Question

At 300 K a first order reaction is 50 % completed in 10 minutes. What is the rate constant value of the reaction at this temperature? \((\log 2 = 0.3)\)}

• A. \(1.15 \times 10^{-1} s^{-1}\)
• B. \(2.15 \times 10^{-1} s^{-1}\)
• C. \(1.15 \times 10^{-2} s^{-1}\)
• D. \(2.15 \times 10^{-3} s^{-1}\)
• E. \(1.15 \times 10^{-3} s^{-1}\)

Hint:

If a first order reaction is 50% complete, the given time is directly the half-life.

Answer 1

Answer: (E)

For first order reaction at 50% completion: \[ t_{1/2}=10 \text{ min} \] So: \[ k=\frac{0.693}{t_{1/2}} \] \[ k=\frac{0.693}{10\times 60} \] \[ k=\frac{0.693}{600}=1.155\times10^{-3}\text{ s}^{-1} \]
Hence, the correct answer is: \[ \boxed{(E)\ 1.15\times10^{-3}\text{ s}^{-1}} \]