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 H2SO4

First, calculate the milliequivalents (meq) of the sulfuric acid solution. The formula for milliequivalents is: \[\text{meq} = \text{Normality} \times \text{Volume (mL)}\]Substituting the given values:\[\text{meq of } \mathrm{H}_{2}\mathrm{SO}_{4} = 10 \times 50 = 500 \, \text{meq}\]

Step 2: Calculate Milliequivalents of HCl

Now, calculate the milliequivalents for the hydrochloric acid solution:\[\text{meq of } \mathrm{HCl} = \text{Normality} \times \text{Volume (mL)} = 12 \times 25 = 300 \, \text{meq}\]

Step 3: Calculate Milliequivalents of HNO3

Next, calculate the milliequivalents for the nitric acid solution:\[\text{meq of } \mathrm{HNO}_{3} = \text{Normality} \times \text{Volume (mL)} = 5 \times 40 = 200 \, \text{meq}\]

Step 4: Calculate Total Milliequivalents

Add the milliequivalents of all solutions together:\[\text{Total meq} = 500 + 300 + 200 = 1000 \, \text{meq}\]

Step 5: Calculate Normality of Resulting Solution

To find the normality of the resulting solution, divide the total milliequivalents by the final volume in mL (1000 mL):\[\text{Normality} = \frac{\text{Total meq}}{\text{Volume (mL)}} = \frac{1000}{1000} = 1 \, \text{N}\]

Step 6: Conclusion

The normality of the resulting solution is found to be \(1\, \text{N}\). Therefore, the correct answer is (c) \(1\, \text{N}\).

Key Concepts

Acid-Base Solutions

Understanding acid-base solutions is central to chemistry, especially when dealing with normality calculations in reactions. These solutions involve acids, which release hydrogen ions (\( \text{H}^+ \)) in the solution, and bases, which provide hydroxide ions (\( \text{OH}^- \)). When mixed, they typically react to form water and a salt.
Acids and bases are usually grouped into strong and weak categories:

• Strong acids and bases: Fully dissociate in water, meaning the concentration of \( \text{H}^+ \) or \( \text{OH}^- \) equals the concentration of the acid or base.
• Weak acids and bases: Only partially dissociate, so the concentration of ions is less than that of the acid or base itself.

Normality in the context of acid-base chemistry refers to the concentration of the \( \text{H}^+ \) or \( \text{OH}^- \) ions that a compound can release or interact with in a reaction. Thus, it's crucial for reactions that depend on complete neutralization.

Milliequivalents Calculation

Milliequivalents (meq) are small units often used in calculating concentrations in solution to simplify acid-base reactions. Calculating milliequivalents involves the concept of equivalent weight, which varies based on the substance:
- **Acids:** The equivalent weight is determined by the amount of hydrogen ions provided per molecule.
- **Bases:** It's determined by the number of hydroxide ions provided per molecule.

• Formula for Milliequivalents: The calculation starts by multiplying the normality (\( N \)) by the volume of the solution in milliliters (\text{mL}): \[\text{meq} = N \times \text{Volume (mL)}\]This step is repeated for each component in a mixture to find the total milliequivalents.
• Purpose: This allows a chemist to understand the full capacity of a solution to react, which is essential in titration and many other chemical processes.

By knowing the milliequivalents, one can easily determine the normality after dilution or reaction.

Molar Concentration

Molar concentration relates to the amount of a solute present per liter of solution, a fundamental concept in chemistry known as molarity (\( M \)). Although this problem centers on normality, understanding molarity helps grasp why normality might differ in some reactions.
- **Molarity Definition:** \[M = \frac{\text{moles of solute}}{\text{liters of solution}}\]While normality focuses on reactive units in a reaction, molarity provides total solute concentration. Comparing the two offers insights into how effective a solution is in actual chemical processes.

• For example, in monoprotic acids like \( \text{HCl} \), normality and molarity are the same, but in polyprotic acids like \( \text{H}_2\text{SO}_4 \), normality might be higher as one molecule provides multiple reactive units (e.g., 2 \( \text{H}^+ \)).

Knowing both normality and molarity can give a full picture of the concentration and reactivity of a solution.