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?

Answer 1

`"1909 mL"`

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 `"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 solute 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 density, 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 sig figs.