MHB Calculation when Mixing Two Compounds....

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To achieve a concentration of 80% compound A from a solution of 70% compound A and 30% compound B, the equation 0.7x + y = 0.8(x + y) can be used, where x is the volume of the 70% solution and y is the volume of 100% compound A added. This equation represents the total amount of compound A in the final mixture as a function of both the initial solution and the added compound. By solving for y in terms of x, the required volume of 100% compound A can be determined. This calculation effectively allows for the adjustment of concentrations in liquid mixtures.
haubenkoch
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Dear Comunity,

I am running into a (probably pretty simple) problem here, yet the most simple things are sometimes upon me...:(

I have a liquid solution which consists of 70% compound A and 30% compound B.
I also have a bottle with 100% compound A.

What I would like to do is to achieve a concentration of 80% compound A and 20% compound B. Can someone tell me how this is calculated?

I was thinking of something like c1*v1=c2*v2 but this doesn't get me anywhere...am I missing something?

Any help on this would be very much appreciated!

 
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I would set it up as follows:

Let $x$ be the amount of solution you currently have, the 7:3 mix. Then let $y$ be the amount of 100% compound A you wish to add. Thus we want:

$$0.7x+y=0.8(x+y)$$

Do you see how both sides of the equation represent the amount of compound A present in the final solution? The left side represents the initial amount of compound A plus the amount added. The right side reflects the fact that we want 80% of the final amount to be compound A.

Now you may solve this for $y$ as a function of $x$. What do you find?
 
Hello, haubenkoch!

We can disregard references to compound B.

I have a liquid solution which is 70% alcohol.
I also have a bottle with 100% alcohol.

I would like a concentration of 80% alcohol.
This is an explanation of MarkFL's solution.Let x = liters of 70% alcohol.
It contains 0.7x liters of alcohol.

We add y liters of 100% alcohol.
It contains y liters of alcohol.

The mixture contains 0.7x + y liters of alcohol. .[1]But we know that the mixture will be
. . x+y liters which is 80% alcohol.
It contains 0.8(x+y) liters of alcohol. .[2]We just described the final amount of alcohol in two ways.

There is our equation! ..0.7x + y \:=\:0.8(x+y)
 
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