In the plot of $\log\frac{[R]o}{[R]}$ versus time for a first order reaction (where [R] represents the concentration of the reactant), the slope and intercept are respectively equal to ______

k/2.303 and zero

The correct answer is Option (3) → k/2.303 and zero

For a first-order reaction:

$\ln [R] = \ln [R]_0 - k t$

Converting to base 10 logarithm:

$\log [R] = \log [R]_0 - \frac{k}{2.303} t$

Rewriting:

$\log \frac{[R]_0}{[R]} = \frac{k}{2.303} t$

• So, if we plot $\log([R]_0/[R])$) versus $t$:
• Slope = $\frac{k}{2.303}$​
• Intercept = 0