It takes 839 kJ/mol to break a carbon carbon triple bond calculate the maximum wavelength of light for which a carbon carbon triple 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 a carbon-carbon triple bond could be broken by absorbing a single photon, we will use the equation:
ΔE = hc/λ
Where:
ΔE is the energy required to break the bond, which is given as 839 kJ/mol.
h is the Planck 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, let's convert the energy from kJ/mol to J:
ΔE = 839 kJ/mol * (1000 J/1 kJ) = 839,000 J/mol
To calculate the energy per photon, we need to divide ΔE by Avogadro's number (6.022 x 10^23 mol^-1):
Energy per photon = ΔE / Avogadro's number = 839,000 J/mol / (6.022 x 10^23 mol^-1) = 1.394 x 10^-18 J
Now we can rearrange the equation to solve for the wavelength:
λ = hc / ΔE
Substituting the known values:
λ = (6.62607015 × 10^-34 J·s * 2.998 × 10^8 m/s) / (1.394 x 10^-18 J)
λ = 143.31 nm
Therefore, the maximum wavelength of light for which a carbon-carbon triple bond could be broken by absorbing a single photon is approximately 143.31 nm (rounded to the correct number of significant digits).
To calculate the maximum wavelength of light for which a carbon-carbon triple bond could be broken by absorbing a single photon, we can use the equation:
E = hc / λ
Where:
E = energy needed to break the bond (839 kJ/mol or 839 * 10^3 J/mol),
h = Planck's constant (6.62607015 × 10^-34 J*s),
c = speed of light (2.998 × 10^8 m/s),
λ = wavelength of light.
First, let's convert the energy into joules:
839 kJ/mol = 839 * 10^3 J/mol
Now, we can rearrange the equation to solve for λ:
λ = hc / E
Substituting the values:
λ = (6.62607015 × 10^-34 J*s * 2.998 × 10^8 m/s) / (839 * 10^3 J/mol)
Simplifying:
λ = (1.98285317 × 10^-25 J*m) / (839 * 10^3 J/mol)
λ = 2.36123826 × 10^-29 m/mol
To convert this into nanometers (nm), we can use the conversion factor:
1 nm = 10^-9 m
λ = (2.36123826 × 10^-29 m/mol) * (1 nm / 10^-9 m)
Simplifying:
λ = 2.36123826 × 10^-20 nm/mol
Now, we can round this to the correct number of significant figures:
λ ≈ 2.4 nm/mol
Therefore, the maximum wavelength of light for which a carbon-carbon triple bond could be broken by absorbing a single photon is approximately 2.4 nm/mol.
To calculate the maximum wavelength of light for which a carbon-carbon triple bond could be broken by absorbing a single photon, we need to use the relationship between energy, wavelength, and frequency of light.
The energy of a photon can be calculated using the equation:
E = h * c / λ
Where:
E is the energy of the photon,
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.
To break a carbon-carbon triple bond, it requires 839 kJ/mol, which is equivalent to 839 kJ / (6.022 x 10^23) = 1.393 x 10^-18 J per molecule.
Let's rearrange the equation to solve for λ:
λ = h * c / E
Now, we can substitute the values into the equation:
λ = (6.62607015 x 10^-34 J·s * 2.998 x 10^8 m/s) / (1.393 x 10^-18 J)
Calculating the value:
λ ≈ 1.429 x 10^-6 m
To express the answer in nanometers (nm), we need to convert meters (m) to nanometers by multiplying by 10^9.
λ ≈ 1.429 x 10^-6 m * 10^9 nm/m
Final result:
λ ≈ 1.429 nm
Therefore, the maximum wavelength of light for which a carbon-carbon triple bond could be broken by absorbing a single photon is approximately 1.429 nm, with the correct number of significant digits.