Problem 110 - A Complete Resource Book in Chemistry for JEE Main

Question

How many grams of dibasic acid (mol. wt 200) should be present in \(100 \mathrm{~mL}\) of the aqueous solution to give \(0.1\) normality? (a) \(1 \mathrm{~g}\) (b) \(1.5 \mathrm{~g}\) (c) \(0.5 \mathrm{~g}\) (d) \(20 \mathrm{~g}\)

Step-by-Step Solution

Answer

The correct answer is (a) 1 g.

Step 1: Understand Normality

Normality is a measure of concentration equivalent to the molarity multiplied by the number of equivalents per mole. In this case, the dibasic acid will have two equivalents per mole.

Step 2: Calculate Equivalent Weight

For the dibasic acid, which has a molecular weight of 200, the equivalent weight is calculated by dividing the molecular weight by the number of acidic protons it can donate (which is 2). \[ \text{Equivalent Weight} = \frac{200}{2} = 100 \]

Step 3: Use Normality Formula

The formula for normality is \( N = \frac{\text{Weight of solute in grams}}{\text{Equivalent weight}\times \text{Volume in L}} \). Rearrange this to solve for the weight of the solute: \[ \text{Weight of solute in grams} = N \times \text{Equivalent weight} \times \text{Volume in L} \]

Step 4: Plug Values into Normality Formula

Insert the given values into the rearranged formula: \[ \text{Weight of solute in grams} = 0.1 \times 100 \times 0.1 = 1 \]

Step 5: Conclusion

The weight of the dibasic acid required to achieve a normality of 0.1 in 100 mL of solution is therefore 1 gram.

Key Concepts

Equivalent Weight

The concept of equivalent weight is crucial in the calculations involving normality, particularly for acids, bases, and salts. Equivalent weight refers to the portion of the compound that can donate one mole of hydrogen ions (H extsuperscript{+}) or accept one mole of electrons in a redox reaction. This is based on the specific reaction the compound is involved in. For instance, a dibasic acid, which can donate two protons, will have its molecular weight divided by two to get the equivalent weight.
For example, our given dibasic acid has a molecular weight of 200. Since it can donate two acidic protons, its equivalent weight is calculated as: \[\text{Equivalent Weight} = \frac{200}{2} = 100\]Understanding equivalent weight is important, because it determines how much of a substance is equivalent to others in chemical reactions. Knowing this allows us to calculate how much of the substance is needed to react with or neutralize another substance fully.

Concentration Calculations

In chemical solutions, concentration calculations are essential for determining how much solute is needed to achieve desired solution strength. This involves understanding how the amount of solute relates to the volume of the solution. In this specific exercise, normality (N) expresses the concentration. It is calculated using the formula: \[N = \frac{\text{Weight of solute in grams}}{\text{Equivalent weight} \times \text{Volume in L}}\] To rearrange this for calculating the weight of the solute, the formula becomes: \[\text{Weight of solute in grams} = N \times \text{Equivalent weight} \times \text{Volume in L} \]For example, in the exercise, we're given a normality of 0.1 in a 100 mL solution. Converting 100 mL to 0.1 L (since 1 L = 1000 mL), and given an equivalent weight of 100, we plug these into the formula: \[\text{Weight of solute in grams} = 0.1 \times 100 \times 0.1 = 1 \]So, 1 gram of the dibasic acid is required to make this solution.

Molarity vs Normality

It's important to understand the difference between molarity and normality when dealing with chemical solutions, as they describe different concentration aspects. They both measure the concentration of a solution, but in different ways.

• Molarity (M) is a straightforward indicator. It measures moles of solute per liter of solution. Molarity is simple and useful when we deal with substances that completely dissociate in a solution, like salts in water.
• Normality (N), on the other hand, is more adaptable. It considers the reactive capacity of a solute. For acids, it accounts for the number of hydrogen ions released, and for bases, the number of hydroxide ions. In redox reactions, it considers electron exchange.

The choice between using molarity and normality depends on the needs of the chemical reaction or process being analyzed. For reactions involving acid-base neutralization, redox reactions, or precipitation, normality is often the preferred unit. It requires a deeper understanding of the substance's reactivity, making it vital for accurately carrying out these reactions.