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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

1 Answer

4 votes

Answer:

(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.

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