For a reversible reaction \( R \rightleftharpoons P \), at constant temperature, both the forward and the backward reactions are first order elementary reactions with rate constants \( k_f \) and \( k_b \), respectively. At time zero, the concentration of \( R \) is \( [R]_0 \) and the concentration of \( P \) is zero. At any given time, \( [R] \) and \( [P] \) are the concentrations of \( R \) and \( P \), respectively. If \( k_b = 4k_f \), the correct graphical representation of the reaction is:
Show Hint
For a reversible first-order reaction,
\[
R \rightleftharpoons P
\]
remember the important relation:
\[
\frac{[P]_{eq}}{[R]_{eq}} = \frac{k_f}{k_b}
\]
After finding the equilibrium ratio, always apply conservation of total concentration:
\[
[R] + [P] = \text{constant}
\]
This makes equilibrium concentration calculations extremely fast in graphical and numerical problems.
