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

Options

A. 1g
B. 20g
C. 2g
D. 0.2g

Answer

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

### Step 1: Understand Normality
Normality (N) is defined as the number of gram equivalents of solute per liter of solution. The formula is:
\[ N = \frac{\text{Number of gram equivalents of solute}}{\text{Volume of solution in liters}} \]

### Step 2: Determine the Equivalent Weight
The equivalent weight of a substance can be calculated using the formula:
\[ \text{Equivalent weight} = \frac{\text{Molecular weight}}{\text{Basicity}} \]
For a dibasic acid, the basicity is 2. Given that the molecular weight is 100, we can calculate the equivalent weight:
\[ \text{Equivalent weight} = \frac{100}{2} = 50 \, \text{g/equiv} \]

### Step 3: Convert Volume to Liters
The volume of the solution is given as 200 mL. We need to convert this to liters:
\[ 200 \, \text{mL} = 200 \times 10^{-3} \, \text{L} = 0.2 \, \text{L} \]

### Step 4: Set Up the Normality Equation
Now we can set up the equation using the normality formula. We know the normality (0.2 N) and the volume (0.2 L):
\[ 0.2 = \frac{\text{mass}}{\text{equivalent weight} \times \text{volume in L}} \]

### Step 5: Rearrange to Find Mass
Rearranging the equation to solve for mass:
\[ \text{mass} = N \times \text{Equivalent weight} \times \text{Volume in L} \]
Substituting the known values:
\[ \text{mass} = 0.2 \times 50 \times 0.2 \]

### Step 6: Calculate the Mass
Now, we can calculate the mass:
\[ \text{mass} = 0.2 \times 50 \times 0.2 = 0.2 \times 10 = 2 \, \text{grams} \]

### Conclusion
Thus, the mass of dibasic acid required is **2 grams**.

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