For a zero order reaction, the plot of concentration, vs time is linear with

Options

A. `+ ve` slope and zero intercept
B. `- ve` slope and zero intercept
C. `+ ve` slope and non-zero intercept
D. `- ve` slope and non-zero intercept

Answer

To solve the question regarding the plot of concentration vs. time for a zero-order reaction, we can follow these steps:

### Step 1: Understand the Zero-Order Reaction
A zero-order reaction is characterized by a constant rate of reaction that does not depend on the concentration of the reactant. This means that the rate of reaction remains constant as the reaction proceeds.

### Step 2: Write the Rate Law
For a zero-order reaction, the rate law can be expressed as:
\[ \text{Rate} = k \]
where \( k \) is the rate constant.

### Step 3: Relate Concentration and Time
For a zero-order reaction, the change in concentration over time can be expressed as:
\[ [A] = [A_0] - kt \]
where:
- \([A]\) is the concentration at time \( t \),
- \([A_0]\) is the initial concentration,
- \( k \) is the rate constant,
- \( t \) is time.

### Step 4: Rearrange the Equation
Rearranging the equation gives:
\[ [A] = [A_0] - kt \]
This equation is in the form of \( y = mx + b \), where:
- \( y \) is \([A]\),
- \( m \) (the slope) is \(-k\),
- \( x \) is \( t \),
- \( b \) (the y-intercept) is \([A_0]\).

### Step 5: Identify the Characteristics of the Plot
From the rearranged equation, we can conclude:
- The plot of concentration \([A]\) vs. time \( t \) is a straight line.
- The slope of the line is negative (\(-k\)), indicating that as time increases, the concentration decreases.
- The y-intercept is \([A_0]\), which is a non-zero value.

### Conclusion
Thus, for a zero-order reaction, the plot of concentration vs. time is linear with a **negative slope** and a **non-zero intercept**.

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