chemical engineering 2 A well-mixed dam has a constant volume of V 20 GL of wate

Question

chemical engineering 2

A well-mixed dam has a constant volume of V 20 GL of water. Water flows into the dam from a stream at a rate of 100 ML/d and an equivalent amount is lost by controlled release from the sluice gates ("d" day). At time t 0, fertiliser run off from upstream farming starts to introduce phosphates into the inlet stream at a concentration of 10 mg/L. Choose which of the following equations describes the mass balance for the rate of change of phosphate concentration X in the dam as a function of time i.e. dx/dt. Assume that the phosphate is not taking part in any reactions and remains dissolved in the liquid phase. O dx/dt (5/d) (10 mg/L-x) dx/dt (0.005/d) (10 mg/L -x) dx/dt (5/d) (10 mg/L) dx/dt (0.005/d) (10 mg/L) None of or more than one of the above answers.

Explanation / Answer

rate of change of concentration is defined as the difference between the final concentration and initial concentration to the time

Here the time is calculated as ratio of volume of the tank to the flow rate of wtare into the tank.

t = 20 GL/(100 ML/d)

= 200 d

So the mass balance equation is

dx/dt = (10 mg/L - x)/200 d

= 0.005/d(10 mg/L - x)

So the correct option is B.

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