SOLUTION: Hector is performing an experiment that requires 160 ml of 40% sulfuric solution. He has a 25% sulfuric acid solution and a 50% sulfuric acid solution. How many ml of each soluti
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Question 795155: Hector is performing an experiment that requires 160 ml of 40% sulfuric solution. He has a 25% sulfuric acid solution and a 50% sulfuric acid solution. How many ml of each solution should he mix to obtain the needed solution? Found 2 solutions by stanbon, DrBeeee:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Hector is performing an experiment that requires 160 ml of 40% sulfuric solution. He has a 25% sulfuric acid solution and a 50% sulfuric acid solution. How many ml of each solution should he mix to obtain the needed solution?
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Equation:
acid + acid = acid
0.25x + 0.50(160-x) = 0.40*160
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25x + 50*160 - 50x = 40*160
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-25x = -10*160
x = (2/5)160
x = 64 ml (amt. of 25% solution needed)
160-x = 96 ml (amt. of 50% solution needed)
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Cheers,
Stan H.
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You can put this solution on YOUR website! Set up two equations, much like you do for coin problems. One for the value and one for the number of coins. On;y now you use liquids with a different percentage concentration and you have the total volume of the combined concentrations.
Let a = the number of milliliters of the 25% sulfuric acid solution
Let b = the number of milliliters of the 50% sulfuric acid solution
Let c = the number of milliliters of the total 40% sulfuric acid solution
Using the volume we have
(1) a + b = c or
(2) a + b = 160
Now for the mixture we have
(3) .25*a + .5*b = .4*c or
(4) a/4 + b/2 = .4*160 or
(5) a/4 + b/2 = 64 or
(6) a + 2*b = 4*64 or
(7) a + 2*b = 256
Now solve (7) and (2) simultaneously to get a and b.
The first step is to subtract (2) from (7) to get
(8) (a + 2*b) - (a + b) = 256 - 160 or
(9) a - a + 2*b - b = 96 or
(10) b = 96
Then from (2) we get
(11) a + 96 = 160 or
(12) a = 160 - 96 or
(13) a = 64
Let's (always) check our answer with (3).
Is (.25*64 + .5*96 = .4*160)?
Is (16 + 48 = 64)?
Is (64 = 64)? Yes
Answer: Hector should mix 64ml of the 25% solution with 96ml of the 50% solution in order to get 160ml at a 40% concentration of sulfuric acid.
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