It takes 614 kJ/mol to break a carbon carbon double bond calculate the maximum wavelength of light for which a carbon carbon double bond could be broken by absorbing a single photon
Be sure your answer has correct number of significant digits in nm
To calculate the maximum wavelength of light, we can use the equation E = hc/λ, where E is the energy of the photon, h is Planck's constant (6.62607015 × 10^-34 Js), c is the speed of light (2.998 × 10^8 m/s), and λ is the wavelength of light.
First, let's convert the given energy from kJ/mol to J/photon:
614 kJ/mol * (1000 J/1 kJ) / Avogadro's number = 1.025 × 10^-19 J/photon
Now we can rearrange the equation and solve for λ:
λ = hc/E
λ = (6.62607015 × 10^-34 Js * 2.998 × 10^8 m/s) / (1.025 × 10^-19 J/photon)
λ = 6.454 × 10^-7 m
Finally, we convert the wavelength from meters to nanometers:
λ = 6.454 × 10^-7 m * (10^9 nm/ 1 m)
λ ≈ 645.4 nm
Therefore, the maximum wavelength of light for which a carbon-carbon double bond could be broken by absorbing a single photon is 645.4 nm.
To calculate the maximum wavelength of light that a carbon-carbon double bond could be broken by absorbing a single photon, we need to use the equation:
E = hc/λ
Where:
E is the energy required to break the bond (in Joules/mol)
h is Planck's constant (6.626 x 10^-34 J.s)
c is the speed of light (2.998 x 10^8 m/s)
λ is the wavelength of light (in meters)
First, let's convert the energy required to break the bond from kJ/mol to J/mol:
E = 614 kJ/mol = 614 x 10^3 J/mol
Next, let's rearrange the equation to solve for the wavelength:
λ = hc/E
Now we can substitute the given values into the equation:
λ = (6.626 x 10^-34 J.s) * (2.998 x 10^8 m/s) / (614 x 10^3 J/mol)
Simplifying the equation gives:
λ = (1.2 x 10^-6 m)/(614 x 10^3 J/mol)
λ = 1.95 x 10^-9 m
Finally, let's convert the wavelength from meters to nanometers by multiplying by 10^9:
λ = 1.95 x 10^-9 m * 10^9 nm/m
The maximum wavelength of light for which a carbon-carbon double bond could be broken by absorbing a single photon is approximately 1.95 nm.
To calculate the maximum wavelength of light for which a carbon-carbon double bond could be broken by absorbing a single photon, we can use the equation:
ΔE = hc/λ
Where:
ΔE is the energy required to break the bond
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 light
First, we need to convert the energy required to break the bond from kilojoules per mole (kJ/mol) to joules (J):
ΔE = 614 kJ/mol × (1000 J/1 kJ) = 614,000 J/mol
Next, we need to convert the energy per mole to energy per photon by dividing by Avogadro's number (6.02214076 × 10^23 mol^-1):
ΔE = 614,000 J/mol ÷ (6.02214076 × 10^23 mol^-1) = 1.020 × 10^-18 J/photon
Now we can rearrange the equation to solve for the wavelength (λ):
λ = hc/ΔE
Substituting the values:
λ = (6.62607015 × 10^-34 J·s) × (2.998 × 10^8 m/s) ÷ (1.020 × 10^-18 J/photon)
Calculating this expression gives us the wavelength in meters. To convert it to nanometers, we multiply the result by 10^9:
λ = (6.62607015 × 10^-34 × 2.998 × 10^8) ÷ (1.020 × 10^-18) × 10^9
Simplifying the equation, we get:
λ = 588 nm
Therefore, the maximum wavelength of light for the carbon-carbon double bond to be broken by absorbing a single photon is approximately 588 nm.