Question 178774
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I sincerely hope that you meant the chemist has 10 milli<i><b>liters</b></i> of solution.  I'm not sure how to interpret the amount of solution when given its <i><b>length.</b></i>


On that assumption, let us proceed.


Let <i>x</i> be the amount of pure acid to be added to the existing solution, so an expression of the amount of pure acid in the mixture is *[tex \Large (0.3)(10) + x].  That's because 30% of the 10 ml of solution is pure acid, and all of the <i>x</i> ml of acid is pure acid.


We want the resulting solution, which has a volume of 10 ml plus <i>x</i> ml, to have a concentration of 50%, meaning that 0.50 of the resulting solution should be pure acid.  Hence *[tex \Large 0.5(10 + x)] is another expression for the amount of pure acid in the mixture and is equivalent to the previous expression.  Hence we can say:


*[tex \Large (0.3)(10) + x = 0.5(10 + x)]


Solve for <i>x</i> to answer your problem.



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