Question
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
Be sure your answer has correct number of significant digits in nm
Answers
GPT 3.5
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.
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.