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QUESTION

# 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

• 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

http://wissen.science-and-fun.de/chemistry/chemistry/density-tables/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 .