A pollutant has leaked into a water tank containing 2000 gallons of water. The tank now is 3% pollutant. How much clean water should be added to the tank to decrease the concentration of the pollutant to a safe level of 0.5%?
TIA!
A pollutant has leaked into a water tank containing 2000 gallons of water. The tank now is 3% pollutant. How much clean water should be added to the tank to decrease the concentration of the pollutant to a safe level of 0.5%?
TIA!
Let the present volume of liquid present in the fluid be Vi.
3% is pollutant.
After adding fresh water, let the vol. of the tank be Vf and pollutant drops to 0.5%. Since the amount of pollutant remains same before and after adding water, we will take a material balance of the pollutant.
therefore,
(3/100)*Vi = (0.5/100)*Vf
We need to know amount of clean water added, i.e. Vf-Vi
Now, initially we had 2000 gallons of water. after addition of pollutant it becomes 97%.
therefore, 97% of Vi = 2000 gallons.
First solve for vVi, then Vf and finally Vf - Vi to get the answer.
Hello eagertolearnCan I suggest an alternative method, using ratios?
Initially, there are 2000 gallons of water in the tank, which is 97% of the total amount. The remaining 3% is pollutant. So the ratio of water to pollutant is . The amount of pollutant in the tank is therefore:gallonsAfter adding extra water, this has to be 0.5% of the total, the other 99.5% being water. So now the ratio of water to pollutant is . Since there are still gallons of pollutant in the tank, the amount of water must now be:
gallonsTherefore, we must add gallons of water.
Grandad