20 ml of 1 N solution of `KMnO_(4)` just reacts with 20 ml of a solution of oxalic acid. The weight of oxalic acid crystals in 1N of the solution is

Options

A. 31.5 g
B. 126 g
C. 63 g
D. 6.3 g

Answer

To solve the problem of finding the weight of oxalic acid crystals in a 1N solution, we will follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- We have a 1N solution of KMnO₄ that reacts with a solution of oxalic acid.
- The volumes of both solutions are 20 ml.

2. **Use the Formula for Weight Calculation**:
- The weight of the solute can be calculated using the formula:
\[ \text{Weight} = \text{Normality} \times \text{Equivalent Weight} \times \frac{\text{Volume}}{1000} \]

3. **Identify the Normality**:
- The normality (N) of the oxalic acid solution is given as 1N.

4. **Calculate the Equivalent Weight of Oxalic Acid**:
- The molecular formula of oxalic acid is \( \text{C}_2\text{H}_2\text{O}_4 \).
- The molar mass (molecular weight) of oxalic acid is calculated as follows:
\[ \text{Molar mass} = 2(12) + 2(1) + 4(16) = 24 + 2 + 64 = 90 \text{ g/mol} \]
- The equivalent weight is calculated using the formula:
\[ \text{Equivalent Weight} = \frac{\text{Molar Mass}}{n} \]
where \( n \) is the number of acidic protons (H⁺ ions) that can be donated. For oxalic acid, \( n = 2 \).
\[ \text{Equivalent Weight} = \frac{90}{2} = 45 \text{ g/equiv} \]

5. **Calculate the Weight of Oxalic Acid**:
- Substitute the values into the weight formula:
\[ \text{Weight} = 1 \times 45 \times \frac{20}{1000} \]
- Simplifying this gives:
\[ \text{Weight} = 1 \times 45 \times 0.02 = 0.9 \text{ grams} \]

6. **Final Result**:
- The weight of oxalic acid crystals in the 1N solution is **0.9 grams**.