Identify the given integrated rate equation

The question gives: $Rt = \log C_0 - \log C_t$

where $R$ is a constant, $C_0$ is the initial concentration, and $C_t$ is the concentration at time $t$.

Rearrange into straight-line form

We write: $\log C_t = \log C_0 - Rt$

This is of the form: $y = c + mx$

with

• $y = \log C_t$
• $x = t$
• intercept $= \log C_0$
• slope $= -R$

Interpret the graph

So, a plot of $\log C_t$ versus $t$ gives a straight line.

Equivalently, plotting time vs $\log C_t$ also represents a linear relation between the two variables.

Check the options

• A: time vs $\log C_t$ → linear relation ✔️
• B: $\dfrac{1}{\text{time}}$ vs $C_t$ → not linear ✖️
• C: time vs $C_t$ → not linear ✖️
• D: $\dfrac{1}{\text{time}}$ vs $\dfrac{1}{C_t}$ → not linear ✖️

Final answer

The correct option is: $\boxed{A}$