For the reaction `A rarr `products , the graph of the fraction of `A` remaining as a function of time `(x-` axis ) is a straight line with `-ve` slpe . The order of the reaction is therefore

Options

A. 1
B. 2
C. zero
D. `-1`

Explanation

To determine the order of the reaction given that the graph of the fraction of A remaining as a function of time is a straight line with a negative slope, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Reaction**:
The reaction is given as \( A \rightarrow \text{products} \). We are interested in the concentration of A over time.

2. **Define Initial Conditions**:
At time \( t = 0 \), the concentration of A is \( [A]_0 = A \) and the concentration of products is \( [B] = 0 \).

3. **Express Fraction of A Remaining**:
At time \( t \), if \( x \) is the amount of A that has reacted, then the concentration of A remaining is:
\[ [A] = A - x \]
The fraction of A remaining at time \( t \) can be expressed as:
\[ \text{Fraction of A remaining} = \frac{[A]}{[A]_0} = \frac{A - x}{A} \]

4. **Graph Interpretation**:
The problem states that the graph of the fraction of A remaining as a function of time is a straight line with a negative slope. This indicates a linear relationship between the fraction of A remaining and time.

5. **Linear Equation Form**:
A straight line can be expressed in the form:
\[ y = mx + c \]
where \( y \) is the fraction of A remaining, \( m \) is the slope (negative in this case), \( x \) is time, and \( c \) is the y-intercept.

6. **Identify the Order of Reaction**:
For a zero-order reaction, the rate of reaction is constant, and the concentration of A decreases linearly over time. The equation for a zero-order reaction can be written as:
\[ [A] = [A]_0 - kt \]
which rearranges to show that the fraction of A remaining decreases linearly with time.

7. **Conclusion**:
Since the graph is a straight line with a negative slope, this indicates that the reaction is a zero-order reaction.

### Final Answer:
The order of the reaction is **zero-order**.

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