Problem 161 - A Complete Resource Book in Chemistry for JEE Main

Question

Find the number of moles of \(\mathrm{KCl}\) in \(1000 \mathrm{~mL}\) of \(3 \mathrm{M}\) solution

Step-by-Step Solution

Answer

There are 3 moles of KCl in the 1000 mL solution.

Step 1: Understand Molarity Concept

Molarity ( M ) is a way to express the concentration of a solution. It is defined as the number of moles of a solute (in this case, KCl ) per liter of solution. The unit is moles per liter (mol/L).

Step 2: Convert Volume to Liters

The problem provides the volume of the solution in milliliters (1000 ext{ mL}). To use molarity, we need this volume in liters, since molarity is defined as moles per liter. We convert milliliters to liters by dividing by 1000. \[ \text{Volume in liters} = \frac{1000 ext{ mL}}{1000} = 1 ext{ L} \]

Step 3: Use Molarity to Find Moles

With the volume 1 ext{ L} and given molarity 3 ext{ M}, we use the formula: \[ \text{Moles of KCl} = \text{Molarity} \times \text{Volume in liters} \] Substituting the values, we get: \[ \text{Moles of KCl} = 3 ext{ M} \times 1 ext{ L} = 3 ext{ moles} \]

Key Concepts

Concentration of Solution

When discussing the concentration of a solution, we are talking about how much solute is present in a given quantity of solvent. In this context, molarity is a common way to express concentration. It measures how many moles of solute are dissolved in one liter of the solution. Molarity, represented as \("M"\), is calculated with the formula: \[M = \frac{\text{moles of solute}}{\text{liters of solution}}. \]
Using molarity makes it easy to understand and compare the concentration of different solutions. For example, a 3 M solution means there are 3 moles of a solute, like \(\text{KCl}\), dissolved in each liter of the solution.
A higher molarity indicates a more concentrated solution, which is why molarity is a valuable measure in chemistry.

Moles of Solute

The concept of a mole is central in chemistry. A mole is a unit that measures the amount of substance, and it contains exactly \(6.022 \times 10^{23}\) entities. These entities can be atoms, molecules, ions, etc., depending on the context.
When dealing with solutions, the number of moles of solute helps us understand precisely how much of a substance is present.
For the problem at hand, determining the number of moles is straightforward with the molarity formula:

• First, ensure the volume is in liters, as molarity uses liters as its unit of volume.
• Then multiply the molarity (moles/liter) by the volume in liters.

This gives us the number of moles present in the solution, like the 3 moles of \(\text{KCl}\) in our problem.

Volume Conversion

Often, problems involving solutions provide volume in milliliters, but molarity requires this in liters. Thus, converting volume into liters is a necessary step.
Here's how to perform such a conversion:

• Divide the volume in milliliters by 1000, since there are 1000 milliliters in one liter.
• This conversion simplifies calculations because it aligns with the molarity unit of moles per liter.

In the example given in the original problem, the volume provided was 1000 milliliters. By dividing by 1000, the volume becomes 1 liter, which partners perfectly with the molarity to find the number of moles.