For a reaction `R to P`, the concentration of a reactant changes from 0.05 M to 0.04 M min 30 minutes. What will be average rate of reaction in minutes?

Options

A. `4 xx 10^(-4) M "min"^(-1)`
B. `8 xx 10^(-4) "min"^(-1)`
C. `3.3 xx 10^(-4) M "mim"^(-1)`
D. `2.2 xx 10^(-4) M "mim"^(-1)`

Explanation

To solve the problem step by step, we will calculate the average rate of the reaction based on the change in concentration of the reactant over time.

### Step 1: Identify the initial and final concentrations
- Initial concentration of reactant (R) = 0.05 M
- Final concentration of reactant (R) = 0.04 M

### Step 2: Calculate the change in concentration (ΔR)
- Change in concentration (ΔR) = Final concentration - Initial concentration
- ΔR = 0.04 M - 0.05 M = -0.01 M

### Step 3: Identify the change in time (ΔT)
- The time period over which this change occurs is given as 30 minutes.
- ΔT = 30 minutes

### Step 4: Write the formula for average rate of reaction
The average rate of reaction is defined as:
\[ \text{Average Rate} = -\frac{\Delta R}{\Delta T} \]
where ΔR is the change in concentration of the reactant and ΔT is the change in time.

### Step 5: Substitute the values into the formula
- Substitute ΔR = -0.01 M and ΔT = 30 minutes into the formula:
\[ \text{Average Rate} = -\frac{-0.01 \text{ M}}{30 \text{ min}} \]

### Step 6: Calculate the average rate
- The negative signs cancel out:
\[ \text{Average Rate} = \frac{0.01 \text{ M}}{30 \text{ min}} \]
\[ \text{Average Rate} = 0.0003333 \text{ M/min} \]
- To express this in scientific notation:
\[ \text{Average Rate} = 3.33 \times 10^{-4} \text{ M/min} \]

### Final Answer
The average rate of the reaction is \( 3.33 \times 10^{-4} \text{ M/min} \).

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