Problem 7 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The mole fraction of a solvent in aqueous solution of a solute is \(0.8\). The molality (in \(\mathrm{mol} \mathrm{kg}^{-1}\) ) of the aqueous solution is : (a) \(13.88 \times 10^{-2}\) (b) \(13.88 \times 10^{-1}\) (c) \(13.88\) (d) \(13.88 \times 10^{-3}\)

Step-by-Step Solution

Answer

The correct answer is (c) 13.88.

Step 1: Understand the Problem

We are given the mole fraction of the solvent in an aqueous solution, which is 0.8. Our task is to find the molality of the solution. Molality is calculated as the number of moles of solute per kilogram of solvent.

Step 2: Understand Mole Fraction

The given mole fraction (0.8) is of the solvent, which means that 80% of the total moles in the solution are from the solvent. If the total moles of solute and solvent combined are 1, then the moles of solvent are 0.8 and the moles of solute are 0.2.

Step 3: Determine Molality Formula

Molality (m) is defined as \( m = \frac{n_{solute}}{m_{solvent}} \), where \( n_{solute} \) is the moles of solute and \( m_{solvent} \) is the mass of the solvent in kilograms. We need to calculate these values based on the mole fraction.

Step 4: Calculate Moles of Solute and Solvent

We consider 1 mole total for simplicity. The moles of solvent are 0.8 and the moles of solute are 0.2 since mole fraction of solvent is 0.8. Solvent is water and its molar mass is 18 g/mol.

Step 5: Calculate Mass of Solvent in kg

Since we have 0.8 moles of water as the solvent, and the molar mass of water is 18 g/mol, the mass of water is \( 0.8 \times 18 = 14.4 \) grams or \( 0.0144 \) kg.

Step 6: Calculate Molality

Use the formula for molality: \( m = \frac{n_{solute}}{m_{solvent}} \). Substitute \( n_{solute} = 0.2 \) and \( m_{solvent} = 0.0144 \).\[ m = \frac{0.2}{0.0144} = 13.88 \] mol/kg.

Key Concepts

Mole Fraction

The concept of mole fraction is crucial in chemistry. It describes the ratio of moles of a component to the total moles in a mixture. In an aqueous solution where the mole fraction of the solvent is given as 0.8, this means that 80% of the total moles are attributable to the solvent. Consequently, the remaining 20% belongs to the solute.

When solving problems, it's often convenient to assume the total number of moles is 1. This simplification allows us to directly interpret the mole fraction values as moles: 0.8 moles of solvent and 0.2 moles of solute. This gives a clear understanding of the distribution of components in an aqueous solution.

Aqueous Solution

An aqueous solution is a type of solution where water is the solvent. It’s a common medium for many chemical reactions because of water’s excellent solvent properties. In the given exercise, water is the solvent in the solution.

The property of being an aqueous solution is primarily because of water's polar nature, which allows it to dissolve various substances effectively.

• Water’s ability to attract ions and polar molecules makes it an exceptional solvent.
• This property plays a crucial role in determining the properties and behavior of the solution, such as its molality.

Understanding the characteristics of an aqueous solution helps in anticipating how the solute dissolves and distributes within the water, a concept that is essential when calculating quantities like molality.

Moles of Solute

Knowing the moles of solute in a solution is a fundamental part of calculating concentrations like molality. Moles measure the amount of substance, based on Avogadro’s number, which defines one mole of anything as having the same number of entities as there are atoms in 12 grams of carbon-12.

In the problem presented, 0.2 moles of solute are present since the mole fraction indicates that 80% is solvent and thus 20% is solute. The actual calculation of molality involves using this number in relation to the kilogram mass of the solvent, which is derived from the known properties of water as the solvent. This establishes the concentration of the solute in relation to the solvent, ensuring solutions are accurately described in terms of their chemical makeup.