Question

A pond initially contains 1000,000 gals of water and an unknown amount of an undesirable chemical. Water containing 0.01 gram of this chemical per gallon flows into the pond at a rate of 300gal/min. The mixture flows out at the same rate so the amount of water in the pond remains constant. Assume that the chemical is uniformly distributed throughout the pond. If initially the amount of chemical is 0.05 gm/gal, what is the chemical concentration after 1 hour?

Answer 1

To find the chemical concentration after 1 hour in the pond, we can use the concept of mass balance. The initial amount of chemical in the pond is 0.05 grams/gallon, and water containing 0.01 gram of the chemical per gallon flows into the pond at a rate of 300 gallons/minute. After 1 hour, the new concentration of the chemical is 0.00017 grams/gallon.

Step-by-step explanation:

To find the chemical concentration after 1 hour, we can use the concept of mass balance. The total mass of the chemical in the pond remains constant, and the rate at which new chemical is added is equal to the rate at which it flows out. The initial amount of chemical in the pond is 0.05 grams/gallon, and the rate of water flow into the pond is 300 gallons/minute, with each gallon containing 0.01 gram of the chemical. After 1 hour (60 minutes), 300 gallons/minute x 60 minutes = 18,000 gallons of water containing the chemical have flowed into the pond.

We can calculate the total mass of the chemical that has flowed into the pond: 18,000 gallons x 0.01 gram/gallon = 180 grams of the chemical.

To find the new concentration, we divide the total mass of the chemical by the total volume of water in the pond after 1 hour. The initial volume of water in the pond is 1,000,000 gallons, and an additional 18,000 gallons have flowed in. So the total volume of water in the pond after 1 hour is 1,000,000 gallons + 18,000 gallons = 1,018,000 gallons.

The new concentration of the chemical can be calculated as follows: 180 grams / 1,018,000 gallons = 0.00017 grams/gallon.