`3.2` moles of hydrogemn iodide was heted in a sealed bulb at `444^(@)C` till the equilibrium state was reached. Its degree of dissociation sat this temperature was found to be `22%`. The number of moles of hydrogen iodide present at equilibrium is

Options

A. `2.496`
B. `1.87`
C. 2
D. 4

Explanation

To solve the problem, we need to determine the number of moles of hydrogen iodide (HI) present at equilibrium after heating and achieving a degree of dissociation of 22%. Here’s a step-by-step breakdown of the solution:

### Step 1: Write the Reaction
The dissociation of hydrogen iodide can be represented by the following balanced chemical equation:
\[ 2 \text{HI} \rightleftharpoons \text{H}_2 + \text{I}_2 \]

### Step 2: Define Initial Moles
Initially, we have:
- Moles of HI = 3.2 moles

### Step 3: Determine Degree of Dissociation
The degree of dissociation (α) is given as 22%, which can be expressed as a fraction:
\[ \alpha = 22\% = \frac{22}{100} = 0.22 \]

### Step 4: Calculate Moles of HI that Dissociate
The moles of HI that dissociate can be calculated as:
\[ \text{Moles of HI that dissociate} = \alpha \times \text{initial moles of HI} \]
\[ = 0.22 \times 3.2 = 0.704 \text{ moles} \]

### Step 5: Calculate Moles of HI Remaining at Equilibrium
To find the moles of HI remaining at equilibrium, we subtract the moles that dissociated from the initial moles:
\[ \text{Moles of HI remaining} = \text{initial moles of HI} - \text{moles that dissociate} \]
\[ = 3.2 - 0.704 = 2.496 \text{ moles} \]

### Conclusion
The number of moles of hydrogen iodide present at equilibrium is:
\[ \boxed{2.496} \]

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