# A certain beverage contains 7.700% ethanol ##(C_2H_6O)## by mass. What volume of this beverage in milliliters contains 3.150 moles of ethanol?

##”1909 mL”##

Your strategy here will be to

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A certain beverage contains 7.700% ethanol ##(C_2H_6O)## by mass. What volume of this beverage in milliliters contains 3.150 moles of ethanol?
• 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

Ethanol- Water- Mixtures

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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