Problem 9 - A Complete Resource Book in Chemistry for JEE Main

Question

The number of moles of \(\mathrm{KCl}\) in \(1000 \mathrm{~mL}\) of 3 molar solution is (a) 2 (b) 3 (c) 4 (d) 6

Step-by-Step Solution

Answer

The number of moles of KCl is 3.

Step 1: Understand the Molarity Formula

The molarity (M) of a solution is defined as the number of moles of the solute per liter of solution. It is given by the formula: \\[\text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}}\] \We need to find the number of moles of KCl in a given volume and molarity.

Step 2: Convert Volume from mL to L

Since Molarity is expressed in terms of liters, we need to convert the given volume from milliliters to liters. There are 1000 milliliters in 1 liter, so: \\[1000 \text{ mL} = 1 \text{ L}\] \Now we know the volume of the solution is 1 liter.

Step 3: Calculate Moles Using Molarity

Using the formula for molarity, we rearrange it to solve for moles of KCl: \\[\text{moles of KCl} = \text{Molarity} \times \text{Volume in L}\] \Substitute the given values: \\[\text{moles of KCl} = 3 \text{ mol} \cdot \text{L}^{-1} \times 1 \text{ L}\] \This calculation gives us 3 moles of KCl.

Key Concepts

Mole Concept

The mole concept is a fundamental aspect of chemistry that allows us to quantify substances. A mole is a unit that measures the amount of a substance using Avogadro's number, which is approximately \(6.022 imes 10^{23}\) entities (such as atoms or molecules). This concept makes it easier to handle the vast number of atoms and molecules involved in chemical reactions.
To put it simply, one mole of any substance contains the same number of entities as one mole of another substance. This standardization helps chemists convert between the mass of a substance and the number of its fundamental particles. For example, 1 mole of KCl will contain the same number of molecules as 1 mole of H₂O.
Understanding the mole concept is crucial for interpreting and predicting the outcomes of chemical reactions, as well as for calculations involving molarity and solution concentration.

Solution Concentration

Solution concentration refers to the amount of solute present in a given volume of solvent. It helps us understand how concentrated or dilute a solution is.
There are several ways to express concentration, and molarity is one of the most common methods used. Molarity (M) is defined as the number of moles of solute present in one liter of solution.

• Molarity (M) = \(\frac{\text{moles of solute}}{\text{liters of solution}}\)

In our original example, the solution is described as "3 molar," meaning there are 3 moles of KCl in every liter of solution. By knowing the molarity, we can easily determine the number of moles in a specific volume, as demonstrated in the step-by-step solution.
This understanding of solution concentration is vital for preparing solutions with desired properties and for conducting quantitative chemical experiments.

Chemical Calculations

Chemical calculations involve various mathematical techniques to analyze and predict the results of chemical reactions. They are essential for determining the quantities of reactants and products in reactions as well as for understanding solution properties.
In the context of molarity and solution concentration, chemical calculations allow us to compute the number of moles of a solute in a given volume of a solution. This is crucial when preparing solutions or mixing them for reactions. For instance, by using the formula for molarity, \(\text{moles} = \text{Molarity} \times \text{Volume}\), we can calculate the number of moles of solute in a solution when given its volume and molarity.

• Example: If a solution has a molarity of 3 mol/L, and the volume is 1 L, the number of moles is computed as \(3 \text{ mol/L} \times 1 \text{ L} = 3 \text{ moles}\).

Such calculations are not only important for laboratory work but also for industrial processes, where they ensure the correct ingredient ratios, affecting the quality and efficiency of production.