For a zero order reaction of the type `A rarr` products, the integrated rate equation may be expressed as

Options

A. `k = ([A]_(0)-[A])/(2).t`
B. `k = ([A]_(0)-[A])/(2t)`
C. `k = ([A]-[A]_(0))/(t)`
D. `k = ([A]_(0)-[A])/(t)`

Explanation

To derive the integrated rate equation for a zero-order reaction of the type \( A \rightarrow \text{products} \), we can follow these steps:

### Step 1: Understand the zero-order reaction
In a zero-order reaction, the rate of reaction is constant and does not depend on the concentration of the reactant \( A \). The rate law for a zero-order reaction can be expressed as:
\[ \text{Rate} = k \]
where \( k \) is the rate constant.

### Step 2: Relate rate to concentration
The rate of change of concentration of \( A \) can be expressed as:
\[ -\frac{d[A]}{dt} = k \]
This indicates that the concentration of \( A \) decreases at a constant rate \( k \).

### Step 3: Integrate the rate equation
To find the integrated form, we can rearrange the equation and integrate:
\[ d[A] = -k \, dt \]
Integrating both sides gives:
\[ \int [A]_0^{[A]} d[A] = -k \int_0^t dt \]
This results in:
\[ [A] - [A]_0 = -kt \]
where \([A]_0\) is the initial concentration of \( A \).

### Step 4: Rearranging the equation
Rearranging the equation gives us the integrated rate equation for a zero-order reaction:
\[ [A] = [A]_0 - kt \]

### Final Answer
The integrated rate equation for a zero-order reaction of the type \( A \rightarrow \text{products} \) is:
\[ [A] = [A]_0 - kt \]

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