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Chemistry problem-wavelength and delta H?
Photochromic sunglasses, which darken when exposed to light, contain a small amount of colorless AgCl(s) embedded in the glass. When irradiated with light, metallic silver atoms are produced and the glass darkens:
AgCl(s) → Ag(s) + ClΔH = 310 kJ/mol
Escape of the chlorine atoms is prevented by the rigid structure of the glass, and the reaction therefore reverses itself as soon as the light is removed. What wavelength of light, in nanometers, would a single AgCl need to absorb to activate this reaction?
310 kJ / mol x (1 mol / 6.02 x 10^23 photons) = 5.15 x 10^-22 kJ = 5.15 x 10^-19 J
E = h x f
f = E / h = 5.15 x 10^-19 J / 6.626 x 10^-34 Js = 7.77 x 10^14 1/s
c = f x w, where c = speed of light, f = frequency, w = wavelength
w = c / f = 3.00 x 10^8 m/s / 7.77 x 10^14 1/s = 3.86 x 10^-7 m
3.86 x 10^-7 m x (1 x 10^9 nm / 1 m) = 386 nm
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