Question

The slope of a graph $\log[A]_t$ versus 't' for first order reaction is $-2.5\times10^{-3}s^{-1}$. Find rate constant of the reaction?

• A. $1.263\times10^{-3}s^{-1}$
• B. $3.471\times10^{-3}s^{-1}$
• C. $5.757\times10^{-3}s^{-1}$
• D. $8.125\times10^{-3}s^{-1}$

Hint:

Always multiply slope by 2.303 if the graph uses $\log_{10}$.

Answer 1

The Correct Option is C

Step 1: Formula
For 1st order: $\log[A]_t = \log[A]_0 - \frac{kt}{2.303}$. The slope of $\log[A]$ vs $t$ is $-k/2.303$.

Step 2: Analysis
$Slope = -2.5 \times 10^{-3} = -k / 2.303$

Step 3: Calculation
$k = 2.5 \times 10^{-3} \times 2.303$
$k = 5.7575 \times 10^{-3}$

Step 4: Conclusion
Hence, the rate constant is $5.757 \times 10^{-3}s^{-1}$. Final Answer: (C)