It takes 338 kJ/mol to break an carbon chlorine single bond calculate the maximum wavelength of light which an carbon chlorine single bond could be broken by absorbing a single photon
Be sure your answer has correct number of significant digits in nm
To find the maximum wavelength of light which a carbon-chlorine single bond could be broken by absorbing a single photon, we can use the equation:
E = hc/λ
Where:
E = energy required to break the bond (in joules)
h = Planck's constant (6.62607015 × 10^-34 J·s)
c = speed of light (2.998 × 10^8 m/s)
λ = wavelength of light (in meters)
First, let's convert the energy required to break the bond from kJ/mol to joules per molecule:
338 kJ/mol = 338,000 J/6.022 × 10^23 molecules
Now, we can calculate the energy required to break a single bond:
Energy per molecule = 338,000 J/ 6.022 × 10^23 molecules = 5.612 × 10^-19 J
Next, we need to convert this energy into electron volts (eV) by dividing it by the elementary charge, which is 1.602176634 × 10^-19 C:
Energy in eV = (5.612 × 10^-19 J) / (1.602176634 × 10^-19 C) = 3.5 eV
Now, we can rearrange the energy equation to solve for the wavelength:
λ = hc / E
Plugging in the values:
λ = (6.62607015 × 10^-34 J·s * 2.998 × 10^8 m/s) / (3.5 eV * 1.602176634 × 10^-19 J/C)
Calculating this equation gives us:
λ ≈ 1.769 × 10^-7 meters
Finally, let's convert this into nanometers:
λ ≈ 1.769 × 10^-7 meters * 10^9 nm/m = 176.9 nm
So, the maximum wavelength of light which a carbon-chlorine single bond could be broken by absorbing a single photon is approximately 176.9 nm.
To calculate the maximum wavelength of light required to break a carbon-chlorine single bond by absorbing a single photon, we need to use the relationship between energy and wavelength, which is given by the equation:
E = hc/λ
Where:
E is the energy of the photon
h is Planck's constant (6.62607015 × 10^-34 J·s)
c is the speed of light (2.998 × 10^8 m/s)
λ is the wavelength of the light
First, let's convert the energy of breaking one mole of carbon-chlorine single bond to joules:
Energy = 338 kJ/mol × (1 mol / 6.022 × 10^23 molecules) × (1000 J / 1 kJ) = 5.61 × 10^-19 J
Now, we can rearrange the equation to solve for the wavelength (λ):
λ = hc / E
Substituting the values:
λ = (6.62607015 × 10^-34 J·s) × (2.998 × 10^8 m/s) / (5.61 × 10^-19 J)
Calculating this expression gives us:
λ ≈ 3.528 × 10^-7 m
Finally, we need to convert this wavelength to nanometers:
λ (nm) = (3.528 × 10^-7 m) × (10^9 nm / 1 m) ≈ 352.8 nm
Therefore, the maximum wavelength of light that can break a carbon-chlorine single bond by absorbing a single photon is approximately 352.8 nm, with three significant digits.
To calculate the maximum wavelength of light required to break a carbon-chlorine single bond, we can use the energy formula E = hc/λ, where E is the energy of a photon, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength of light.
First, we need to convert the energy given in kilojoules per mole (kJ/mol) to joules per molecule (J). Since there are Avogadro's number (6.022 x 10^23) of molecules in one mole, we can use the conversion factor:
(338 kJ/mol) × (1000 J/1 kJ) ÷ (6.022 x 10^23 molecules/1 mol)
This will give us the energy required to break a single bond in joules.
Next, we substitute the obtained energy value into the energy formula to calculate the wavelength:
E = hc/λ
λ = hc/E
λ = (6.626 x 10^-34 J·s) × (3.00 x 10^8 m/s) / (energy in joules)
Finally, we convert the wavelength from meters (m) to nanometers (nm) using the conversion factor:
(λ in meters) × (10^9 nm/1 m)
Calculating the above equation with the given information will provide you with the maximum wavelength of light needed to break a carbon-chlorine single bond. Ensure that you round your final answer to the correct number of significant digits in nanometers.