AgCl >Ag + Cl
The silver metal that is formed causes the lenses to darken. The enthalpy change for this reaction is 3.10 102 kJ/mol. Assuming all this energy must be supplied by light, what is the maximum wavelength of light that can cause this reaction?
386nm
E = hc/wavelength.
You know E, h, and c. Calculate wavelength.
thats not E, its kJ/mol
E IS measured in Joules. You will need to change kJ to Joules by multiplying by 1000. And you will need to convert from a mol to a single photon by dividing by Avogadro's number;however, that is the proper equation to use. OR you could use
E = h*frequency but the question asks for wavelength and you get it with one equation if you use the first one and it takes the second equation + a third one; i.e., c = wavelength*frequency if you use the second one.
Well, it seems like these silver atoms really like to darken lenses! To figure out the maximum wavelength of light that can cause this reaction, we need to use a little equation called the energy-wavelength relationship.
Now, the energy of a photon of light can be calculated using the equation E = hc/λ, where E is the energy, h is Planck's constant, c is the speed of light, and λ is the wavelength.
Since the enthalpy change for the reaction is given as 3.10 x 10^2 kJ/mol, we can calculate the energy change per mole using good old Avogadro's number. Dividing the enthalpy change by Avogadro's number will give us the energy change per particle.
Once we have the energy change per particle, we can plug it into the energy-wavelength equation and simply solve for λ.
So, let's get this clown show on the road!
To determine the maximum wavelength of light that can cause the given reaction, we need to consider the relationship between energy, wavelength, and frequency of light.
The energy of a photon is given by the equation:
E = hc/λ
Where:
E = energy of the photon
h = Planck's constant (6.626 x 10^-34 J·s)
c = speed of light in a vacuum (3.0 x 10^8 m/s)
λ = wavelength of light
Since the enthalpy change for the reaction is given as 3.10 x 10^2 kJ/mol, we need to convert this to energy per mole.
1 kJ = 1000 J
1 mol = 6.022 x 10^23 particles
So, the energy per particle (E per mole) is:
Energy per mole = (3.10 x 10^2 kJ/mol) × (1000 J/1 kJ) / (6.022 x 10^23 particles/1 mol)
Now, let's calculate the energy per particle:
Energy per particle = [(3.10 x 10^2 kJ/mol) × (1000 J/1 kJ)] / (6.022 x 10^23 particles/1 mol)
Next, we can calculate the energy of a single photon by dividing the energy per particle by Avogadro’s number (6.022 x 10^23):
Energy per photon = [(3.10 x 10^2 kJ/mol) × (1000 J/1 kJ)] / (6.022 x 10^23 particles/1 mol) / (6.022 x 10^23 particles)
Now that we have the energy per photon, we can rearrange the equation E = hc/λ to solve for wavelength (λ):
λ = hc / E
Lastly, substitute the values of Planck's constant (h) and the speed of light (c) into the equation:
λ = (6.626 x 10^-34 J·s) × (3.0 x 10^8 m/s) / Energy per photon
Now, plug in the value of the energy per photon that we calculated earlier, and solve for the maximum wavelength by converting it to the appropriate unit.
The final result will give you the maximum wavelength of light that can cause the given reaction.