Question

Consider a first order reaction: \[ A \rightarrow \text{products} \] 3 different solutions are taken and the rate of reaction of: Solution 1: 100 mL 10M \( A \) \( \rightarrow r_1 \) Solution 2: 200 mL 10M \( A \) \( \rightarrow r_2 \) Solution 3: 100 mL 10M \( A \) + 100 mL water \( \rightarrow r_3 \) The correct order of the rates of reactions is,

• A. \( r_1 = r_2 = r_3 \)
• B. \( r_1 = r_2<r_3 \)
• C. \( r_1 = r_2>r_3 \)
• D. \( r_1<r_2 = r_3 \)

Hint:

For a first-order reaction, the rate depends linearly on the concentration of the reactant.

Answer 1

The Correct Option is C

Step 1: Rate law for first-order reaction.
For a first-order reaction, the rate is directly proportional to the concentration of the reactant. Therefore, the rate of reaction will be: \[ \text{Rate} = k[A] \] Step 2: Solution analysis.
- In Solution 1 and Solution 2, the concentration of \( A \) is the same (10M), but the volume is different, so the rate depends on the concentration. Hence, \( r_1 = r_2 \). - In Solution 3, the concentration of \( A \) is halved due to the addition of water, leading to a smaller rate \( r_3 \). Step 3: Conclusion.
Thus, \( r_1 = r_2>r_3 \). Final Answer: \[ \boxed{r_1 = r_2>r_3} \]