0.98 g of a polybasic acid (molar mass 98) requires 30 mL of 0.5M `Ba(OH)_(2)` for complete neutralization. The basicity of acid is …………

Options

A. (a) 1
B. (b) 2
C. (c) 3
D. (d) 4

Explanation

To determine the basicity of the polybasic acid, we will follow these steps:

### Step 1: Understand the Problem
We are given:
- Mass of the acid = 0.98 g
- Molar mass of the acid = 98 g/mol
- Volume of Ba(OH)₂ solution = 30 mL = 0.030 L
- Molarity of Ba(OH)₂ = 0.5 M

We need to find the basicity of the acid, which is defined as the valency factor of the acid.

### Step 2: Calculate Moles of the Acid
Using the formula for moles:
\[ \text{Moles of acid} = \frac{\text{mass}}{\text{molar mass}} = \frac{0.98 \, \text{g}}{98 \, \text{g/mol}} = 0.01 \, \text{mol} \]

### Step 3: Calculate the Equivalents of the Base
The equivalents of the base (Ba(OH)₂) can be calculated using the formula:
\[ \text{Equivalents of base} = \text{Molarity} \times \text{Volume (in L)} \times \text{valency factor} \]
For Ba(OH)₂, the valency factor is 2 (since it provides 2 OH⁻ ions).

Calculating the equivalents of the base:
\[ \text{Equivalents of base} = 0.5 \, \text{mol/L} \times 0.030 \, \text{L} \times 2 = 0.03 \, \text{equivalents} \]

### Step 4: Set Equivalents of Acid Equal to Equivalents of Base
Since the reaction is a complete neutralization, the equivalents of the acid must equal the equivalents of the base:
\[ \text{Equivalents of acid} = \text{Equivalents of base} \]

### Step 5: Calculate the Valency Factor (Basicity) of the Acid
The equivalents of the acid can be expressed as:
\[ \text{Equivalents of acid} = \text{Moles of acid} \times \text{valency factor} \]
Let \( x \) be the valency factor (basicity) of the acid:
\[ 0.01 \, \text{mol} \times x = 0.03 \, \text{equivalents} \]
Solving for \( x \):
\[ x = \frac{0.03}{0.01} = 3 \]

### Conclusion
The basicity of the acid is 3.