Decomposition of `H_2O_2` was studied by a titration against `KMnO_4` solution. It was found that 0.4 mole of `H_2O_2` was reduced to 0.2 mole in 20 minutes and to 0.1 mole in 40 minutes and to 0.05 mole after one hour. The order of reaction will be :

Options

A. 0
B. 1
C. 2
D. 3

Answer

To determine the order of the reaction for the decomposition of hydrogen peroxide (H₂O₂), we can analyze the data provided and apply the principles of chemical kinetics. Here’s a step-by-step solution:

### Step 1: Analyze the Data
We have the following data on the decomposition of H₂O₂:

- 0.4 moles of H₂O₂ reduced to 0.2 moles in 20 minutes.
- 0.2 moles reduced to 0.1 moles in 20 minutes (from 20 to 40 minutes).
- 0.1 moles reduced to 0.05 moles in 20 minutes (from 40 to 60 minutes).

### Step 2: Calculate the Change in Concentration
From the data:
- From 0.4 to 0.2 moles: Change = 0.2 moles in 20 minutes.
- From 0.2 to 0.1 moles: Change = 0.1 moles in 20 minutes.
- From 0.1 to 0.05 moles: Change = 0.05 moles in 20 minutes.

### Step 3: Determine the Rate of Reaction
The rate of reaction can be calculated as the change in concentration over time.

1. For the first interval (0.4 to 0.2 moles):
\[ \text{Rate}_1 = \frac{0.2 \text{ moles}}{20 \text{ minutes}} = 0.01 \text{ moles/min} \]

2. For the second interval (0.2 to 0.1 moles):
\[ \text{Rate}_2 = \frac{0.1 \text{ moles}}{20 \text{ minutes}} = 0.005 \text{ moles/min} \]

3. For the third interval (0.1 to 0.05 moles):
\[ \text{Rate}_3 = \frac{0.05 \text{ moles}}{20 \text{ minutes}} = 0.0025 \text{ moles/min} \]

### Step 4: Observe the Relationship Between Rate and Concentration
The rates of reaction are decreasing as the concentration of H₂O₂ decreases. This suggests that the reaction rate is dependent on the concentration of H₂O₂.

### Step 5: Identify the Order of Reaction
To identify the order of reaction, we can look at how the rate changes with concentration:

- The rate decreases as the concentration decreases, indicating that the reaction is not zero-order (where the rate would remain constant regardless of concentration).
- The rate is proportional to the concentration raised to a power.

### Step 6: Test for First Order
For a first-order reaction, the rate is directly proportional to the concentration of the reactant. We can express this as:
\[ \text{Rate} = k[\text{H}_2O_2] \]
If we take the natural logarithm of the concentration and plot it against time, we should see a linear relationship for a first-order reaction.

### Conclusion
Based on the decreasing rate of reaction with decreasing concentration and the analysis of the data, we conclude that the reaction follows first-order kinetics.

### Final Answer
The order of the reaction is **first order**.

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