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19.28 Discuss the economic possibilities of using photochem- ical reactions to produce valuable products with electricity at 5 cents per kilowatt-hour. Assume that 5% of the electric en- ergy consumed by a quartz—mercury vapor lamp goes into light, and 30% of this is photochemically effective. (a) How much will it cost to produce 1 Ib (453.6 g) of an organic compound having a molar mass of 100 g mol" !, if the average effective wavelength is assumed to be 400 nm and the reaction has a quantum yield of 0.8 molecule per photon? (b) How much will it cost if the reaction involves a chain reaction with a quantum yield of 100? 19.34 A cold high-voltage mercury lamp is to be used for a cer- tain photochemical reaction that responds to ultraviolet light of 253.7 nm. The chemical analysis of the product is sensitive to only 10~4 mol. The lamp consumes 150 W and converts 5% of the electric energy into radiation, of which 80% is at 253.7 nm. The amount of the light that gets into the monochroma- tor and passes out the exit slit is only 5% of the total radiation of the lamp. Fifty percent of this 253.7 nm radiation from the monochromator is absorbed in the reacting system. The quan- tum yield is 0.4 molecule of product per quantum of light ab- sorbed. How long an exposure must be given in this experiment if it is desired to measure the photochemical change with an ac- curacy of 1%? 19.36 A uranyl oxalate actinometer is exposed to light of wave- length 390 nm for 1980 s, and it is found that 24.6 cm> of 0.004 30 mol L~! potassium permanganate is required to titrate an aliquot of the uranyl oxalate solution after illumination, in comparison with 41.8 cm? before illumination. Using the known quantum yield of 0.57, calculate the number of joules absorbed per second. The chemical reaction for the titration is 2MnO,~ + 5H)C,O,4 + 6H* = 2Mn?* + 10CO, + 8H,O 19.37 A photochemical reaction of biological importance is the production of vitamin D, which prevents rickets and brings about the normal deposition of calcium in growing bones. Steen- bock found that rickets could be prevented by subjecting the food as well as the patient to ultraviolet light below 310 nm. When ergosterol is irradiated with ultraviolet light below 310 nm, vitamin D is produced. When irradiated ergosterol was in- cluded in a diet otherwise devoid of vitamin D, it was found that absorbed radiant energy of about 7.5 x 10~> J was nec- essary to prevent rickets in a rat when fed over a period of 2 weeks. The light used has a wavelength of 265 nm. (a) How many quanta are necessary to give 7.5 X 10-9 J? (b) If vitamin D has a molar mass of the same order of magnitude as ergosterol 
