In a reaction `2X to Y`, the concentration of X decreases from 3.0 mole/litre to 2.0 moles/litre in 5 minutes. The rate of reaction is

Options

A. 0.1 mol `L^(-1) "min"^(-1)`
B. 5 mol `L^(-1) "min"^(-1)`
C. 1 mol `L^(-1) "min"^(-1)`
D. 0.5 mol `L^(-1) "min"^(-1)`

Explanation

To find the rate of the reaction given the decrease in concentration of reactant X, we can follow these steps:

### Step 1: Identify the change in concentration
The initial concentration of X is 3.0 moles/litre, and the final concentration after 5 minutes is 2.0 moles/litre.

\[ \Delta [X] = [X]_{\text{final}} - [X]_{\text{initial}} = 2.0 \, \text{mol/L} - 3.0 \, \text{mol/L} = -1.0 \, \text{mol/L} \]

### Step 2: Calculate the change in concentration over time
The change in concentration occurs over a time interval of 5 minutes.

\[ \Delta t = 5 \, \text{minutes} \]

### Step 3: Calculate the rate of reaction
The rate of reaction can be expressed as:

\[ \text{Rate} = -\frac{1}{2} \frac{\Delta [X]}{\Delta t} \]

Here, the factor of \(-\frac{1}{2}\) accounts for the stoichiometry of the reaction \(2X \rightarrow Y\), meaning that for every 2 moles of X that react, the rate is calculated based on the change in concentration of X.

Substituting the values:

\[ \text{Rate} = -\frac{1}{2} \frac{-1.0 \, \text{mol/L}}{5 \, \text{minutes}} = \frac{1.0 \, \text{mol/L}}{10 \, \text{minutes}} = 0.1 \, \text{mol/L/minute} \]

### Step 4: Write the final answer
The rate of the reaction is:

\[ \text{Rate} = 0.1 \, \text{mol/L/minute} \]