How many g of dibasic acid (mol.wt.`200)` should be present in `100ml`of its aqueous solution to give decinormal strength?

Options

A. `1g`
B. `2g`
C. `10g`
D. `20g`

Explanation

To determine how many grams of dibasic acid (with a molar mass of 200 g/mol) should be present in 100 mL of its aqueous solution to achieve a decinormal strength (0.1 N), we can follow these steps:

### Step 1: Understand Normality
Normality (N) is defined as the number of equivalents of solute per liter of solution. For a dibasic acid, which can donate two protons (H⁺ ions), the normality is related to molarity (M) by the formula:
\[ N = n \times M \]
where \( n \) is the number of protons that can be donated (for dibasic acid, \( n = 2 \)).

### Step 2: Calculate Molarity for Decinormal Solution
Since we want a decinormal solution:
\[ N = 0.1 \, \text{N} \]
Using the relationship between normality and molarity for a dibasic acid:
\[ 0.1 = 2 \times M \]
Now, solve for \( M \):
\[ M = \frac{0.1}{2} = 0.05 \, \text{M} \]

### Step 3: Calculate the Amount of Acid Needed
Next, we need to find out how many moles of dibasic acid are required in 100 mL (0.1 L) of solution:
\[ \text{Moles of dibasic acid} = M \times \text{Volume in L} \]
\[ \text{Moles of dibasic acid} = 0.05 \, \text{mol/L} \times 0.1 \, \text{L} = 0.005 \, \text{mol} \]

### Step 4: Convert Moles to Grams
Now, we convert moles to grams using the molar mass of the dibasic acid:
\[ \text{Mass (g)} = \text{Moles} \times \text{Molar Mass} \]
\[ \text{Mass (g)} = 0.005 \, \text{mol} \times 200 \, \text{g/mol} = 1 \, \text{g} \]

### Final Answer
To achieve a decinormal strength in 100 mL of aqueous solution, you need **1 gram** of dibasic acid.

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