Question

For the reaction, \(A+B\rightarrow P\), the rate law is rate \(= k[A][B]^2\). The rate of reaction is \(0.25\text{ Ms}^{-1}\) when \([A] = 1\) M, \([B] = 0.2\) M at \(25^{\circ}\)C. Calculate the rate constant of the reaction at the same temperature.

• A. \(6.25\text{ M}^{-2}\text{s}^{-1}\)
• B. \(6.0\text{ M}^{-2}\text{s}^{-1}\)
• C. \(6.5\text{ M}^{-2}\text{s}^{-1}\)
• D. \(6.75\text{ M}^{-2}\text{s}^{-1}\)

Hint:

Substitute the given rate and concentrations into the rate law and solve for k.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The rate law links the rate of a reaction with the concentrations of the reactants. The constant of proportionality \(k\) is the rate constant.

Step 2: Key Formula or Approach:
\[ \text{rate} = k[A][B]^2 \Rightarrow k = \frac{\text{rate}}{[A][B]^2} \]

Step 3: Detailed Explanation:
\[ k = \frac{0.25}{(1)(0.2)^2} = \frac{0.25}{0.04} = 6.25 \]
The reaction is third order overall (1 + 2), so the unit of \(k\) is \(\text{M}^{-2}\text{s}^{-1}\).

Step 4: Check the options.
All four options have the correct unit. Only 6.25 equals \(0.25 / 0.04\).

Final Answer:
The rate constant is 6.25 \(\text{M}^{-2}\text{s}^{-1}\), option (A). \[ \boxed{6.25\ \text{M}^{-2}\text{s}^{-1}} \]