For the reaction `H_2(g)+I_2-2HI(g)` the rate of reaction is expressed as:

Options

A. `-(Delta[I_2])/(Delta t)=-(Delta[H_2])/(Delta t)=1/2 (Delta[HI])/(Delta t)`
B. `-(Delta[I_2])/(Delta t)=(Delta[H_2])/(Delta t)= (Delta[HI])/(2Delta t)`
C. `-(Delta[I_2])/(Delta t)=-1/2(Delta[H_2])/(Delta t)= (Delta[HI])/(Delta t)`
D. None of these

Answer

To express the rate of the reaction \( H_2(g) + I_2(g) \rightarrow 2HI(g) \), we need to consider the changes in concentration of the reactants and products over time. Here’s a step-by-step breakdown of how to write the rate expression for this reaction:

### Step 1: Write the balanced chemical equation
The balanced equation for the reaction is:
\[ H_2(g) + I_2(g) \rightarrow 2HI(g) \]

### Step 2: Define the rate of reaction
The rate of a reaction can be defined in terms of the change in concentration of the reactants and products over time. The general form is:
\[ \text{Rate} = -\frac{d[H_2]}{dt} = -\frac{d[I_2]}{dt} = \frac{1}{2}\frac{d[HI]}{dt} \]
Where:
- \([H_2]\) is the concentration of hydrogen gas.
- \([I_2]\) is the concentration of iodine gas.
- \([HI]\) is the concentration of hydrogen iodide.

### Step 3: Write the rate expressions
From the balanced equation, we can express the rates of change in concentration as follows:
- The rate of disappearance of \( H_2 \) is given by:
\[ -\frac{d[H_2]}{dt} \]
- The rate of disappearance of \( I_2 \) is given by:
\[ -\frac{d[I_2]}{dt} \]
- The rate of appearance of \( HI \) is given by:
\[ \frac{1}{2}\frac{d[HI]}{dt} \]

### Step 4: Combine the rate expressions
Now, we can combine these expressions into a single rate equation:
\[ -\frac{d[H_2]}{dt} = -\frac{d[I_2]}{dt} = \frac{1}{2}\frac{d[HI]}{dt} \]

### Step 5: Use the differential notation
We can express the rates using the differential notation:
\[ \text{Rate} = -\frac{d[H_2]}{dt} = -\frac{d[I_2]}{dt} = \frac{1}{2}\frac{d[HI]}{dt} \]

### Conclusion
Thus, the rate of the reaction can be expressed in terms of the change in concentration of the reactants and products over time.