Question #56180

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Answer 1 · 2016-06-17T17:12:24

$V_(60)=216.6"ml"$

$V_(15)=433.3"ml"$

You use the idea that

$"concentration=amount of substance/volume of solution"$

In symbols:

$c=n/v$

This means that

$n=cxxv$

In questions like this the total amount of substance does not change so we can write:

$(60xxV_(60))+(15xxV_(15))=30xx650" "color(red)((1))$

We also know that the total volume is $650"ml"$ so we can also write:

$V_(60)+V_(15)=650" "color(red)((2))$

So we have set up two simultaneous equations. There are two equations and two unknowns so they can be solved easily.

From $color(red)((2))$ we can rearrange:

$V_(60)=(650-V_(15))$

We now substitute this expression for $V_(60)$ into $color(red)((1))rArr$

$60(650-V_(15))+15V_(15)=19500$

$:.39000-60V_(15)+15V_(15)=19500$

$:.39000-45V_(15)=19500$

$:.45V_(15)=39000-19500=19500$

$:.V_(15)=19500/45=433.3"ml"$

From $color(red)((2))$ we know that:

$V_(60)+V_(15)=650$

$:.V_(60)=650-V_(15)$

$:.V_(60)=650-433.3=216.6"ml"$