Problem 25 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

\(6.023 \times 10^{22}\) molecules are present in \(10 \mathrm{~g}\) of a substance ' \(x^{\prime}\). The molarity of a solution containing \(5 \mathrm{~g}\) of substance ' \(x\) ' in \(2 \mathrm{~L}\) solution is \(\times 10^{-3}\) [Main Sep. 03, 2020 [II)]

Step-by-Step Solution

Answer

Molarity is \(25 \times 10^{-3}\) mol/L.

Step 1: Understand the Problem

We are given the number of molecules in 10g of a substance and need to find the molarity of a solution with 5g of that substance in 2L of solution. To find the molarity, we first need to determine the molar mass of the substance using Avogadro's number.

Step 2: Use Avogadro’s Number to Find Moles in 10g

We know that Avogadro's number is approximately \(6.022 imes 10^{23}\) molecules/mol. The problem states there are \(6.023 imes 10^{22}\) molecules in 10g. Thus, the number of moles, \(n\), in 10g is calculated as follows:\[n = \frac{6.023 \times 10^{22} \text{ molecules}}{6.022 \times 10^{23} \text{ molecules/mol}} = 0.1 \text{ mol}\]

Step 3: Calculate Molar Mass of Substance

Given that 10g of the substance corresponds to 0.1 moles, the molar mass, \(M\), can be calculated with the formula:\[M = \frac{\text{mass}}{\text{moles}} = \frac{10 \text{ g}}{0.1 \text{ mol}} = 100 \text{ g/mol}\]

Step 4: Find Moles in 5g of Substance

Using the molar mass found in Step 3, calculate the moles in 5g of the substance:\[\text{moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{5 \text{ g}}{100 \text{ g/mol}} = 0.05 \text{ mol}\]

Step 5: Calculate Molarity of the Solution

Molarity \(M\) is defined as moles of solute per liter of solution. Using the moles calculated in Step 4, the molarity is:\[M = \frac{0.05 \text{ mol}}{2 \text{ L}} = 0.025 \text{ mol/L}\]

Step 6: Final Step: Adjust Molarity to \(\times 10^{-3}\) format

The molarity calculated is 0.025 mol/L. Converting this to the hinted format, we have:\[0.025 \text{ mol/L} = 25 \times 10^{-3} \text{ mol/L}\]

Key Concepts

Avogadro's Number

Avogadro's number is a fundamental constant pivotal in chemistry, especially when dealing with atomic-scale entities. It represents the number of constituent particles, typically atoms or molecules, in one mole of a given substance. The value of Avogadro's number is approximately \(6.022 \times 10^{23}\) particles/mol.

This concept allows chemists to convert between the number of particles and the amount of substance in moles. For example, if you have a certain amount of molecules, you can reliably calculate how many moles those molecules constitute by dividing the number of molecules by Avogadro's number.

• Essential for understanding the scale of chemical reactions and quantities.
• Key for calculating and interpreting molar masses.
• Helps in converting between masses and moles.

Avogadro's number effectively bridges the microscopic world of atoms and molecules with the macroscopic amounts used in laboratory settings, making it an indispensable tool for both theoretical and applied chemistry.

Molar Mass

Molar mass is a term that refers to the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is computed by summing the atomic masses of all the elements present in a compound, as found in the periodic table. By understanding molar mass, one is able to convert between the mass of a sample and the number of moles it contains, which is vital for stoichiometric calculations.

In practice, calculating molar mass involves a simple ratio:\[M = \frac{\text{mass of substance (g)}}{\text{amount of substance (mol)}}\]
For instance, if a substance 'x' has a molar mass of 100 g/mol, this means 100 grams of this substance contains exactly one mole of entities, such as molecules.

• Used to convert grams to moles and vice versa.
• Important for determining concentrations in solutions.
• Fundamental for calculating and predicting chemical reaction yields.

Understanding the molar mass helps you to dissect and predict how molecules will behave under different conditions, especially in chemical reactions.

Mole Concept

The mole concept is a cornerstone of stoichiometry in chemistry. It acts as a standard bridge between the mass of a substance and the quantity of particles it contains. It is defined such that one mole contains exactly \(6.022 \times 10^{23}\) particles, as per Avogadro's number.

The mole concept helps chemists express amounts of a chemical substance in a way that is easy to reference and work with. This concept is crucial for various reasons, including:

• Providing a direct way to convert from microscopic to macroscopic scales.
• Facilitating the measurement and comparison of chemical substances.
• Essential for quantitative analysis and chemical equation balancing.

In practice, when dealing with weight, volume, and particles of chemicals, the mole concept serves as the quantitative means to connect these different measurements. It allows for the accurate determination of the amount of a substance needed for reactions, known as stoichiometric calculations, with solutions and in solid states.