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?

Question

Olivia Anton · Accepted Answer

#"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 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

https://tutor.hix.ai

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.

Kai Bowman · Answer

undefined First, calculate the mass of ethanol in 3.150 moles: $ \text{Mass of ethanol} = \text{moles} \times \text{molar mass of ethanol} = 3.150 \, \text{moles} \times 46.07 \, \text{g/mol} = 145.3555 \, \text{g} $.

Next, find the mass of the beverage needed to contain this amount of ethanol: $ \text{Mass of beverage} = \frac{\text{Mass of ethanol}}{\text{Percentage of ethanol}} = \frac{145.3555 \, \text{g}}{7.700\%} $.

Then, calculate the volume of the beverage: $ \text{Volume of beverage (in mL)} = \frac{\text{Mass of beverage (in g)}}{\text{Density of beverage (in g/mL)}} $.