SOLUTION: Oxalic acid is one of the finest available wood bleaching agents. It is an acid, and the concentration used is critical to both safety and the bleaching result. Daulton plans to us

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Oxalic acid is one of the finest available wood bleaching agents. It is an acid, and the concentration used is critical to both safety and the bleaching result. Daulton plans to us      Log On


   

Question 1193242: Oxalic acid is one of the finest available wood bleaching agents. It is an acid, and the concentration used is critical to both safety and the bleaching result. Daulton plans to use the acid on a wood table to lighten dark streaks and colorations in the wood so that the wood will stain a uniform colour. He finds 2 solutions in the workshop. Solution 1 has a concentration of 0.05 g/mL, and Solution 2 has a concentration of 0.01 g/mL. He starts with 150 mL of Solution 1 and needs to add Solution 2 to get a final solution with a concentration of 0.025 g/mL. He uses the following formula to determine the amount of Solution 2 required:
C(x)= (amount of oxalic acid in Solution 1 + amount of oxalic acid in Solution 2)/(amount of Solution 1+ amount of Solution 2)
For this question, after substituting known values, the following rational expression is obtained:
0.025=((0.05)(150)+0.01x)/(150+x)
Determine how much of Solution 2 needs to be added. Clearly outline all steps. Slove this as a system and show your solution graphically
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
.
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0.05 g/mL and 0.01 g/mL
want 150 mL of the 0.01 g/mL solution and is to make 0.025 g/mL solution result.

v, how much of the 0.05 0.025 g/mL solution is needed

highlight_green%280.05%2A150%2B0.01%2Av=0.025%2A%28v%2B150%29%29
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5%2A150%2B1%2Av=2.5v%2B2.5%2A150
v-2.5v=2.5%2A150-5%2A150
%282.5-1%29v=150%285-2.5%29
1.5v=150%285-2.5%29
v=150%28%285-2.5%29%2F%282.5-1%29%29
v=150%282.5%2F1.5%29
highlight%28v=250%29


---------------------------THIS WAS WRONG-------------------
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cross%280.05v%2B0.01%2A150=0.025%2A%28150%2Bv%29%29

0.05v%2B0.01%2A150=0.025%2A150%2B0.025v
5v%2B150=2.5%2A150%2B2.5v
2.5v=2.5%2A150-150
2.5v=1.5%2A150
highlight_green%28v=150%281.5%2F2.5%29%29
highlight%28v=90%29

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


The equation to be solved is given in the post; but the other tutor insists on using the description of the problem to come up with his own equation -- which is unfortunately wrong, since it doesn't reflect the given information correctly.

0.025=%28%280.05%29%28150%29%2B0.01x%29%2F%28150%2Bx%29
0.025%28150%2Bx%29=%280.05%29%28150%29%2B0.01x
3.75%2B0.025x=7.5%2B.01x
0.015x=3.75
x=3.75%2F0.15=250

ANSWER: He needs to add 250 mL of solution 2

NOTE: A little common sense can be used to check your answer -- and, in particular, to see that the answer from the other tutor can't be right.

The 0.025 g/mL concentration of the mixture is closer to the 0.01 concentration of solution 2 than it is to the 0.05 concentration os solution 1; that means the mixture must contain more of solution 2 than it does of solution 1.

Given that there are 150 mL of solution 1, the answer that there are 90 mL of solution 2 makes no sense, while the answer that there are 250 mL of solution 2 does make sense.