For a certain reaction `R to` products, a plot of log [R] versus time gives a straight line with a slope of `-1.46"sec"^(-1)` The order of reaction is

Options

A. Zero
B. One
C. two or a half
D. Fractional

Explanation

To determine the order of the reaction based on the provided information, we can follow these steps:

### Step 1: Understand the relationship between concentration and time for different orders of reactions.
- For a zero-order reaction: [R] vs. time is linear.
- For a first-order reaction: ln[R] vs. time is linear.
- For a second-order reaction: 1/[R] vs. time is linear.

### Step 2: Analyze the given information.
- We are given that a plot of log [R] versus time gives a straight line. This suggests that the reaction follows first-order kinetics because the first-order reaction is characterized by a linear relationship when plotting the natural logarithm of the concentration.

### Step 3: Identify the slope of the line.
- The slope of the line is given as -1.46 sec^(-1). This value is indicative of the rate constant (k) for a first-order reaction.

### Step 4: Relate the slope to the order of the reaction.
- For first-order reactions, the rate constant (k) has units of time^(-1) (e.g., sec^(-1)). The negative slope indicates the decrease in concentration over time, which is consistent with first-order kinetics.

### Step 5: Conclude the order of the reaction.
- Since the plot of log [R] versus time is linear and the slope corresponds to a first-order rate constant, we conclude that the reaction is a **first-order reaction**.

### Final Answer:
The order of the reaction is **1** (first order).

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