Nitrogen oxides, NO_x (a mixture of NO and NO_2 collectively designated as NO_2)

Question

Nitrogen oxides, NO_x (a mixture of NO and NO_2 collectively designated as NO_2), play an essential role in the production of pollutants found in photochemical smog. The NO_x in the atmosphere is slowly broken down to N_2 and O_2 in a first-order reaction. The average half-life of NO_x in the smokestack emissions in a large city during daylight is 3.9 hours. Starting with 3.40 mg in an experiment, what quantity of NO_x remains after 4.43 hours? Nitrogen oxides. NO_x (a mixture of NO and NO_2 collectively designated as NO_x), play an essential role in the production of pollutants found in photochemical smog. The NO_x in the atmosphere is slowly broken down to N_2 and O_2 in a first -order reaction. The average half-life of NO_x in the smokestack emissions in a large city during daylight is 3.9 hours. How many hours of daylight must have elapsed to decrease 3.40 mg of NO_x to 7.90 times 10^- 6 mg?

Explanation / Answer

Q1.

HL = 3.9h

m = 3.4 mg of mass

find NOx final.. t = 4.43 h

so

Mfinal = Minitial* (1/2)^(t/HL)

Mfinal = 3.4* (1/2)^(4.43/3.9) = 1.5471 mg left NOx

b)

apply now:

Mfinal = Minitial* (1/2)^(t/HL)

(7.9*10^-6) = (3.4) * (1/2) ^ (t/3.9)

solve for t

ln((7.9*10^-6) / 3.4 ) = ln(0.5) * t/3.9

ln((7.9*10^-6) / 3.4 ) / ln(0.5) = t/3.9

t = 3.9*18.71 = 72.969 h

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