Assuming total absorption of the light by the sample, what is the maximum amount (in moles) of CH3X that breaks apart when a cuvette containing a solution of CH3X is irradiated with 280-nm light with a power of 885 mW for 10.0 minutes, given that the quantum yield for the reaction CH3X → CH3 + X is f = 0.24?

Verified step by step guidance

1. 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}), \( c \) is the speed of light (3.00 \times 10^8 \text{ m/s}), and \( \lambda \) is the wavelength (280 \text{ nm} = 280 \times 10^{-9} \text{ m}).
2. Determine the total energy supplied by the light source using the formula: \( \text{Total Energy} = \text{Power} \times \text{Time} \), where the power is 885 mW (or 885 \times 10^{-3} \text{ W}) and the time is 10.0 minutes (or 600 seconds).
3. Calculate the total number of photons using the formula: \( \text{Number of Photons} = \frac{\text{Total Energy}}{E} \), where \( E \) is the energy of a single photon calculated in step 1.
4. Use the quantum yield (\( f = 0.24 \)) to find the number of moles of CH3X that dissociate. The formula is: \( \text{Moles of CH3X} = \frac{\text{Number of Photons} \times f}{N_A} \), where \( N_A \) is Avogadro's number (6.022 \times 10^{23} \text{ mol}^{-1}).
5. The result from step 4 gives the maximum amount of CH3X in moles that breaks apart under the given conditions.

Key Concepts

Quantum Yield

Quantum yield is a measure of the efficiency of a photochemical reaction, defined as the ratio of the number of molecules that react to the number of photons absorbed. In this case, a quantum yield of 0.24 indicates that for every four photons absorbed, one molecule of CH3X breaks apart. Understanding quantum yield is crucial for calculating the amount of substance that reacts under specific light conditions.

Photon Energy and Light Power

The energy of a photon is determined by its wavelength, with shorter wavelengths corresponding to higher energy. The power of the light source, measured in milliwatts (mW), indicates the rate at which energy is emitted. To find the total energy delivered over a period, one must multiply the power by the time in seconds, which is essential for determining how many photons are available to induce the reaction.

Moles and Stoichiometry

A mole is a unit in chemistry that represents 6.022 x 10²³ entities, such as atoms or molecules. Stoichiometry involves the calculation of reactants and products in chemical reactions based on balanced equations. In this context, understanding how to convert the number of photons absorbed into moles of CH3X that dissociate is vital for solving the problem and determining the maximum amount of substance that reacts.