Question

The fluorescence lifetime of benzene in cyclohexane is 29 ns when air is completely removed. in the presence of 0.0072 m dissolved O2 , the measured fluorescence lifetime is 5.7 ns because of quenching.

Calculate the rate constant kQ for the quenching reaction

Answer 1

To calculate the quenching rate constant (kQ) for benzene, use the Stern-Volmer equation with the provided fluorescence lifetimes and quencher concentration, solving for kQ.

Step-by-step explanation:

The question involves the calculation of the quenching rate constant (kQ) for the reaction of benzene with dissolved O2 which decreases the fluorescence lifetime of benzene. To find the rate constant for quenching (kQ), we can use the Stern-Volmer equation, which relates the fluorescence lifetimes in the absence and presence of a quencher:

\( \frac{\tau_0}{\tau} = 1 + k_Q \times [Q] \times \tau_0 \)

where:

• \(\tau_0\) is the fluorescence lifetime without the quencher (29 ns),
• \(\tau\) is the fluorescence lifetime with the quencher (5.7 ns),
• \([Q]\) is the concentration of the quencher (0.0072 M), and
• \(k_Q\) is the quenching rate constant.

Plugging in the given values, we get:

\( \frac{29}{5.7} = 1 + k_Q \times 0.0072 \times 29 \)

Solving for kQ provides us the quenching rate constant value. This application is crucial in understanding reaction mechanisms and dynamics in photochemical processes.