Two samples of HI each of 5 s were taken separately in two vessels of volume 5 and 10 litres respectively at `27^@C.` The extent of dissociation of HI will be

Options

A. more in the 5-litre vessel
B. more in the 10-litre vessel
C. equal in both vessels
D. nil at both

Answer

To find the extent of dissociation of HI in two different volumes, we will follow these steps:

### Step 1: Write the dissociation reaction
The dissociation of hydrogen iodide (HI) can be represented as:
\[ 2 \text{HI} \rightleftharpoons \text{H}_2 + \text{I}_2 \]

### Step 2: Calculate the initial concentration of HI
Given that we have 5 grams of HI, we first need to find the number of moles of HI. The molar mass of HI (Hydrogen = 1 g/mol, Iodine = 127 g/mol) is:
\[ \text{Molar mass of HI} = 1 + 127 = 128 \text{ g/mol} \]

Now, we can calculate the number of moles of HI:
\[ \text{Number of moles of HI} = \frac{\text{mass}}{\text{molar mass}} = \frac{5 \text{ g}}{128 \text{ g/mol}} \approx 0.0391 \text{ moles} \]

Next, we calculate the concentration of HI in both vessels.

For the 5-liter vessel:
\[ \text{Concentration of HI} = \frac{0.0391 \text{ moles}}{5 \text{ L}} = 0.00782 \text{ M} \]

For the 10-liter vessel:
\[ \text{Concentration of HI} = \frac{0.0391 \text{ moles}}{10 \text{ L}} = 0.00391 \text{ M} \]

### Step 3: Determine the change in moles (Δn)
In the reaction, we have:
- 2 moles of HI dissociate to produce 1 mole of H2 and 1 mole of I2.
- Therefore, the change in moles (Δn) for the reaction is:
\[ \Delta n = (1 + 1) - 2 = 0 \]

### Step 4: Analyze the effect of volume on equilibrium
Since Δn = 0, the equilibrium constant (K) is not affected by changes in pressure or volume. This means that the concentrations of the products and reactants will adjust to maintain the same ratio, regardless of the volume.

### Step 5: Conclusion
The extent of dissociation of HI will be the same in both vessels because the concentrations of HI are different, but the equilibrium constant remains unchanged due to Δn = 0. Therefore, the extent of dissociation will be equal in both cases.

### Final Answer
The extent of dissociation of HI will be the same in both vessels.

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