`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. 1.87
B. 2.496
C. `4.00`
D. `2.00`

Answer

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

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

### Step 2: Initial Moles
We start with 3.2 moles of hydrogen iodide (HI) at the beginning (initial state).

### Step 3: Degree of Dissociation
The degree of dissociation (α) is given as 22%. This means that 22% of the initial moles of HI will dissociate into H2 and I2.

### Step 4: Calculate the Amount Dissociated
To find the moles of HI that dissociate, we can calculate:
\[ \text{Moles dissociated} = \alpha \times \text{Initial moles of HI} \]
Since α is 22%, we convert this percentage into a fraction:
\[ \alpha = \frac{22}{100} = 0.22 \]

Now, calculate the moles dissociated:
\[ \text{Moles dissociated} = 0.22 \times 3.2 = 0.704 \text{ moles} \]

### Step 5: Calculate Remaining Moles of HI
Since 2 moles of HI produce 1 mole of H2 and 1 mole of I2, the amount of HI that dissociates is:
\[ 2\alpha = 2 \times 0.704 = 1.408 \text{ moles} \]

Now, we can find the remaining moles of HI at equilibrium:
\[ \text{Moles of HI at equilibrium} = \text{Initial moles of HI} - \text{Moles dissociated} \]
\[ \text{Moles of HI at equilibrium} = 3.2 - 1.408 = 1.792 \text{ moles} \]

### Step 6: Final Answer
Thus, the number of moles of hydrogen iodide present at equilibrium is:
\[ \text{Moles of HI at equilibrium} = 3.2 - 1.408 = 1.792 \text{ moles} \]

### Summary
The number of moles of hydrogen iodide present at equilibrium is **1.792 moles**.

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