Problem 22 - A Complete Resource Book in Chemistry for JEE Main

Question

A boy drinks \(500 \mathrm{~mL}\) of \(9 \%\) glucose solution. The number of glucose molecules he has consumed are [mol. wt of glucose \(=180]\) (a) \(0.5 \times 10^{23}\) (b) \(1.0 \times 10^{23}\) (c) \(1.5 \times 10^{23}\) (d) \(2.0 \times 10^{23}\)

Step-by-Step Solution

Answer

The boy consumed approximately \(1.5 \times 10^{23}\) glucose molecules, which is option (c).

Step 1: Calculate the Mass of Glucose

First, determine the mass of glucose in the solution. The solution is 500 mL (which is equivalent to 500 g of water since the density is approximately 1 g/mL for dilute aqueous solutions). The concentration is given as 9%, meaning there are 9 grams of glucose in 100 grams of solution. Therefore:\[ \text{Mass of glucose} = \left(\frac{9}{100}\right) \times 500 = 45 \text{ grams} \]

Step 2: Calculate Moles of Glucose

Now, we need to calculate the number of moles of glucose using the molecular weight of glucose (180 g/mol). Apply the formula for moles:\[ \text{Moles of glucose} = \frac{\text{mass}}{\text{molecular weight}} = \frac{45}{180} = 0.25 \text{ moles} \]

Step 3: Calculate Number of Molecules

To find the number of glucose molecules, use Avogadro's number, which is approximately \(6.022 \times 10^{23}\) molecules/mol. Multiply it by the total moles calculated:\[ \text{Number of glucose molecules} = 0.25 \times 6.022 \times 10^{23} \approx 1.5055 \times 10^{23} \]Rounding to the options given, the answer is approximately \(1.5 \times 10^{23}\).

Key Concepts

Understanding Glucose Solution Concentration

When you hear the term "glucose solution concentration," it refers to the amount of glucose present in a specific volume of solution. In this exercise, the boy drinks a solution where the concentration is 9%. This means that, for every 100 grams of the solution, there are 9 grams of glucose. This is often referred to as a weight/weight percentage since it compares the weight of the glucose to the weight of the solution. In a more visual sense, if you had a container filled with 100 marbles, 9 of those would represent the glucose, while the remaining 91 would represent the water and other components that make up the solution.

• The solution amount consumed is 500 mL. For most dilute aqueous solutions, this volume is comparable to 500 grams due to the density of water being approximately 1 gram/mL.
• By applying the given concentration (9%), you multiply 0.09 (which is 9%) by 500 grams, leading to 45 grams of glucose in the solution consumed by the boy.

Understanding this concept is crucial, as it helps in accurately determining the amount of a particular substance in a mixture, which is a fundamental step in many scientific calculations.

The Art of Molecular Weight Calculation

The calculation of molecular weight is an essential step in chemistry as it helps convert between mass and moles, which are a count of molecules. In this context, molecular weight is the mass of one mole of a substance, measured in grams per mole (g/mol). For glucose, as given, the molecular weight is 180 g/mol.Calculating moles involves converting the measured mass of glucose into the number of moles. This becomes highly useful when dealing with chemical reactions and solutions. Here's how you do it for glucose:

• First, you need the mass of glucose, which we previously calculated as 45 grams.
• The formula for calculating moles is: \[ \text{Moles of glucose} = \frac{\text{mass of glucose}}{\text{molecular weight of glucose}} \]
• Substituting in our numbers gives: \[ \text{Moles of glucose} = \frac{45}{180} = 0.25 \]

This clearly demonstrates how molecular weight serves as a bridge between mass and the quantity of molecules, facilitating our understanding and calculation of substances at a molecular level.

Applying Avogadro's Number

Avogadro's number is a cornerstone of chemistry, enabling us to translate between the macroscopic world of grams and the microscopic world of molecules. It is defined as approximately \(6.022 \times 10^{23}\), representing the number of molecules in one mole of any substance. Here, we use it to determine how many glucose molecules are in the 0.25 moles we calculated earlier.The calculation is straightforward:

• The total number of molecules is calculated by multiplying the number of moles by Avogadro's number:
• \[ \text{Number of glucose molecules} = 0.25 \times 6.022 \times 10^{23} \]
• This yields approximately \(1.5055 \times 10^{23}\) glucose molecules.

By rounding to align with the given answer choices, we appropriately conclude that the boy consumed about \(1.5 \times 10^{23}\) glucose molecules. Avogadro's number acts as a bridge from the scale of moles to the scale of individual molecules, affirming its fundamental role in chemical calculations.