Which graph represents zero-order reaction `[A(g) rarr B (g)]` ?

Options

A.
B.
C.
D.

Answer

To determine which graph represents a zero-order reaction for the equation \([A(g) \rightarrow B(g)]\), 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 reactants. The rate law can be expressed as:
\[ -\frac{d[A]}{dt} = k \]
where \(k\) is the rate constant.

### Step 2: Derive the Concentration Equation
For a zero-order reaction, the concentration of reactant \(A\) changes linearly over time. The integrated rate law for a zero-order reaction is given by:
\[ [A] = [A_0] - kt \]
where \([A_0]\) is the initial concentration of \(A\) and \(t\) is time.

### Step 3: Analyze the Graphs
From the equation \([A] = [A_0] - kt\), we can infer that:
- The graph of \([A]\) versus time \(t\) will be a straight line with a negative slope (since \(k\) is positive).
- The y-intercept of this graph will be \([A_0]\).
- As time increases, the concentration of \(A\) decreases linearly until it reaches zero.

### Step 4: Identify the Correct Graph
Now, we need to look at the provided graphs and identify which one shows a straight line with a negative slope. The graph should start at \([A_0]\) and decrease linearly over time.

### Step 5: Conclusion
After analyzing all the graphs, the correct graph that represents a zero-order reaction will be the one that shows a linear decrease in concentration of \(A\) over time.

### Final Answer
The graph that represents a zero-order reaction is the one that shows a straight line with a negative slope.

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