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?
1 Answer
Explanation:
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 percent concentration by mass to find the volume of solution that would contain that many grams of ethanol

do a quick search for the density of an ethanol solution that has that percent concentration of ethanol
So, ethanol's molar mass is equal to
#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 solute and the total mass of the solution, multiplied by
#color(blue)("% w/w" = "mass of solute"/"mass of solution" xx 100)#
Now, a
#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 density, which you can find here
http://wissen.scienceandfun.de/chemistry/chemistry/densitytables/ethanolwatermixtures/
The density of a
#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 sig figs.