 Solution

Rearrangement gives the Stern-Volmer equationThus a straight-line plot against $[Q]$ has unit intercept and slope $K_{\mathrm{SV}}=k_Q{\tau }_0$. Determine $k_Q=K_{\mathrm{SV}}/{\tau }_0$ using an independently measured unquenched lifetime, or use known $k_F$ in the restricted model. Yield measurements alone do not separate two unknown rate constants. Equivalently the slope of $1/{\varphi }_Q$ is $k_Q/k_F$.

Use the absorbed intensity rather than incident intensity to normalize samples, and correct solvent/background signals, quencher absorption and fluorescence reabsorption. Under dynamic fluorescence quenching the lifetime ratio should follow the same straight line as the yield ratio. A reduced intensity without the corresponding lifetime change suggests static fluorescence quenching or an optical artefact; curvature can also indicate multiple populations or more complicated kinetics.