Using Beer’s Law Al = elcl, calculate the percentage of 4,257 nm light emitted b

Question

Using Beer’s Law Al = elcl, calculate the percentage of 4,257 nm light emitted by the surface of the earth which is absorbed within 100 meters of the earth’s surface. Use two different concentrations in your calculations: 200 ppm and 400 ppm

Carbon dioxide has a strong infrared absorption band centered at l = 4,257 nm (energy = hc/l = 4.67 ´ 10–20 J photon–1 = 2,349 cm–1; see Fig. 3); the molar extinction coefficient for this band is eCO2= 1,214 M–1 cm–1.

Carbon Dioxide Variations 400 The Industrial Revolution Has 350 Caused A Dramatic Rise in CO 300 1400 1200 1800 2000 1000 1600 Year (AD) Ice Age Cycles 400 300 200 100 Thousands of Years Ago 400 350 300 250 O 200

Explanation / Answer

When,

[CO2] = 200 ppm

           = 200/44 x 1000

           = 4.54 x 10^-3 M

Absorbance = molar absorptivity x concentration x path length

let the path length = 1 cm

then,

absorbance = 1214 x 4.54 x 10^-3

                    = 5.5

percent light emitted = inv.log(2-5.5)

                                  = 0.0003%

When,

[CO2] = 400 ppm

           = 400/44 x 1000

           = 9.1 x 10^-3 M

Absorbance = molar absorptivity x concentration x path length

let the path length = 1 cm

then,

absorbance = 1214 x 9.1 x 10^-3

                    = 11.05

percent light emitted = inv.log(2-11.05)

                                  = 9 x 10^-10%

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