# A liquid has a molecular weight of 105.141g/mol. Its density is 1.173g/mL. What is the molarity of the pure liquid?

Dec 25, 2015

$\text{11.16 M}$

#### Explanation:

Your strategy here will be to pick a sample of this compound and try to find how many moles it contains per liter.

Although molarity is usually defined as moles of solute per liters of solution, you can extend this concept to pure liquids, provided that you figure out how many moles you'd get per liter of pure liquid.

As you know, a substance's molar mass tells you the mass of one mole of that substance. In this case, the liquid is said to have a molar mass of $\text{105.141 g/mol}$, which means that one mole will have a mass of $\text{105.141 g}$.

To make the calculations easier, let's pick a $\text{105.141-g}$ sample of this liquid, the equivalent of one mole. You know from the given density that every milliliter of this liquid will have a mass of $\text{1.173 g}$.

This means that our sample will occupy a volume of

105.141 color(red)(cancel(color(black)("g"))) * "1 mL"/(1.173color(red)(cancel(color(black)("g")))) = "89.63427 mL"

Convert this volume to liters

89.63427 color(red)(cancel(color(black)("mL"))) * "1 L"/(1000color(red)(cancel(color(black)("mL")))) = "0.08963427 L"

Finally, the molarity of the solution will be - remember that our sample contains exactly one mole of this liquid

$\textcolor{b l u e}{c = \frac{n}{V}}$

c = "1 mole"/"0.08963427 L" = color(green)("11.16 M")

The answer is rounded to four sig figs, the number of sig figs you have for the density of the liquid.