A student is studying the photodissociation (dissociation with light) of I2 into 2I. When a sample of I2 is irradiated with a power of 255 mW at 590 nm for 35 seconds, 0.0256 mmol of I forms. Assuming complete absorption of the incident radiation, what is the quantum yield, f, of the reaction? (See Problem 93 for definition of quantum yield.)

Verified step by step guidance

1. Identify the given values: power (P) = 255 mW, wavelength (\(\lambda\)) = 590 nm, time (t) = 35 s, moles of I formed = 0.0256 mmol.
2. Convert the power from milliwatts to watts: 1 mW = 0.001 W, so 255 mW = 0.255 W.
3. Calculate the energy of a single photon using the formula \(E = \frac{hc}{\lambda}\), where \(h\) is Planck's constant (6.626 \times 10^{-34} \text{ J s}) and \(c\) is the speed of light (3.00 \times 10^8 \text{ m/s}). Convert \(\lambda\) from nm to meters.
4. Calculate the total energy absorbed by the sample using the formula \(\text{Total Energy} = P \times t\).
5. Determine the number of photons absorbed using the formula \(\text{Number of photons} = \frac{\text{Total Energy}}{E}\), and then calculate the quantum yield \(f\) using \(f = \frac{\text{moles of I formed}}{\text{Number of photons absorbed}}\).

Key Concepts

Photodissociation

Photodissociation is a process in which a chemical compound breaks down into its components upon absorbing light. In the case of I2, the molecule absorbs photons, leading to the dissociation into two iodine atoms (2I). Understanding this concept is crucial for analyzing reactions that involve light as a driving force for breaking chemical bonds.

Quantum Yield

Quantum yield (f) is a measure of the efficiency of a photochemical reaction, defined as the ratio of the number of molecules reacted to the number of photons absorbed. It provides insight into how effectively light energy is converted into chemical energy. A quantum yield greater than one indicates that more products are formed than the number of photons absorbed, while a yield less than one suggests inefficiencies in the process.

Power and Energy Calculations

Power, measured in watts (W), is the rate at which energy is delivered or consumed. In photodissociation, the power of the light source can be used to calculate the total energy delivered over a specific time period. This energy is essential for determining the number of photons absorbed, which is necessary for calculating the quantum yield of the reaction.