Final answer:
The concentration of the liquid alum solution is 359.26 mg/ml. The optimum dosage rate of liquid alum cannot be determined without the jar test results. The amount of liquid alum used per day at the treatment plant for an average day flow rate of 3200 m^3 is 1,149.632 g/day. The cost of liquid alum per year is $209.968.
Step-by-step explanation:
(a) To find the concentration of the liquid alum solution in mg/ml, we need to convert the weight percent to concentration. First, we need to find the weight of dry alum in the solution. If the solution is 48.5 wt% dry alum, then 100g of solution contains 48.5g of dry alum.
Since the density of the solution is 1.35 g/ml, 100 ml of solution weighs 135g. Therefore, the concentration of the liquid alum solution is (48.5g/135ml) x (1000 mg/1g) = 359.26 mg/ml.
(b) The optimum dosage rate of liquid alum can be determined using jar test results. However, the jar test results are not provided in the question. Without the jar test results, it is not possible to determine the optimum dosage rate.
(c) To determine the amount of liquid alum used per day at the treatment plant for an average day flow rate of 3200 m^3, we need to calculate the dosage rate.
The dosage rate can be calculated by multiplying the flow rate (in m^3/day) by the concentration of the liquid alum solution (in mg/ml). Thus, the amount of liquid alum used per day is (3200 m^3/day) x (359.26 mg/ml) = 1,149,632 mg/day = 1,149.632 g/day.
(d) To determine the cost of liquid alum per year, we need to calculate the amount of liquid alum used per year and multiply it by the cost of liquid alum. The amount of liquid alum used per year is the amount used per day multiplied by the number of days in a year.
Considering an average year of 365 days, the amount of liquid alum used per year is 1,149.632 g/day x 365 days = 419,935.28 g/year. The cost of liquid alum per year would be (419,935.28 g) x ($50/100 kg) = $209.968/year.