For the reaction: `2HIrarr H_(2)+I_(2)`, the expresison `-d(HI)//2dt` represents

Options

A. The rate of formation of `HI`
B. The rate of disappearance of `HI`
C. The instantaneous rate of the reaction
D. The average rate of reaction

Answer

To solve the question regarding the expression \(-\frac{d[HI]}{2dt}\) for the reaction \(2HI \rightleftharpoons H_2 + I_2\), we need to analyze what this expression represents in terms of the reaction kinetics.

### Step-by-Step Solution:

1. **Understanding the Reaction**:
The reaction given is:
\[ 2HI \rightleftharpoons H_2 + I_2 \]
This indicates that two moles of hydrogen iodide (HI) decompose to form one mole of hydrogen (H₂) and one mole of iodine (I₂).

2. **Rate of Reaction**:
The rate of a reaction can be expressed in terms of the change in concentration of the reactants and products over time. For the reaction, we can define the rates as follows:
- The rate of disappearance of HI is given by \(-\frac{d[HI]}{dt}\).
- The rate of appearance of H₂ is given by \(\frac{d[H_2]}{dt}\).
- The rate of appearance of I₂ is given by \(\frac{d[I_2]}{dt}\).

3. **Stoichiometry of the Reaction**:
From the stoichiometry of the reaction, we can relate the rates:
\[ -\frac{1}{2}\frac{d[HI]}{dt} = \frac{d[H_2]}{dt} = \frac{d[I_2]}{dt} \]
This means that for every 2 moles of HI that react, 1 mole of H₂ and 1 mole of I₂ are produced.

4. **Interpreting the Expression**:
The expression \(-\frac{d[HI]}{2dt}\) can be interpreted as:
\[ -\frac{d[HI]}{2dt} = \text{Rate of reaction} \]
This expression represents the instantaneous rate of the reaction, which indicates how fast the reaction is occurring at a particular moment in time.

5. **Conclusion**:
Therefore, the expression \(-\frac{d[HI]}{2dt}\) represents the instantaneous rate of the reaction.

### Final Answer:
The expression \(-\frac{d[HI]}{2dt}\) represents the instantaneous rate of the reaction.

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