Theresa Morgan, a chemist, has a 15% hydrochloric acid solution and a 65% hydrochloric acid solution.

Question

How many liters of each should she mix to get 1650 liters of a hydrochloric acid solution with a 60% acid concentration?

Answer 1

15F + 65S = 60(1650)

F + S = 1650

F = 1650-S

15(1650-S) +65S = 99000

50S = 99000-24750= 74250

S = 74250/50 = 7425/5 = 1485 liters of 65% solution

F = 1650-1485 = 165 liters of 15% solution

65 is much closer to 60 than 15 is, so you know there will be mostly 65% solution with relatively little 15%

Answer 2

Hi Summer G

Reads like you need to dilute some 65% HCl down with 15% HCl to make 1650 ml of 60% HCl .

We can set up a substitution for this dilution

We need

1650 x 0.60 = 990 mls of acid from the solutions given above

Equation 1

x + y = 1650 ml total solution

Equation 2

0.15x + 0.65y = 990 mls of acid

We can set up the dilution in terms of x by solving Equation 2 for y

0.65y = 990 - 0.15x

y = 990/.65 - (0.15/.65)x

y = 1523 - 0.2308x

Substitute the above equation for y into the original Equation 1

x + 1523 - 0.2308x = 1650

0.7692x = 1650 - 1523

0.7692x = 127

x = 127/.0.7692

x = 165 mls

We can find y by using Equation 1

x + y = 1650

165 + y = 1650

y = 1650 - 165

y = 1485

We can use equation 2 to check and see that we have 990 mls of acid

0.15x + 0.65y = 990

0.15(165) + 0.65(1485) = 990

24.75 + 965.25 = 990

990 = 990