Problem 56 - A Complete Resource Book in Chemistry for JEE Main

Question

\(50 \mathrm{~mL}\) of \(10 \mathrm{~N} \mathrm{H}_{2} \mathrm{SO}_{4}, 25 \mathrm{~mL}\) of \(12 \mathrm{~N} \mathrm{HCl}\) and \(40 \mathrm{~mL}\) of \(5 \mathrm{~N} \mathrm{HNO}_{3}\) are mixed and the volume of the mixture is made \(1000 \mathrm{~mL}\) by adding water. The normality of resulting solution will be (a) \(9 \mathrm{~N}\) (b) \(4 \mathrm{~N}\) (c) \(1 \mathrm{~N}\) (d) \(2 \mathrm{~N}\)

Step-by-Step Solution

Answer

(c) 1 N

Step 1: Calculate Milliequivalents of Each Component

The milliequivalents (meq) of a solution can be calculated using the formula \( \text{meq} = \text{Volume (mL)} \times \text{Normality (N)} \).- For \( H_2SO_4 \): \( 50 \text{ mL} \times 10 \text{ N} = 500 \text{ meq} \)- For \( HCl \): \( 25 \text{ mL} \times 12 \text{ N} = 300 \text{ meq} \)- For \( HNO_3 \): \( 40 \text{ mL} \times 5 \text{ N} = 200 \text{ meq} \)

Step 2: Determine Total Milliequivalents in the Mixture

Add the milliequivalents of all components together to get the total milliequivalents:\[500 \text{ meq} + 300 \text{ meq} + 200 \text{ meq} = 1000 \text{ meq}\]

Step 3: Calculate Normality of the Resulting Solution

To find the normality of the resulting solution, use the formula:\[\text{Normality (N)} = \frac{\text{Total milliequivalents}}{\text{Total volume in mL}}\]Substituting the known values:\[\text{Normality} = \frac{1000 \text{ meq}}{1000 \text{ mL}} = 1 \text{ N}\]

Step 4: Conclusion: Determine the Correct Answer Option

Since the normality of the resulting solution is \(1\text{ N}\), the correct answer is (c) \(1 \text{ N} \).

Key Concepts

Milliequivalents

Milliequivalents (meq) are a measure often used in chemistry to express amounts of reactive capacity. One equivalent is the amount of substance that will react with or supply one mole of hydrogen ions in an acid-base reaction. The term "milliequivalent" is one-thousandth of an equivalent, useful for calculations involving large numbers. When dealing with chemical solutions, normality (N) indicates the concentration of equivalents per liter of solution. Multiplied by the volume of the solution in milliliters, it gives us the milliequivalents.
This exact calculation allows chemists to easily work with and precisely adjust the presence of ions in solution, which is vital for reactions that require exact stoichiometric balance.

• Formula: milliequivalents (meq) = Volume in mL × Normality (N)
• Ensures accurate reactive measurement, essential in titrations and reactions.

Understanding milliequivalents helps in the calculation of concentrations after mixing multiple solutions, crucial for predicting how a mixture will behave chemically.

Acid-Base Solution

An acid-base solution results from the interaction of acidic and basic substances. Acids, like hydrochloric acid (HCl), sulfuric acid (H₂SO₄), and nitric acid (HNO₃), release hydrogen ions ( H⁺ ) in solution, contributing to acidity. Bases, on the other hand, release hydroxide ions which neutralize acids. In the context of acid-base reactions, normality plays a key role. It indicates how many equivalents of the acidic or basic component are present, directly influencing how the solution reacts. In a mixed solution, as explored in this exercise, each acid contributes its own set of hydrogen ions as per its normality.
This sum forms the total measure of the acidity of the final solution when diluted.

• Acids release hydrogen ions which define their reactivity in solutions.
• The resulting solution's behavior relies on these interactions and overall normality.

Overall, understanding the concept of acid-base solutions helps predict resultant pH values and the neutrality or reactivity of a solution after mixing and dilution.

Dilution

Dilution in chemistry is a process of reducing the concentration of a solute in solution, usually by adding more solvent. It is not merely adding volume, but rather it decreases the number of particles per unit volume, thus concentrating less per milliliter. When you dilute a solution, the overall amount of solute—what you initially measured in milliequivalents—remains constant, only its distribution changes. This principle is crucial when you prepare solutions of desired concentrations, like in this exercise where an initial mix was diluted to 1000 mL.

• Preserves total solute while decreasing concentration.
• Significant when ensuring solutions meet a specific normality requirement.

Utilizing the total milliequivalents across the new volume yields the resulting normality. Hence, by understanding dilution, one can formulate specific normality solutions necessary for specific chemical tasks or reactions.