In the presence of acid, the initial concentration of cane sugar was reduced from 0.2 M to 0.1 M in 5 h and to 0.05 M in 10 h. The reaction must be of

Options

A. zero order
B. first order
C. second order
D. fractional order

Explanation

To determine the order of the reaction based on the given data, we can follow these steps:

### Step 1: Gather the Given Data
The initial concentration of cane sugar is given as:
- Initial concentration (C₀) = 0.2 M
- Concentration after 5 hours (C₁) = 0.1 M
- Concentration after 10 hours (C₂) = 0.05 M

### Step 2: Analyze the Concentration Changes
- The concentration decreases from 0.2 M to 0.1 M in 5 hours.
- The concentration decreases from 0.1 M to 0.05 M in the next 5 hours.

### Step 3: Identify the Time Intervals
- The first interval (from 0.2 M to 0.1 M) takes 5 hours.
- The second interval (from 0.1 M to 0.05 M) also takes 5 hours.

### Step 4: Determine the Relationship Between Concentrations and Time
Notice that:
- The concentration is halved from 0.2 M to 0.1 M in 5 hours.
- The concentration is halved again from 0.1 M to 0.05 M in another 5 hours.

This indicates that the time taken to halve the concentration (T₁/₂) is constant.

### Step 5: Conclude the Order of the Reaction
In first-order reactions, the half-life (T₁/₂) is independent of the initial concentration. Since we observe that the time taken to halve the concentration remains constant regardless of the starting concentration, we can conclude that the reaction is first-order.

### Final Answer
The reaction must be of **first order**.

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