Problem 60 - A Complete Resource Book in Chemistry for JEE Main

Question

When \(18 \mathrm{~g}\) of glucose is dissolved in \(180 \mathrm{~g}\) of water then the mole fraction of glucose is (a) \(0.0099\) (b) \(0.0999\) (c) \(0.9999\) (d) \(0.9111\)

Step-by-Step Solution

Answer

The mole fraction of glucose is approximately 0.0099 (option a).

Step 1: Calculate Moles of Glucose

First, calculate the number of moles of glucose. The molar mass of glucose (C₆H₁₂O₆) is approximately 180 g/mol. Use the formula:\[ ext{Moles of glucose} = \frac{ ext{mass}}{ ext{molar mass}} = \frac{18 ext{ g}}{180 ext{ g/mol}} = 0.1 ext{ moles}\]

Step 2: Calculate Moles of Water

Determine the moles of water. The molar mass of water (H₂O) is approximately 18 g/mol. Use:\[ ext{Moles of water} = \frac{180 ext{ g}}{18 ext{ g/mol}} = 10 ext{ moles}\]

Step 3: Calculate Total Moles in Solution

Find the total number of moles in the solution by adding the moles of glucose and moles of water:\[ ext{Total moles} = 0.1 ext{ moles of glucose} + 10 ext{ moles of water} = 10.1 ext{ moles}\]

Step 4: Calculate Mole Fraction of Glucose

The mole fraction of glucose is calculated using the formula:\[ ext{Mole fraction of glucose} = \frac{ ext{Moles of glucose}}{ ext{Total moles in solution}} = \frac{0.1}{10.1} \]Calculate:\[\frac{0.1}{10.1} \approx 0.0099\]

Key Concepts

Moles of Glucose

When dealing with chemical solutions, determining the number of moles of a solute, like glucose, is a key step in various calculations. The mole is a unit of measurement for the amount of substance, and it is based on the number of atoms in 12 grams of the carbon-12 isotope. To calculate the moles of glucose in a given mass, we use the formula:

• Moles = \( \frac{\text{mass}}{\text{molar mass}} \)

In our problem, glucose has a molar mass of approximately 180 g/mol. If you have 18 grams of glucose, you calculate the moles as follows:

• Moles of glucose = \( \frac{18 \text{ g}}{180 \text{ g/mol}} = 0.1 \text{ moles} \)

This calculation helps us understand how many molecules of glucose are present in the solution.

Moles of Water

The process for calculating the moles of water is similar to that of glucose. Water is a common solvent, and knowing its molarity helps in various chemical processes. Water has a molar mass of about 18 g/mol, which is much lighter compared to glucose. Given 180 grams of water, you can find the moles by following these steps:

• Moles of water = \( \frac{180 \text{ g}}{18 \text{ g/mol}} = 10 \text{ moles} \)

Understanding the number of moles of water is crucial, especially when it serves as the solvent in which other substances are dissolved. This helps us in further calculations like finding the mole fraction.

Molar Mass Calculation

Molar mass is fundamental to converting between mass and moles, which is essential in stoichiometry and solution chemistry. The molar mass is the weight of one mole of a given substance and is calculated by summing the atomic masses of the elements in a molecule.

• Glucose (C₆H₁₂O₆) has a molar mass: \(6 \times 12 + 12 \times 1 + 6 \times 16 = 180 \text{ g/mol} \)
• Water (H₂O) has a molar mass: \(2 \times 1 + 16 = 18 \text{ g/mol} \)

These calculations are vital for determining the amounts of substances in reactions and solutions. The concept of molar mass allows chemists to use a manageable number of molecules when performing experiments or chemical reactions.