It takes 146kJ/mol to break a oxygen oxygen single bond calculate the maximum wavelength of light for which a oxygen oxygen single 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 for which an oxygen-oxygen 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 (convert kJ to J by multiplying by 1000)
h = Planck's constant (6.62607015 × 10^-34 J·s)
c = speed of light in a vacuum (3.00 × 10^8 m/s)
λ = wavelength of light in meters (convert nm to m by dividing by 10^9)
First, let's convert the energy required to break the bond to joules:
146 kJ/mol * (1000 J/kJ) = 146,000 J/mol
Now we need to convert this to energy required per molecule. Since there is Avogadro's number (6.02214076 × 10^23) of molecules in a mole:
146,000 J/mol / (6.02214076 × 10^23 molecules/mol) = 2.42 × 10^-19 J/molecule
Now, we can substitute the values into the equation:
2.42 × 10^-19 J = (6.62607015 × 10^-34 J·s)(3.00 × 10^8 m/s) / λ
Rearranging the equation to solve for λ:
λ = (6.62607015 × 10^-34 J·s)(3.00 × 10^8 m/s) / (2.42 × 10^-19 J)
λ ≈ 8.21 × 10^-7 meters
Converting this value to nanometers:
λ ≈ 8.21 × 10^-7 meters * (10^9 nm/1 meter) ≈ 821 nm
Therefore, the maximum wavelength of light for which an oxygen-oxygen single bond could be broken by absorbing a single photon is approximately 821 nm.
To calculate the maximum wavelength of light needed to break an oxygen-oxygen single bond, you can use the formula:
E = hc/λ
Where:
E = energy required to break the bond (in joules)
h = Planck's constant (6.626 x 10^-34 J·s)
c = speed of light (2.998 x 10^8 m/s)
λ = wavelength of light (in meters)
First, convert the energy required to break the bond from kilojoules per mole (kJ/mol) to joules:
146 kJ/mol * (1 mole / 6.022 x 10^23 molecules) * (1000 J / 1 kJ) = 2.425 x 10^-19 J
Now, rearrange the formula to solve for wavelength:
λ = hc / E
λ = (6.626 x 10^-34 J·s) * (2.998 x 10^8 m/s) / (2.425 x 10^-19 J)
Calculating the value:
λ = 8.185 x 10^-7 m
Finally, convert the wavelength from meters to nanometers:
λ (nm) = (8.185 x 10^-7 m) * (1 nm / 10^-9 m)
Calculating the value:
λ (nm) = 818.5 nm
Therefore, the maximum wavelength of light required to break an oxygen-oxygen single bond is approximately 818.5 nm.
To calculate the maximum wavelength of light required to break an oxygen-oxygen single bond, we can use the equation:
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 (2.998 x 10^8 m/s), and λ is the wavelength of light.
First, let's convert the given energy from kJ/mol to J/molecule:
1 kJ/mol = 1000 J/mol
146 kJ/mol = 146,000 J/mol
To convert energy to J/molecule, we need to divide by Avogadro's number (6.022 x 10^23 molecules/mol):
146,000 J/mol / (6.022 x 10^23 molecules/mol) = 2.42 x 10^-19 J/molecule
Now we can substitute this value of E into the equation and solve for λ:
E = hc/λ
2.42 x 10^-19 J/molecule = (6.626 x 10^-34 J·s)(2.998 x 10^8 m/s)/λ
Solving for λ, we get:
λ = (6.626 x 10^-34 J·s)(2.998 x 10^8 m/s) / (2.42 x 10^-19 J/molecule)
λ = 8.218 x 10^-7 m
However, we need to convert the result to nanometers (nm). Since 1 meter (m) is equal to 10^9 nanometers (nm), we can multiply our result by 10^9:
λ = 8.218 x 10^-7 m * 10^9 nm
λ = 8.218 x 10^2 nm
Therefore, the maximum wavelength of light required to break an oxygen-oxygen single bond is approximately 821.8 nm.