SOLUTION: Sulfuric acid (H2SO4) can be used to remove water from organic materials leaving behind a residue of black carbon. If beaker A contains a 15% solution of sulfuric acid and beaker B

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Question 150851: Sulfuric acid (H2SO4) can be used to remove water from organic materials leaving behind a residue of black carbon. If beaker A contains a 15% solution of sulfuric acid and beaker B contains a 20% solution of sulfuric acid, how much from each beaker should be used to make 6 liters of a 18% solution of sulfuric acid?

Found 3 solutions by Fombitz, josmiceli, stanbon:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let's call the amount from beaker A, A.
Let's call the amount from beaker B, B.
The total final volume is 6 liters.
1.A%2BB=6
The final concentration is 18%.
2.A%280.15%29%2BB%280.20%29=%28A%2BB%29%280.18%29
Let's multiply equation 2 by 100 to get rid of decimals.
2.15A%2B20B=18%28A%2BB%29
2.15A%2B20B=18A%2B18B%29
2.3A-2B=0
We can use eq. 2 to solve for B in terms of A.
2.3A-2B=0
2B=3A
B=%283%2F2%29A
Now substitute this into eq. 1 and solve for A.
1.A%2BB=6
A%2B%283%2F2%29A=6
%285%2F2%29A=6
A=12%2F5
Now back substitute to find B,
B=%283%2F2%29A
B=%283%2F2%29%2812%2F5%29
B=18%2F5
2.4 liters of solution A and 3.6 liters of solution B.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
In words:
(liters of acid in beaker A) + (liters of acid in beaker B) / (total liters of solution in A and B) = % solution of acid
Let A = liters of solution needed from beaker A
Let B = liters of solution needed from beaker B
%28.15A+%2B+.2B%29+%2F+%28A+%2B+B%29+=+.18
Note that we are told A+%2B+B+=+6liters
%28.15A+%2B+.2B%29+%2F+6+=+.18
Multiply both sides by 6
.15A+%2B+.2B+=+1.08
And since A+%2B+B+=+6
B+=+6+-+A
.15A+%2B+.2%2A%286+-+A%29+=+1.08
.15A+%2B+1.2+-+.2A+=+1.08
-.05A+=+-.12
A+=+2.4liters
Given is A+%2B+B+=+6
B+=+6+-+2.4
B+=+3.6
2.4 liters of solution are needed from beaker A
and 3.6 liters of solution are needed from beaker B
check answer:
%28.15A+%2B+.2B%29+%2F+6+=+.18
%28.15%2A2.4+%2B+.2%2A3.6%29+%2F+6+=+.18
%28.36+%2B+.72%29+%2F+6+=+.18
1.08+%2F+6+=+.18
1.08+=+.18%2A6
1.08+=+1.08
OK

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
If beaker A contains a 15% solution of sulfuric acid and beaker B contains a 20% solution of sulfuric acid, how much from each beaker should be used to make 6 liters of a 18% solution of sulfuric acid?
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EQUATIONS:
Quantity Equation: a + b = 6 L
Active Ingrediant: 0.15a + 0.20b = 0.18(6) = 1.08
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Rearrange for elimination:
15a + 15b = 90
15a + 20b = 108
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Subtract 1st from 2nd to get:
5b = 18
b = 3.6 L (amt. of 15% solution in the mix)
Since a+b=6, a = 6-3.6 = 2.4 L (amt. of 20% solution in the mix)
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Cheers,
Stan H.