Question

Solution A is an $80\%$ acid solution. Solution B is a $30\%$ acid solution. (a) Find the amount of Solution A (in mL) that must be added to $500$ mL of Solution B in order to produce a $70\%$ acid solution. (b) Find the amount of Solution A and Solution B (in mL) that can be combined in order to form a $100$ mL solution that is $50\%$ acid. (c) Does there exist a combination of Solution A and Solution B that is $90\%$ acid

Answer 1

(a)
`2000\text{ ml}` (b)
`40\text{ ml and }60\text{ ml}` (c)NO

Explanation:

GIVEN: Solution A is an
`\$80\%` acid solution. Solution B is a
`\$30\%` acid solution.

TO FIND: (a) Find the amount of Solution A (in mL) that must be added to
`500 \text{ml}` of Solution B in order to produce a
`70\%` acid solution. (b) Find the amount of Solution A and Solution B (in mL) that can be combined in order to form a
`100 \text{ml}` solution that is
`50\%` acid. (c) Does there exist a combination of Solution A and Solution B that is
`90\%` acid.

SOLUTION:

(a)

Let total amount of solution A added be
`x`

Total amount of mixture
`=500+x\text{ ml}`

As resulting solution is
`70\%` acid solution.

Amount of acid in final solution is sum of acid in both solutions

`(70)/(100)(500+x)=(80)/(100)x+(30)/(100)*500`

`35000+70x=80x+15000`

`x=2000\text{ ml}`

(b)

Let amount of Solution A be
`x\text{ ml}`

Amount of solution B
`=100-x\text{ ml}`

As resulting solution is
`50\%` acidic solution

Amount of acid in final solution is sum of acid in both solutions

`(50)/(100)*100=(80)/(100)x+(30)/(100)(100-x)`

`5000=80x+3000-30x`

`50x=2000`

`x=40\text{ ml}`

Amount of solution B
`=100-40=60\text{ ml}`

(c)

No as concentration of final solution can not be greater than one with higher concentration.