How many grams of dibasic acid (mol. weight 200) should be present in 100 mL of the aqueous solution to give strength 0.2 N?

Options

A. 1g
B. 2g
C. 3g
D. 0.2g

Answer

To solve the problem of how many grams of dibasic acid (molecular weight = 200) should be present in 100 mL of an aqueous solution to give a strength of 0.2 N, we can follow these steps:

### Step 1: Understand the Concept of Normality
Normality (N) is defined as the number of gram equivalents of solute per liter of solution. For a dibasic acid, the basicity is 2, meaning it can donate two protons (H⁺ ions) per molecule.

### Step 2: Convert Volume from mL to L
We have 100 mL of solution, which we need to convert to liters:
\[ 100 \, \text{mL} = 0.1 \, \text{L} \]

### Step 3: Calculate the Equivalent Weight
The equivalent weight of a dibasic acid can be calculated using the formula:
\[ \text{Equivalent Weight} = \frac{\text{Molecular Weight}}{\text{Basicity}} \]
Given that the molecular weight is 200 and the basicity is 2:
\[ \text{Equivalent Weight} = \frac{200}{2} = 100 \, \text{g/equiv} \]

### Step 4: Use the Normality Formula
The formula for normality is:
\[ N = \frac{\text{Number of Gram Equivalents}}{\text{Volume of Solution in Liters}} \]
Rearranging this gives:
\[ \text{Number of Gram Equivalents} = N \times \text{Volume in Liters} \]
Substituting the values:
\[ \text{Number of Gram Equivalents} = 0.2 \, \text{N} \times 0.1 \, \text{L} = 0.02 \, \text{equivalents} \]

### Step 5: Calculate the Mass of the Acid
Now we can find the mass of the dibasic acid using the equivalent weight:
\[ \text{Mass} = \text{Number of Gram Equivalents} \times \text{Equivalent Weight} \]
Substituting the values:
\[ \text{Mass} = 0.02 \, \text{equivalents} \times 100 \, \text{g/equiv} = 2 \, \text{g} \]

### Conclusion
The mass of dibasic acid required to prepare 100 mL of a 0.2 N solution is **2 grams**.

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