Question

How many moles are present in \(2.5\) litre of \(0.2\) \(\mathrm{MH}_{2} \mathrm{SO}_{4} ?\) (a) \(0.25\) (b) \(0.5\) (c) \(0.75\) (d) \(0.2\)

Short answer

There are 0.5 moles of \( H_2SO_4 \) present in the solution; the correct answer is (b).

Step-by-step solution

Understanding Molarity

Molarity (M) is defined as the number of moles of solute per litre of solution. Mathematically, it is represented as:\[ M = \frac{n}{V} \]where \( n \) is the number of moles and \( V \) is the volume of the solution in litres.

Calculating Moles Using Molarity Formula

Rearrange the formula to find the number of moles: \[ n = M \times V \] Substitute the given values: Molarity \( M = 0.2 \) M (mol/L) and Volume \( V = 2.5 \) L. So: \[ n = 0.2 \times 2.5 \]

Performing the Calculation

Calculate the product: \[ n = 0.2 \times 2.5 = 0.5 \]

Choosing the Correct Option

Based on the calculation result \( n = 0.5 \), the correct answer is (b) \(0.5\).

Key concepts

Calculating Moles

Before diving into any calculations, it's important to understand what a 'mole' represents in chemistry. A mole is a fundamental unit in chemistry that provides a bridge between the atomic scale and the real-world amounts that we work with in the laboratory. It is defined as exactly 6.02214076 × 10²³ particles, atoms, or molecules of a substance. This number is called Avogadro's number.
When asked to calculate the number of moles in a solution, we use the concept of molarity, which is the number of moles of a solute (in this case, a chemical compound) dissolved in one litre of solution. The formula to find the number of moles using molarity is:

• \( n = M \times V \)

where \( n \) is the number of moles, \( M \) is the molarity, and \( V \) is the volume in litres. By rearranging this formula, we can easily find the quantity of the solute in moles based on the solution's volume and concentration.

Understanding Solution Concentration

The term 'solution concentration' refers to the amount of solute that is dissolved in a given quantity of solvent or solution. The concentration of a solution can be expressed in various ways, but molarity is one of the most common methods.
Molarity (M) expresses the concentration as the number of moles of solute per litre of solution, making it a straightforward method to link the concept of moles to a real-world application. It is particularly useful when preparing chemical solutions as it helps chemists specify the number of moles of solute in each litre of the prepared solution.
To determine molarity, the formula is:

• \( M = \frac{n}{V} \)

where \( n \) is the number of moles of solute, and \( V \) is the volume of the solution in litres. This formula is essential for calculating the precise amount of solute needed to achieve a particular solution concentration.

Performing Molar Calculations

Molar calculations allow chemists to translate between the volume of a solution and the actual amount of substance (in moles) dissolved in it. These calculations are critical for ensuring accurate chemical reactions and formulations.
To perform molar calculations effectively:

• Identify the molarity and volume of the solution.
• Use the formula to find moles: \( n = M \times V \).
• Substitute the given values to calculate the number of moles.

For example, in the exercise provided, we are given 2.5 litres of a 0.2 M \( \text{H}_2\text{SO}_4 \) solution. By applying the molarity formula, we find that the number of moles (\( n \)) is 0.5. This straightforward approach enables chemists to accurately determine the quantities needed for reactions and other operations.