# Question #10436

##### 1 Answer

#### Explanation:

In order to be able to calculate this solution's **molarity**, you must first determine how many **moles** of ethanol,

To do that, use ethanol's **molar mass**, which is equal to **one mole** of that compound.

In this case, **one mole** of ethanol has a mass of

#1.77 color(red)(cancel(color(black)("g"))) * ("1 mole C"_2"H"_5"OH")/(46.07color(red)(cancel(color(black)("g")))) = "0.03842 moles C"_2"H"_5"OH"#

Now, a solution's *molarity* tells you how many *moles of solute* you get **per liter of solution**. This means that you can find a solution's molarity by finding out how many moles of solute you get in **one liter** of solution.

Your solution is said to have a volume of *liters* by using

#color(purple)(|bar(ul(color(white)(a/a)color(black)("1 L" = 10^3"mL")color(white)(a/a)|)))#

#85.0 color(red)(cancel(color(black)("mL"))) * "1 L"/(10^3color(red)(cancel(color(black)("mL")))) = 85.0 * 10^(-3)"L"#

So, the number of moles of solute present in **one liter** of this solution will be

#1 color(red)(cancel(color(black)("L solution"))) * ("0.03842 moles C"_2"H"_5"OH")/(85.0 * 10^(-3)color(red)(cancel(color(black)("L solution")))) = "0.452 moles C"_2"H"_5"OH"#

Since **one liter** of solution contains **moles** of ethanol, it follows that the solution's molarity will be equal to

#"molarity" = c = color(green)(|bar(ul(color(white)(a/a)"0.452 mol L"^(-1)color(white)(a/a)|)))#

The answer is rounded to three **sig figs**.