For the reaction
`2HX to H_(2) + X_(2)`
`-(d[HX])/(dt)` = rate

Options

A. rate w.r.t `HX = +1/2(d[HX])/(dt)`
B. rate w.r.t `HX = -1/2(d[HX])/(dt)`
C. rate w.r.t `HX = +(d[HX])/(dt)`
D. rate w.r.t HX `=-(d[HX])/(dt)`

Explanation

To find the rate of the reaction `2HX → H2 + X2` with respect to the concentration of HX, we can follow these steps:

### Step 1: Write the balanced chemical equation
The balanced equation for the reaction is:
\[ 2HX \rightarrow H_2 + X_2 \]

### Step 2: Understand the relationship between reactants and products
In a chemical reaction, the rate of change of concentration of reactants and products is related to their stoichiometric coefficients. For the given reaction:
- The stoichiometric coefficient of HX is 2.
- The stoichiometric coefficients of H2 and X2 are both 1.

### Step 3: Write the rate expression
The rate of the reaction can be expressed in terms of the change in concentration of the reactants and products. The general form is:
\[ \text{Rate} = -\frac{1}{\text{stoichiometric coefficient}} \frac{d[\text{Reactant}]}{dt} \]
For the reactant HX, we have:
\[ \text{Rate} = -\frac{1}{2} \frac{d[HX]}{dt} \]

For the products H2 and X2, the rate expressions will be:
\[ \text{Rate} = \frac{1}{1} \frac{d[H_2]}{dt} \]
\[ \text{Rate} = \frac{1}{1} \frac{d[X_2]}{dt} \]

### Step 4: Combine the rate expressions
Since the rate of the reaction is constant, we can equate the expressions:
\[ -\frac{1}{2} \frac{d[HX]}{dt} = \frac{d[H_2]}{dt} = \frac{d[X_2]}{dt} \]

### Step 5: Conclusion
Thus, the rate of the reaction with respect to HX is given by:
\[ -\frac{1}{2} \frac{d[HX]}{dt} = \text{Rate} \]

### Final Answer
The rate of the reaction with respect to HX is:
\[ \text{Rate} = -\frac{1}{2} \frac{d[HX]}{dt} \]

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