = 0.018 \text{ kg} \). Then by dividing the moles of NaOH, 0.2, by the mass of the solvent in kilograms, we obtained a molality of approximately 11.11 mol/kg.Understanding molality is crucial for tasks like boiling point elevation or freezing point depression, where molality directly impacts how substances dissolve and mix.

Defining Solution Concentration

Solution concentration refers to the abundance of a solute distributed within a solvent in a given solution. Concentration can be expressed in various forms, each suited to different types of reactions and conditions:

• Mole Fraction: Useful for reactions involving gaseous substances or when dealing with solvents with a wide range of densities.
• Molality: Ideal for processes affected by temperature and pressure because it's based on mass, not volume.
• Molarity: Commonly used in laboratories for reactions taking place in aqueous solutions at constant temperature.

The choice between these depends on the specific requirements of the experiment or process. Understanding the different ways to express concentration allows chemists and researchers to accurately describe and predict the behavior of solutions under various conditions.