The concentration of a reactant decreases from 0.2 M to 0.1 M in 10 minutes . The rate of the reaction is ______.

Options

A. 0.01 M
B. `10^(-2)`
C. `0.01 mol dm^(-3) "min"^(-1) `
D. 1 mol

Answer

To find the rate of the reaction, we can follow these steps:

### Step 1: Identify the initial and final concentrations
- The initial concentration of the reactant is given as \( [A]_0 = 0.2 \, \text{M} \).
- The final concentration after the reaction is \( [A]_t = 0.1 \, \text{M} \).

### Step 2: Calculate the change in concentration
- The change in concentration (\( \Delta [A] \)) can be calculated as:
\[ \Delta [A] = [A]_0 - [A]_t = 0.2 \, \text{M} - 0.1 \, \text{M} = 0.1 \, \text{M} \]

### Step 3: Identify the time interval
- The time interval (\( \Delta t \)) during which this change occurs is given as \( 10 \, \text{minutes} \).

### Step 4: Calculate the rate of reaction
- The rate of reaction (\( r \)) is defined as the change in concentration over the change in time:
\[ r = \frac{\Delta [A]}{\Delta t} = \frac{0.1 \, \text{M}}{10 \, \text{minutes}} = 0.01 \, \text{M/min} \]

### Step 5: Write the final answer with units
- Thus, the rate of the reaction is:
\[ r = 0.01 \, \text{M/min} \]

### Final Answer:
The rate of the reaction is \( 0.01 \, \text{M/min} \).

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