It takes 157kJ/mol to break a nitrogen oxygen single bond calculate the maximum wavelength of light for which a nitrogen 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, we'll use 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 (2.998 x 10^8 m/s)
λ = wavelength of light (in meters)
First, we need to convert the energy from kJ/mol to J/mol and then to J:
1 kJ = 1000 J
1 mol = 6.022 x 10^23 molecules
Energy per molecule = 157 kJ/mol / (6.022 x 10^23 molecules/mol)
Energy per molecule = 2.61 x 10^-22 J
Now we can calculate the maximum wavelength using the equation:
E = hc/λ
λ = hc / E
λ = (6.626 x 10^-34 J · s) / (2.61 x 10^-22 J)
λ = 2.53 x 10^-12 m
Lastly, let's convert the wavelength from meters to nanometers:
1 m = 1 x 10^9 nm
λ = 2.53 x 10^-12 m * 1 x 10^9 nm/m
λ = 2.53 nm
Therefore, the maximum wavelength of light for which a nitrogen oxygen single bond could be broken by absorbing a single photon is 2.53 nm.
To calculate the maximum wavelength of light required to break a nitrogen-oxygen single bond, you can use the equation:
E = hc/λ
where E is the energy required to break the bond, 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, convert the given energy into joules:
Energy = 157 kJ/mol = 157 x 10^3 J/mol
Since we are dealing with a single bond, we can divide the energy by Avogadro's number to get the energy per molecule:
Energy per molecule = (157 x 10^3 J/mol) / (6.022 x 10^23 molecules/mol)
Now we can rearrange the equation to solve for the wavelength of light:
λ = hc/E
Substituting the values, we get:
λ = (6.626 x 10^-34 J·s) x (2.998 x 10^8 m/s) / (Energy per molecule)
Now, plug in the value for energy per molecule and calculate the maximum wavelength:
λ = (6.626 x 10^-34 J·s) x (2.998 x 10^8 m/s) / [(157 x 10^3 J/mol) / (6.022 x 10^23 molecules/mol)]
Calculating this expression will give you the maximum wavelength of light for breaking the nitrogen-oxygen single bond.
To calculate the maximum wavelength of light for which a nitrogen oxygen single 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 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 the light.
Given that it takes 157 kJ/mol to break a nitrogen oxygen single bond, we need to convert this energy to joules per bond.
1 kJ/mol is equal to 6.022 x 10^23 J/bond. Therefore, 157 kJ/mol is equal to (157 x 6.022 x 10^23) J/bond.
Next, we calculate the energy of a single bond:
(157 x 6.022 x 10^23) J/bond / 6.022 x 10^23 bonds/mol = 157 J/bond.
Now, we can substitute this energy value into the equation:
157 J/bond = (6.626 x 10^-34 J·s)(2.998 x 10^8 m/s)/λ
Rearranging the equation to solve for λ:
λ = (6.626 x 10^-34 J·s)(2.998 x 10^8 m/s) / 157 J/bond
Calculating the value of λ:
λ = 3.83384103 x 10^-9 m
Finally, we convert the wavelength from meters to nanometers by multiplying by 10^9:
λ = 3.83384103 x 10^-9 m x 10^9 nm/m = 383.384 nm
Therefore, the maximum wavelength of light for which a nitrogen oxygen single bond could be broken by absorbing a single photon is 383 nm (rounded to the nearest whole number) with appropriate significant digits.