##”1909 mL”##
Your strategy here will be to
use ethanol’s molar mass to determine how many grams would contain the given number of moles
use the given to find the volume of solution that would contain that many grams of ethanol
do a quick search for the of an ethanol solution that has that of ethanol
So, ethanol’s molar mass is equal to ##”46.07 g/mol”##, which means that every mole of ethanol will have a mass of ##”46.07 g”##. In your case, the given number of moles will have a mass of
##3.150 color(red)(cancel(color(black)(“moles C”_2″H”_6″O”))) * “46.07 g”/(1color(red)(cancel(color(black)(“mole C”_2″H”_6″O”)))) = “145.12 g”##
As you know, a solution’s percent concentration by mass is defined as the ratio between the mass of the and the total mass of the solution, multiplied by ##100##
##color(blue)(“% w/w” = “mass of solute”/”mass of solution” xx 100)##
Now, a ##”7.700% w/w”## ethanol solution will contain ##”7.700 g”## of ethanol for every ##”100 mL”## of solution. This means that you’d get ##”145.12 g”## of ethanol in
##145.12 color(red)(cancel(color(black)(“g C”_2″H”_6″O”))) * “100 g solution”/(7.700color(red)(cancel(color(black)(“g C”_2″H”_6″O”)))) = “1884.7 g solution”##
Now, to get the volume of this solution, you need to use its , which you can find here
The density of a ##”7.700% w/w”## ethanol solution is about ##”0.98725 g/mL”## at room temperature. This means that you have
##1884.7 color(red)(cancel(color(black)(“g”))) * ” 1mL”/(0.98725 color(red)(cancel(color(black)(“g”)))) = color(green)(“1909 mL”)##
The answer is rounded to four .
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