The van't Hoff factor for `0.1 M Ba(NO_(3))_(2)` solution is `2.74`. The degree of dissociation is

Options

A. `91.3%`
B. `87%`
C. `100%`
D. `74%`

Explanation

To find the degree of dissociation (α) for the given solution of barium nitrate, we can follow these steps:

### Step 1: Understand the Dissociation of Ba(NO₃)₂
When barium nitrate (Ba(NO₃)₂) dissolves in water, it dissociates into ions:
\[ \text{Ba(NO}_3\text{)}_2 \rightarrow \text{Ba}^{2+} + 2 \text{NO}_3^{-} \]
This means that for each formula unit of Ba(NO₃)₂, we get a total of 3 ions (1 Ba²⁺ and 2 NO₃⁻).

### Step 2: Identify the Van't Hoff Factor (i)
The van't Hoff factor (i) is given as 2.74. The van't Hoff factor represents the effective number of particles in solution after dissociation.

### Step 3: Use the Formula for Van't Hoff Factor
The formula for the van't Hoff factor is:
\[ i = 1 + \alpha(n - 1) \]
Where:
- \( i \) = van't Hoff factor
- \( \alpha \) = degree of dissociation
- \( n \) = number of particles formed from one formula unit (in this case, n = 3)

### Step 4: Substitute Known Values into the Formula
Substituting the known values into the formula:
\[ 2.74 = 1 + \alpha(3 - 1) \]
\[ 2.74 = 1 + 2\alpha \]

### Step 5: Solve for α
Now, we can rearrange the equation to solve for α:
\[ 2.74 - 1 = 2\alpha \]
\[ 1.74 = 2\alpha \]
\[ \alpha = \frac{1.74}{2} \]
\[ \alpha = 0.87 \]

### Step 6: Convert to Percentage
To express the degree of dissociation as a percentage, multiply by 100:
\[ \text{Degree of dissociation} = 0.87 \times 100 = 87\% \]

### Final Answer
The degree of dissociation of the 0.1 M Ba(NO₃)₂ solution is **87%**.

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