SOLUTION: I laboratory tech nation needs to make a 21 L batch of a 40% acid solution how can the laboratory technician combine a batch of an acid solution that is a peer acid with another th

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Question 1050621: I laboratory tech nation needs to make a 21 L batch of a 40% acid solution how can the laboratory technician combine a batch of an acid solution that is a peer acid with another that is 10% to get the desired concentration
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = liters of pure acid needed
Let +b+ = liters of 10% acid solution needed
--------------------------------------------
(1) +a+%2B+b+=+21+
(2) +%28+a+%2B+.1b+%29+%2F+21+=+.4+
----------------------------
(2) +a+%2B+.1b+=+.4%2A21+
(2) +a+%2B+.1b+=+8.4+
(2) +10a+%2B+b+=+84+
Subtract (1) from (2)
(2) +10a+%2B+b+=+84+
(1) +-a+-+b+=+-21+
--------------------
+9a+=+63+
+a+=+7+
and
(1) +a+%2B+b+=+21+
(1) +7+%2B+b+=+21+
(1) +b+=+14+
----------------------
7 liters of pure acid are needed
14 liters of 10% acid solution are needed
-------------------------------------
check:
(2) +%28+a+%2B+.1b+%29+%2F+21+=+.4+
(2) +%28+7+%2B+.1%2A14+%29+%2F+21+=+.4+
(2) +%28+7+%2B+1.4+%29+%2F+21+=+.4+
(2) +8.4%2F21+=+.4+
(2) +8.4+=+.4%2A21+
(2) +8.4+=+8.4+
OK