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Chemistry · General chemistry I · Worked example

Find the wavelength that can break a bond

A bond has a dissociation energy of 400. kJ/mol. What is the longest wavelength of light whose photons can break it?

λ=h⁢cE

Energy for one bond

Divide the molar energy by Avogadro’s number: each bond needs 6.64 × 10⁻¹⁹ J.

4.00×105 J/mol6.022×1023 mol−1=6.64×10−19 J
4.00×105 J/mol6.022×1023 mol−1=6.64×10−19 J

Solve for the wavelength

Rearrange E = hc/λ to λ = hc/E.

λ=(6.626×10−34)⁢(2.998×108)6.64×10−19 m=2.99×10−7 m
λ=(6.626×10−34)⁢(2.998×108)6.64×10−19=2.99×10−7 m

Interpret

2.99 × 10⁻⁷ m is 299 nm, in the ultraviolet. Shorter wavelengths carry more energy and can also break the bond; longer ones, including all visible light, cannot.

Result

299 nm, in the ultraviolet.

Your turn

Can one photon of 650 nm light break that 400. kJ/mol bond?

Show the answer and explanation

No: a mole of 650 nm photons carries only 184 kJ.

Per mole, E = N_A·hc/λ = (6.022 × 10²³)(6.626 × 10⁻³⁴)(2.998 × 10⁸)/(6.50 × 10⁻⁷) = 1.84 × 10⁵ J/mol = 184 kJ/mol, less than half of 400 kJ/mol.

(6.022×1023)⁢(6.626×10−34)⁢(2.998×108)6.50×10−7=1.84×105
(6.022×1023)⁢(6.626×10−34)6.50×10−7×2.998×108=1.84×105

Keep exploring

In Photons & spectrophotometry, enter 400 kJ/mol as the known energy: the studio returns the wavelength, 299 nm.

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