Question

A 5 molar solution of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is diluted from 1 litre to a volume of 10 litres, the normality of the solution will be (a) \(0.5 \mathrm{~N}\) (b) \(1 \mathrm{~N}\) (c) \(2.5 \mathrm{~N}\) (d) \(5 \mathrm{~N}\)

Short answer

The normality of the solution is 1 N (option b).

Step-by-step solution

Understand Normality and Molarity

Normality is a measure of concentration equivalent to molarity multiplied by the number of equivalents. For sulfuric acid (\(\mathrm{H}_{2} \mathrm{SO}_{4}\)), the number of equivalents is 2 because it can donate two protons (\(\mathrm{H}^+\)). Thus, normality is twice the molarity for sulfuric acid.

Calculate Initial Normality

Given a 5 M solution of \(\mathrm{H}_{2} \mathrm{SO}_{4}\), the normality \(N\) before dilution is twice the molarity. \[N = 2 \times M = 2 \times 5 = 10 \mathrm{~N}\]

Apply Dilution Formula

When a solution is diluted, the amount of solute remains the same. Use the dilution formula: \[C_1V_1 = C_2V_2\]where \(C_1\) and \(V_1\) are the initial concentration and volume, and \(C_2\) and \(V_2\) are the final concentration and volume.

Insert Known Values into Dilution Formula

Substitute the known values into the formula. \[10 \mathrm{~N} \times 1 \mathrm{~L} = C_2 \times 10 \mathrm{~L}\]Solve for \(C_2\), the final concentration after dilution.

Solve for Final Normality

Divide both sides by \(10 \mathrm{~L}\) to solve for \(C_2\):\[C_2 = \frac{10 \mathrm{~N} \times 1 \mathrm{~L}}{10 \mathrm{~L}} = 1 \mathrm{~N}\]

Select the Correct Answer

The final normality is \(1 \mathrm{~N}\). Thus, the correct answer is option (b) \(1 \mathrm{~N}\).

Key concepts

Molarity

Molarity is one of the most common ways to express concentration in chemistry. It's defined as the number of moles of solute per liter of solution. Molarity is denoted by the symbol "M" and the formula for calculating it is: \[ M = \frac{\text{moles of solute}}{\text{liters of solution}} \]To put it simply, molarity tells us how many moles of a substance are present in one liter of solution. Because it's based on volume, changes in temperature and pressure can affect molarity, since they can cause the volume to expand or contract.Understanding molarity is crucial when preparing solutions in the lab because it informs us of how concentrated a solution is. This direct information helps in predicting reaction outcomes and ensuring stoichiometric precision in experiments. When working with acids, like sulfuric acid, knowing the molarity helps calculate normality and understand the behavior of the solution during chemical reactions.

Dilution

Dilution is the process of decreasing the concentration of a solution by increasing the volume of the solvent, usually water. The dilution process doesn't change the amount of solute, but it spreads it through a greater volume, lowering the concentration. To calculate the new concentration after dilution, you can use the dilution formula:\[ C_1V_1 = C_2V_2 \]Here, \(C_1\) and \(V_1\) refer to the initial concentration and volume, while \(C_2\) and \(V_2\) refer to the final concentration and volume after dilution.The fundamental idea is that the amount of solute in the solution before and after dilution must remain the same.Commonly applied in various fields, dilution allows scientists and chemists to prepare solutions of desired concentrations from more concentrated stock solutions. This is particularly useful when precise concentrations are necessary for specialized chemical reactions or titrations.

Sulfuric Acid

Sulfuric acid, with the chemical formula \(\mathrm{H}_2\mathrm{SO}_4\), is a strong diprotic acid, meaning it can donate two protons (\(\mathrm{H}^+\)). This property affects both its normality calculations and its behavior in chemical reactions. As it releases two protons, each molecule of sulfuric acid can potentially participate in two equivalent reactions per mole.Some key features of sulfuric acid include:

• Being widely used in industry and laboratory settings, especially in the manufacture of fertilizers, chemicals, and in refining petroleum.
• Its high corrosiveness, requiring careful handling and specific storage protocols.
• Its ability to act as a strong dehydrating agent, making it useful in certain synthesis processes.

Understanding sulfuric acid's characteristics is essential for safely handling it and using it accurately in experiments, where correct molarity and normality must be taken into account.

Chemical Equivalence

Chemical equivalence relates to the concept of normality, particularly how substances react with each other. It's the concept used to equate different substances in terms of their potential to undergo reaction.For acids, chemical equivalence is defined by the number of protons an acid can donate. In the case of sulfuric acid, its equivalence factor is 2, as it can donate 2 \(\mathrm{H}^+\) ions per molecule.This means that in reactions involving proton transfer, such as neutralization reactions, the action of sulfuric acid can be predicted by considering its equivalence factor.Knowing the equivalence factor allows the calculation of normality from molarity, using the formula:\[ N = \text{equivalence factor} \times M \]This helps in planning appropriate titration procedures and ensuring that chemical reactions are balanced. Chemical equivalence is a crucial concept for achieving control over chemical processes and ensuring reactions proceed as intended.