The quantum yield of light-induced chemical reactions...

The quantum yield of light-induced chemical reactions (called photochemical reactions) measures the efficiency of the process. The quantum yield, $\phi, \quad$ is defined as: $$\phi=\frac{\text { number of reaction events }}{\text { number of photons absorbed }}Suppose\quad the\quad quantum\quad yield$$ for the reaction $\mathrm{CH}_{3} \mathrm{X} \longrightarrow \mathrm{CH}_{3}+\mathrm{X}$ is $\phi=0.24 .$ A cuvette containing a solution of $\mathrm{CH}_{3} \mathrm{X}$ is irradiated with 280 -nm light with a power of 885 $\mathrm{mW}$ for 10.0 minutes. Assuming total absorption of the light by the sample, what is the maximum amount (in moles) of $\mathrm{CH}_{3} \mathrm{X}$ that breaks apart?

The quantum yield of light-induced chemical reactions (called photochemical reactions) measures the efficiency of the process. The quantum yield, $\phi, \quad$ is defined as:
$$\phi=\frac{\text { number of reaction events }}{\text { number of photons absorbed }}Suppose\quad the\quad quantum\quad yield$$
for the reaction $\mathrm{CH}_{3} \mathrm{X} \longrightarrow \mathrm{CH}_{3}+\mathrm{X}$ is $\phi=0.24 .$ A cuvette containing a solution of $\mathrm{CH}_{3} \mathrm{X}$ is irradiated with 280 -nm light with a power of 885 $\mathrm{mW}$ for 10.0 minutes. Assuming total absorption of the light by the sample, what is the maximum amount (in moles) of $\mathrm{CH}_{3} \mathrm{X}$ that breaks apart?

Key Concepts

Photon Flux Calculation from Light Power

Photon flux is determined from the power of the light source and the energy per photon, allowing one to calculate the total number of photons emitted or absorbed over a given time period. This concept is essential when analyzing how many reaction events can occur based on the number of photons available.

Quantum Yield

Quantum yield is a measure of the efficiency of a photochemical reaction, defined as the ratio of the number of reaction events (or product molecules formed) to the number of photons absorbed. It provides insight into how effectively absorbed light leads to the desired chemical transformation.

Photon Energy and Wavelength Relationship

The energy of a photon is directly related to its wavelength through Planck’s equation (E = hc/?), where h is Planck’s constant and c is the speed of light. This relationship is fundamental for converting wavelength or frequency information into energy values, which is key in photochemistry for quantifying photon interactions.

Stoichiometric Conversion Using Avogadro's Number

The conversion from the number of reaction events (or photons) to moles involves using Avogadro’s number, which relates the number of individual molecules or particles to a mole. This stoichiometric approach is crucial for quantitatively understanding the extent of chemical reaction in terms of moles.

Transcript

00:01 How's it going people? here, we're given a laser with a known wavelength and power.

00:05 We know the laser has shone on the material for 10 minutes, that material has a quantum yield of 0 .24, expressed in number of reactions per number of photons absorbed, and we have to calculate how many reactions in modes has occurred in the span of 10 minutes.

00:20 Now, let's gather our thoughts, make sure we know what we're calculating it for and what we need.

00:26 And i have rearranged the equation as the following, 0 .24.

00:30 Which is the quantum yield ratio, equal to number of reactions per number of photons absorb.

00:35 Let's rearrange this equation further.

00:38 We have number of reactions on one side.

00:41 The number of reactions is what we want in the end, which is equal to 0 .24 times number of photons.

00:48 Now, how do we calculate the number of photons from the given information? now, we know the wavelength of 280 nanometers.

00:56 We can calculate the energy.

00:57 The energy is expressed in energy per photon.

01:03 We know the power in milliwats, from millawatts.

01:08 We can calculate the energy total.

01:11 Because watts are basically joules per second, and the time span is 10 minutes.

01:16 So we can calculate how many energies in total have this laser produced in the span of 10 minutes overall.

01:23 So again, the wavelength gives us idea how many energy does one photon carry, and the power gives us the idea of how many energy total has this laser produced.

01:34 So we know the total energy.

01:35 We know the energy per photon, and that's how we calculate the number of photons.

01:42 All right, so john, we're jumping back into the reactions here.

01:45 I'll write this down at 0 .24 times the number of photons expressed in total energy, total energy received in 10 minutes over the energy per photon.

02:06 This is basically another expression for number of photons, but this way we can actually calculate from the raw numbers that we're given.

02:13 So we have 0 .24 times total energy.

02:18 As we said before, the total energy we can get from the watts ratio, the watts here.

02:23 We have 885 kilowatts of power here.

02:30 We note that 1 ,000 milawatt is basically 1 watt.

02:36 And we know that 1 watt is basically 1 joules per second.

02:41 And we know that 10 minutes have basically 10 times 60 seconds per minute.

02:56 That's our total energy calculation all down here...