Consider a tank used in certain hydrodynamic experiments. after one experiment the tank contains 900 l of a dye solution with a concentration of 1 g/l. to prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of 9 l/min, the well-stirred solution flowing out at the same rate. find the time that will elapse before the concentration of dye in the tank reaches 1% of its original value. (round your answer to one decimal place.)

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Shyanne Chandler

Chemistry

4 April, 17:51

Consider a tank used in certain hydrodynamic experiments. after one experiment the tank contains 900 l of a dye solution with a concentration of 1 g/l. to prepare for the next experiment, the tank is to be rinsed with fresh water flowing in at a rate of 9 l/min, the well-stirred solution flowing out at the same rate. find the time that will elapse before the concentration of dye in the tank reaches 1% of its original value. (round your answer to one decimal place.)

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Jorden Ward · Answer 1

Soln: •t: in min •Q (t) : quantity of dye in the tank at time t •r in = 0: rate of dye poured into the tank per min. Since it is fresh water, so it is zero. •r out = density of dye*rate of fluid = Q/900*9: rate of dye flowing out. •Q (0) = 1*900 g: initial amount of dye in the tank. •{dQ/dt=rin-rout = 0-Q100 Q (0) = 900g•Q (t) = Ce-1/100t •Q (0) = 900, C = 900, Q (t) = 900e-1/100t •Q (t) = 0.01·Q (0), Q (0) e-1/100t = 0.01*Q (0),-t100 = ln 0.01, t = 460min