Answer:
There must be added 500 cm3 of alcohol to bring the concentration to 80%.
Explanation:
Concentration
The concentration of a solution is a measure of the amount of solute that has been dissolved in a given amount of solution.
In the container, there are 2 liters (2000 cubic centimeters) of a solution, 75% of which is alcohol (solute) and 25% of water (solvent).
The original amount of alcohol is:
H = 2000*75% = 1500 cc
The original amount of water is:
W = 2000*25% = 500 cc
When we add x cc of pure alcohol, there are 1500+x cc of alcohol out of 2000+x cc of solution.
The new concentration is calculated as:
[tex]\displaystyle \frac{1500+x}{2000+x}[/tex]
And it's known this concentration is 80% (0.8), thus:
[tex]\displaystyle \frac{1500+x}{2000+x}=0.8[/tex]
Multiplying by 2000+x:
[tex]1500+x = 0.8(2000+x)[/tex]
Operating:
[tex]1500+x = 1600+0.8x[/tex]
Rearranging:
[tex]x-0.8x=1600-1500[/tex]
[tex]0.2x=100[/tex]
[tex]x=100/0.2[/tex]
x= 500
There must be added 500 cm3 of alcohol to bring the concentration to 80%
