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 solution.

Step 1: Understanding Molarity

Molarity is a measure of the concentration of a solute in a solution. It is expressed as the number of moles of solute (in this case, KCl) per liter of solution. The unit is moles per liter (M).

Step 2: Analyzing the Given Information

We are given a 3 M KCl solution, which means there are 3 moles of KCl in every 1 liter (1000 mL) of the solution.

Step 3: Calculating the Number of Moles

Since the solution is 3 M, and the volume of the solution is 1000 mL (which is equivalent to 1 Liter), the number of moles of KCl is calculated by multiplying the molarity by the volume (in liters).\[\text{Number of moles} = \text{Molarity} \times \text{Volume in Liters} = 3 \text{ M} \times 1 \text{ L} = 3 \text{ moles}.\]

Step 4: Verifying the Solution

We confirm that a 3 M solution contains 3 moles per Liter of solution. Since our solution is exactly 1 Liter, indeed it contains 3 moles of KCl.

Key Concepts

Understanding Moles

Moles are a fundamental concept in chemistry, providing a bridge between the atomic world and the macro world that we can observe. A mole is a unit that measures the amount of substance, allowing chemists to count particles like atoms, ions, or molecules by weighing them.

The definition of a mole is based on Avogadro's number, which is approximately \(6.022 \times 10^{23}\) particles per mole. Imagine moles as a dozen; just as a dozen always means twelve items regardless of the item, a mole always equates to \(6.022 \times 10^{23}\) particles of any substance.

When dealing with compounds like KCl (Potassium Chloride), these particles are generally molecules. Thus, to find the number of moles, one must understand how much of a substance you have by comparing it to its molar mass, which is the mass of one mole of a given substance (in grams).

• You gather the masses of individual elements in the compound, as found on the periodic table.
• Add them to find the molar mass of the substance.
• Use weight of your sample and divide by the molar mass to determine how many moles you have.

Solution Concentration and Molarity

Solution concentration refers to how much solute (in this case, KCl) is present in a solution compared to the volume of the entire solution. The most common measure is molarity.

Molarity (M) is defined as the number of moles of solute per liter of solution. It is expressed in units of moles per liter (mol/L). This measurement is essential for reactions occurring in solutions, as it tells you exactly how much of a substance is present in a given volume, which is crucial for stoichiometry calculations in chemistry.

• "3 M" indicates 3 moles of solute in every liter of solution.
• Molarity is particularly useful in preparing solutions and making dilutions.
• The higher the molarity, the more concentrated the solution is.

Understanding molarity helps chemists prepare solutions with precise concentrations, critical in research, medicine, and industry.

Volume Conversion in Solutions

Volume conversion is an essential skill when calculating solution concentration. In chemistry, you often need to convert between units like milliliters (mL) and liters (L), since molarity refers to moles per liter. Understanding how to convert volumes is crucial for accurate calculations.

There are 1000 milliliters in a liter. Converting between these units involves simple multiplication or division.

• To convert mL to L, divide by 1000.
• To convert L to mL, multiply by 1000.

For example, if you have 1000 mL of solution, you convert this to liters by dividing by 1000, giving you 1 L.

This conversion is not only a math exercise; it is vital in practical lab scenarios where precision is critical. Understanding both the concept and the simple calculations helps ensure you measure and mix solutions accurately.