For the reaction
`H_(2) (g)+I_(2)(g) rarr 2HI(g)`, the rate of disappearance of `HI` will be `1.0 xx 10^(-4) mol L^(-1) s^(-1)`. The rate of appearance of `HI` will be

Options

A. `1.0 xx 10^(-4) mol L^(-1) s^(-1)`
B. `2.0 xx 10^(-4) mol L^(-1) s^(-1)`
C. `0.50 xx 10^(-4) mol L^(-1) s^(-1)`
D. `4.0 xx 10^(-4) mol L^(-1) s^(-1)`

Explanation

To find the rate of appearance of HI in the reaction \( H_2(g) + I_2(g) \rightarrow 2HI(g) \), we can follow these steps:

### Step 1: Understand the Reaction Stoichiometry
The balanced equation shows that 1 mole of \( H_2 \) reacts with 1 mole of \( I_2 \) to produce 2 moles of \( HI \). This means that the rates of disappearance and appearance are related through their stoichiometric coefficients.

### Step 2: Write the Rate Expressions
From the balanced equation, we can express the rates as follows:
- Rate of disappearance of \( H_2 \): \( -\frac{1}{1} \frac{d[H_2]}{dt} \)
- Rate of disappearance of \( I_2 \): \( -\frac{1}{1} \frac{d[I_2]}{dt} \)
- Rate of appearance of \( HI \): \( \frac{1}{2} \frac{d[HI]}{dt} \)

### Step 3: Relate the Rates
According to the stoichiometry of the reaction:
\[ -\frac{d[H_2]}{dt} = -\frac{d[I_2]}{dt} = \frac{1}{2} \frac{d[HI]}{dt} \]

### Step 4: Substitute the Given Rate
We are given the rate of disappearance of \( HI \):
\[ -\frac{d[HI]}{dt} = 1.0 \times 10^{-4} \, \text{mol L}^{-1} \text{s}^{-1} \]

### Step 5: Calculate the Rate of Appearance of \( HI \)
Since the rate of appearance of \( HI \) is positive, we take the negative of the rate of disappearance:
\[ \frac{d[HI]}{dt} = 1.0 \times 10^{-4} \, \text{mol L}^{-1} \text{s}^{-1} \]

### Step 6: Find the Rate of Disappearance of \( I_2 \)
Using the stoichiometric relationship:
\[ -\frac{d[I_2]}{dt} = \frac{1}{2} \left( 1.0 \times 10^{-4} \right) \]
\[ -\frac{d[I_2]}{dt} = 0.5 \times 10^{-4} \, \text{mol L}^{-1} \text{s}^{-1} \]

### Step 7: Finalize the Rate of Appearance of \( HI \)
Thus, the rate of appearance of \( HI \) is:
\[ \text{Rate of appearance of } HI = 1.0 \times 10^{-4} \, \text{mol L}^{-1} \text{s}^{-1} \]

### Summary
The rate of appearance of \( HI \) is \( 1.0 \times 10^{-4} \, \text{mol L}^{-1} \text{s}^{-1} \).

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