Question 966256

Note that the concentrations in this problem are  Volume-to-Volume  concentrations,  and they have the dimension of  {{{mL/mL}}}  (i.e., actually,  are non-dimensional).

The amount  (the volume)  of pure acid in  250 mL  of  8%  acid solution is   0.08*250 mL = 20 mL.


Let &nbsp;<B>x</B>&nbsp; be the amount &nbsp;(the volume)&nbsp; of pure acid we have to add to &nbsp;250 mL&nbsp; of &nbsp;8%&nbsp; acid solution to get &nbsp;20%&nbsp; solution. 


Then the volume of the obtained solution will be &nbsp;(250 + x)&nbsp; mL &nbsp;and the volume of the pure acid in it will be &nbsp;(20 + x)&nbsp; mL. 


The concentration of the obtained solution is &nbsp;{{{(20+x)/(250+x)}}}, &nbsp;and it should be &nbsp;20%. 

It gives an equation


{{{(20+x)/(250+x)}}} = 0.2.


To solve it, &nbsp;multiply both sides by &nbsp;{{{250 + x}}}. &nbsp;You will get 


20 + x = 0.2*(250 + x).


Open the parentheses and simplify step by step:


20 + x = 50 + 0.2*x

0.8*x = 50 - 20 = 30.


Hence, &nbsp;x = {{{30/0.8}}} = 37.5 mL.


<B>Answer</B>. 37.5 mL &nbsp;of pure acid should be added to &nbsp;250 mL&nbsp; of &nbsp;8%&nbsp; acid solution to get &nbsp;20%&nbsp; acid solution.