# 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?

Dec 10, 2015

$\text{1909 mL}$

#### 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 $\text{46.07 g/mol}$, which means that every mole of ethanol will have a mass of $\text{46.07 g}$. 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 $100$

$\textcolor{b l u e}{\text{% w/w" = "mass of solute"/"mass of solution} \times 100}$

Now, a $\text{7.700% w/w}$ ethanol solution will contain $\text{7.700 g}$ of ethanol for every $\text{100 mL}$ of solution. This means that you'd get $\text{145.12 g}$ 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 $\text{7.700% w/w}$ ethanol solution is about $\text{0.98725 g/mL}$ 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.