A tank originally contains 100 gal of fresh water. Then water containing 12 lb of salt per gallon is poured into the tank at a rate of 2 gal/min, and the mixture is allowed to leave at the same rate. After 10 min the process is stopped, and fresh water is poured into the tank at a rate of 4 gal/min, with the mixture again leaving at the same rate. Find the amount of salt in the tank at the end of an additional 10 min. (Round your answer to two decimal places.)

Then, freshwater is added at a rate of 4 gal/min. The solution is being diluted so that the concentration of the resulting solution is 96% of the previous solution. After minute 1, the solution will have a concentration that is 96% of the original solution:

Concentration of the solution after minute 1 = 2.40 lb/gal · 0.96 = 2.304 lb/gal

After minute 2:

2.304 lb/ gal · 0.96 = 2.21184 lb/gal

Since 2.304 lb/gal = 2.40 lb/gal · 0.96

we can rewrite the expression for minute 2:

2.40 lb/gal · 0.96 · 0.96 = 2.21184 lb/gal

And for minute 3:

2.40 lb/gal · 0.96 · 0.96 · 0.96= concentration after 3 minutes

And for minute n

2.40 lb/gal · 0.96ⁿ = concentration after n minutes

Then, after 10 minutes of this process:

2.40 lb/gal · 0.96¹⁰ = 1.60 lb/gal

The amount of salt in the tank will be:

1.60 lb/gal · 100 gal = 160 lb salt

azikennamdi azikennamdi · Answer 2 · 2022-06-01T17:48:30+02:00

The amount (or concentration) of salt that will be found in the tank at the end of an additional 10 min is given as: 1.60 lb.

What is the definition of concentration of chemistry?

The amount of a substance in a defined space is referred to as concentration in chemistry.

What is the explanation for the answer given above?

We know that when the first minute of the process has elapsed, the tank will have a concentration of 0.24 lb/ gal.

This is computed using the formula:

amount of salt added / volume of the tank = concentration in the tank.

Hence, plugging in the values, we have: 2 gal · 12 lb/gal /100 gal = 0.24 lb/gal.

Step 2

After the minute 2, 24 lb of salt (2 gals · 12 lb/gal) will be incorporated into the 100 gals and the final concentration of the tank will be:

(24 lb + 24 lb) /100 gal = 0.48 lb /gal

Following the above, we can state that

every minute the concentration of the tank will increase by 0.24 lb/gal

Thus, the concentration of the tank after 10 min will be:

Concentration of salt in the tank after 10 min = 0.24 lb/gal x 10 = 2.40 lb/gal

Step 3

Recall that at this point, fresh water is added at a rate of 4 gal/min. this means that the solution is being diluted so that the concentration of the resulting solution is 96% of the previous solution.

When a minute has elapsed, the solution will have a concentration that is 96% of the original solution:

The concentration of the solution after the first minute thus

= 2.40 lb/gal · 0.96 = 2.304 lb/gal

After the second minute: 2.304 lb/ gal · 0.96 = 2.21184 lb/gal

Since 2.304 lb/gal = 2.40 lb/gal · 0.96, we can rewrite the equation for the second minute:

2.40 lb/gal · 0.96 · 0.96 = 2.21184 lb/gal

Minute 3:

2.40 lb/gal · 0.96 · 0.96 · 0.96 = concentration after 3 minutes

And for n minutes:

2.40 lb/gal · 0.96ⁿ = Concentration after n minutes.

We can thus submit that after 10 minutes of this process that

2.40 lb/gal · 0.96¹⁰ = 1.60 lb/gal

Hence, the amount of salt in the tank will be: 1.60 lb/gal · 100 gal = 160 lb salt

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