SOLUTION: A laboratory technician prepares 200 mL of 35% ethyl alcohol from a 95% ethyl alcohol stock solution. Determine, to the nearest mL, the amount of 95% ethyl alcohol that is neede

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Question 515871: A laboratory technician prepares 200 mL of 35% ethyl alcohol from a 95% ethyl alcohol stock solution.
Determine, to the nearest mL, the amount of 95% ethyl alcohol that is needed.
Determine, to the nearest mL, the amount of distilled water that is added.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ml of 95% alcohol needed
Let +b+ = ml of water needed
given:
(1) +a+%2B+b+=200+ ml
(2) +.95a+%2F+%28+a+%2B+b+%29+=+.35+
----------------------
(2) +.95a++=+.35%2A%28a+%2B+b%29+
(2) +.95a+=+.35a+%2B+.35b+
(2) +.6a+=+.35b+
(2) +60a+=+35b+
(2) +12a+=+7b+
and,
(1) +a+=+200+-+b+
By substitution:
(2) +12%2A%28+200+-+b+%29+=+7b+
(2) +2400+-+12b+=+7b+
(2) +19b+=+2400+
(2) +b+=+126.32+
and
(1) +a+=+200+-+b+
(1) +a+=+200+-+126.32+
(1) +a+=+73.68+
74 ml of 95% alcohol are needed
126 ml of water are needed
check answer:
(2) +.95a+%2F+%28+a+%2B+b+%29+=+.35+
(2) +.95%2A74+%2F+200+=+.35+
(2) +70.3+%2F+200+=+.35+
(2) +70.3+=+70+
close enough