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

Question

Find the number of moles of 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: Understand Molarity

Molarity (M) is the number of moles of solute per liter of solution. So, a 3 M solution has 3 moles of solute in every 1 liter (1000 mL) of solution.

Step 2: Identify Given Information

We are given a solution with a volume of \(1000 \text{ mL}\) and a molarity of \(3 \text{ M}\). This means there are \(3\) moles of KCl in every \(1000 \text{ mL}\) of solution.

Step 3: Apply Molarity Formula

Since the molarity is given as 3 M, it implies that 3 moles of KCl are present in \(1000 \text{ mL}\) (which is equal to \(1 \text{ L}\)).

Step 4: Calculate Moles of KCl

Using the given molarity of \(3 M\), we calculate the moles of KCl in \(1000 \text{ mL}\) directly. Since \(1000 \text{ mL} = 1 \text{ L}\), the moles of KCl is simply the molarity multiplied by the volume in liters:\[ \text{Moles of KCl} = 3 \text{ M} \times 1 \text{ L} = 3 \text{ moles} \]

Key Concepts

Moles of Solute

The term "moles of solute" refers to the amount of a substance in terms of a unit called "mole." The mole is a standard unit in chemistry that measures a specific number of molecules, atoms, or ions, which is Avogadro's number: approximately \(6.022 \times 10^{23}\). In the context of solutions, the "solute" is the component that is dissolved, and it is quantified in moles to specify its amount.To find the moles of a solute, you often use the formula:

• Moles of solute = Molarity (M) × Volume (in liters)

This is derived from the definition of molarity, which relates to how many moles of a solute are present in a known volume of solution. Let's imagine you have a 3 M KCl solution, and you need to find out how many moles of KCl are in \(1000\text{ mL}\). Since the molarity represents moles per liter, simply multiply the molarity by the volume in liters (which in this case is \(1 \text{ L}\) because \(1000 \text{ mL} = 1 \text{ L}\)). Thus, you find there are 3 moles of KCl in this solution.

Solution Concentration

Solution concentration is a measure of how much solute is dissolved in a given amount of solvent or solution. One of the most common expressions of concentration is molarity (M), which is defined as the number of moles of solute per liter of solution. Molarity is calculated using:

• Molarity (M) = Moles of Solute / Liters of Solution

In a 3 M solution of KCl, the concentration indicates there are 3 moles of KCl in every liter of the solution. This gives a clear indication of how concentrated the solution is. More moles equate to a higher concentration, meaning more solute is present in the same volume of solvent. Understanding solution concentration is crucial for preparing solutions in laboratories or adjusting the strength and potency of chemical reactions and mixtures.

Volume Conversion to Liters

Volume conversion to liters is an essential step when working with solutions. Given the frequent use of milliliters (mL) in chemical solutions and molarity calculations, it's important to convert these volumes into liters, as molarity is defined in terms of liters. The conversion factor is simple:

• 1 liter (L) = 1000 milliliters (mL)
• Therefore, 1000 mL = 1 L

Whenever you're given volume in milliliters, convert it to liters by dividing by 1000. For example, when calculating the number of moles in a 3 M KCl solution with a volume of \(1000\text{ mL}\), converting \(1000\text{ mL}\) to liters gives \(1\text{ L}\). This conversion is crucial as it ensures that your subsequent calculations using molarity are accurate and valid.