Question 773669
Data To Know First:
5% Vinegar is as weight/weight.  Density 1.00 gram/ml.
Pure 100% Acetic Acid, assumed weight/weight, Density 1.049 gram/cm^3


Use mass to do the main solving.
Letting a = grams of acetic acid (100% acid),
the mass of acid in the 1 liter of 5% is -------
{{{1*(1.00)*(1000)}}} {{{L*(g/ml)*(ml/L)}
={{{1000}}} grams, where "g" was an abbreviation for "grams"


Equation first all in mass is then:
{{{highlight((1000*0.05+1.00*a)/(1000+a)=0.81)}}}
Note that the 1.00 in the rational equation stands for "100%" for "a".


The algebraic steps, not shown here, will lead to .....
{{{a=4000}}} grams
from which you must use density to find the result in volume liters:
{{{highlight(4000*(1/1.049)(1/1000)=3.81)}}} Liters
The units conversion here is {{{g*(cm^3/g)(L/cm^3)=L}}}