Problem 17 - A Complete Resource Book in Chemistry for JEE Main

Question

The number of moles of sodium hydroxide present in \(2.5 \mathrm{~L}\) and \(0.5 \mathrm{M}\) aqueous solution will be (a) \(1.25\) (b) \(0.5\) (c) \(12.5\) (d) 5

Step-by-Step Solution

Answer

(a) 1.25

Step 1: Identify the Known Variables

We know that the concentration of the solution, also known as molarity (M), is given as \(0.5\, \text{M}\), and the volume of the solution is \(2.5\, \text{L}\).

Step 2: Recall the Formula for Moles

To find the number of moles, we can use the formula: \(\text{Moles} = \text{Concentration (M)} \times \text{Volume (L)}\).

Step 3: Substitute Values into the Formula

Substitute the known values into the formula: \(\text{Moles} = 0.5\, \text{M} \times 2.5\, \text{L}\).

Step 4: Calculate the Number of Moles

Perform the multiplication: \(0.5 \times 2.5 = 1.25\). Therefore, the number of moles of sodium hydroxide in the solution is \(1.25\).

Step 5: Verify the Answer Choice

The calculated number of moles, \(1.25\), matches answer choice (a).

Key Concepts

Molarity

Molarity is a way to express the concentration of a solution. It is defined as the number of moles of solute divided by the volume of the solution in liters. This concentration is expressed in moles per liter (mol/L) and often denoted with the letter \( M \). Knowing the molarity of a solution helps chemists understand how much of a substance is present in a given volume of solution.
To find molarity, use the formula:

• \( M = \frac{n}{V} \)

where \( n \) is the number of moles of solute, and \( V \) is the volume of the solution in liters.
This formula simplifies calculations and helps in predicting how different solutions will react with each other.

Volume of solution

Volume of solution is a critical part of calculating solution concentrations and reacting quantities. It tells us how much space a liquid solution occupies, usually measured in liters (L).
In our context, when we know the volume of the solution, we can determine how concentrated the solute is, provided we know the molarity.
Understanding volume is also vital when diluting solutions or when combining different solutions for chemical reactions. For precise calculations in experiments, knowing the exact volume is crucial.

Number of moles

The number of moles refers to a measure of how much of a chemical substance is present. Moles provide a bridge between the atomic scale and the scale we can work with in the lab. One mole is equivalent to Avogadro's number, which is approximately \(6.022 \times 10^{23}\) particles (atoms, molecules, ions, etc.).
To calculate the number of moles in a solution, you can use the formula
\[ \text{Moles} = \text{Molarity} \times \text{Volume} \]
In our example exercise, by multiplying the molarity (0.5 M) with the volume (2.5 L), we determined that there were 1.25 moles of sodium hydroxide in the solution. This concept is essential because it allows scientists to quantify substances and predict the outcome of chemical reactions.

Aqueous solution concentration

Aqueous solution concentration refers to how much solute is dissolved in a solvent, with water being the solvent. Concentration can be expressed in different units, but molarity is one of the most common. It indicates the strength or weakness of a solution.
In practical terms, when dealing with aqueous solutions, understanding concentration helps us determine:

• How much solute is needed for a desired reaction.
• The dilutions required to achieve a specific concentration.
• The potential reactivity and interactions of a solution.

This knowledge is specifically useful in experiments involving chemical reactivity and where precise calculations are crucial for success and safety.