Question

What volume (in mL) of `".220 M"` ethanol solution contains `2.90 xx 10^-3` `"mol"` ethanol?

Answer 1

The answer is 13.2 mL.

Explanation:

`"Volume of EtOH" = 2.90 × 10^"-3" color(red)(cancel(color(black)("mol EtOH"))) × "1 L EtOH"/(0.220 color(red)(cancel(color(black)("mol EtOH")))) = "0.0132 L EtOH" = "13.2 mL EtOH"`

Answer 2

`"13.2 mL"`

Explanation:

The idea here is that the molarity of the solution can be converted to the number of moles of solute present in

`"1 L" = 10^3` `"mL"`

of solution. In your case, a `"0.220-M"` solution of ethanol will contain `0.220` moles of ethanol for every `10^3` `"mL"` of solution.

This implies that `2.90 * 10^(-3)` moles of ethanol will be present in

`2.90 * color(blue)(cancel(color(black)(10^(-3))))color(red)(cancel(color(black)("moles ethanol"))) * overbrace((color(blue)(cancel(color(black)(10^3)))color(white)(.) "mL solution")/(0.220color(red)(cancel(color(black)("moles ethanol")))))^(color(blue)("= 0.220 M"))`

`= color(darkgreen)(ul(color(black)("13.2 mL solution")))`

The answer is rounded to three sig figs.