It takes 498kJ/mol to break a oxygen oxygen doublebond calculate the maximum wavelength of light for which a oxygen oxygen 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 for which an oxygen-oxygen 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 (498 kJ/mol), h is Planck's constant (6.62607015 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 energy required to joules (J) from kJ/mole to J/mole:
498 kJ/mol = (498 x 10^3) J/mol = 4.98 x 10^5 J/mol
Now, we can rearrange the equation to solve for λ:
λ = hc/E
λ = (6.62607015 x 10^-34 J·s)(2.998 x 10^8 m/s)/(4.98 x 10^5 J/mol)
λ = (1.98644582 x 10^-25 J·m)/(4.98 x 10^5 J/mol)
λ = 3.98839259 x 10^-31 m/mol
Finally, we can convert m/mol to nm:
(3.98839259 x 10^-31 m/mol)(10^9 nm/1 m) = 3.98839259 x 10^-22 nm/mol
Therefore, the maximum wavelength of light for which an oxygen-oxygen double bond could be broken by absorbing a single photon is approximately 3.99 x 10^-22 nm, using the correct number of significant digits.
To calculate the maximum wavelength of light required to break an oxygen-oxygen double bond, we can use the equation:
E = hc/λ
where E is the energy of the 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.
To convert the given energy into joules, we can use the conversion factor:
1 kJ = 1000 J
Therefore, the energy of the photon (E) is:
E = (498 kJ/mol) x (1000 J/1 kJ) x (1 mol/6.022 x 10^23 molecules)
E = (498 x 1000) / (6.022 x 10^23) J
Now we can rearrange the equation to solve for λ:
λ = hc/E
λ = (6.626 x 10^-34 J s) x (2.998 x 10^8 m/s) / ((498 x 1000) / (6.022 x 10^23) J)
λ = (6.626 x 2.998 x 6.022) / (498 x 1000) 10^(-34 + 8 + 23) m
Now, let's calculate the maximum wavelength in nm by converting meters to nanometers:
1 m = 10^9 nm
λ = [(6.626 x 2.998 x 6.022) / (498 x 1000) ] 10^(-34 + 8 + 23 - 9) nm
λ = [39.9856 / 498] 10^(-12) nm
λ = 0.0801465863453815 x 10^(-12) nm
Since we need the correct number of significant digits in nm, the maximum wavelength of light that could break an oxygen-oxygen double bond is approximately 0.08 nm.
To calculate the maximum wavelength of light for which an oxygen-oxygen double bond could be broken by absorbing a single photon, we can use the equation:
E = hc/λ
where E is the energy of the photon, h is the Planck constant (6.62607015 × 10^-34 J·s), c is the speed of light (2.998 × 10^8 m/s), and λ is the wavelength of light.
First, we need to convert the given energy of breaking the double bond from kJ/mol to J/molecule. Since we know Avogadro's number (6.02214076 × 10^23 molecules/mol), we can convert the energy to J/molecule:
E_J = (498 kJ/mol) / (6.022 × 10^23 molecules/mol) = 8.27 × 10^(-20) J/molecule
Next, we can substitute this energy value into the equation to solve for the maximum wavelength:
E_J = hc/λ
Rearranging the equation to solve for λ, we have:
λ = hc/E_J
Plugging in the values for Planck's constant (h) and the speed of light (c), we get:
λ = (6.62607015 × 10^-34 J·s) * (2.998 × 10^8 m/s) / (8.27 × 10^(-20) J/molecule)
Calculating this expression will give us the maximum wavelength in meters. To convert this to nanometers (nm), we multiply the result by 10^9:
λ_nm = λ * 10^9
Performing the calculations, we find:
λ = 2.405 nm
Therefore, the maximum wavelength of light for which an oxygen-oxygen double bond could be broken by absorbing a single photon is 2.405 nm (rounded to the correct number of significant digits).