# Question #2b0e3

Feb 20, 2015

The molarity of a solution is the number of moles of solute per liter of solution.

$\text{Molarity (M)}$ = $\text{moles of solute"/"liters of solution}$

For example, a 0.10 M HCl solution (read as "point one molar") contains 0.10 mole of HCl in every liter of solution. Anytime you see the abbreviation M, you should think of it as mol/L.

Problem 1. What is the molarity of a solution that contains 1.724 moles of ${\text{H"_2"SO}}_{4}$ in $\text{2.50 L}$ of solution? .

Calculation:
$\text{Molarity (M)}$ = $\text{1.724 mol H"_2"SO"_4"/"2.50 "L}$ = $\text{0.6896 mol}$$\text{H"_2"SO"_4"/L}$ = $\text{0.690 mol H"_2"SO"_4"/L}$ (due to three significant figures in 2.50 L.)

The container for this solution would be labeled $\text{0.690 M H"_2"SO"_4}$ and would be called $\text{0.690 molar H"_2"SO"_4}$ or sulfuric acid.

Problem 2. 70.0 grams of glucose ($\text{C"_6"H"_12"O"_6}$), are dissolved in enough water to make 2.00 L of solution. What is its molarity?

First determine the molar mass of glucose, which is 180.1559 g/mol. Next, divide the given mass by the molar mass to get moles.

Calculation:
$\text{70.0 g C"_6"H"_12"O"_6}$$\div$$\text{180.1559 g/mol}$ = $\text{0.389 mol C"_6"H"_12"O"_6}$

Now determine the molarity of the glucose solution.

Calculation:
$\text{0.389 mol C"_6"H"_12"O"_6"/"2.00 "L}$ = $\text{0.195 mol C"_6"H"_12"O"_6"/L}$

The container for this solution would be labeled $\text{0.195 M C"_6"H"_12"O"_6}$. We would say that it is a 0.195 molar solution of glucose.

Problem 3. What is the molarity of a solution prepared by dissolving 15.0 g of sodium hydroxide (NaOH) in enough water to make a total of 225 mL of solution?

First determine the number of moles in 15.0 g of NaOH by dividing the given mass by the molar mass for NaOH, which is 39.997 g/mol.

Calculation:
$\text{15.0 g NaOH}$$\div$$\text{39.997 g/mol}$ = $\text{0.375 mol NaOH}$

The volume has been given in mL. You need to convert 225 mL to liters.

Calculation:
$\text{225 mL}$ x $\text{1 L"/"1000 mL}$ = $\text{0.225 L}$

Now determine the molarity.

Calculation:
$\text{Molarity}$ = $\text{0.375 mol NaOH"/"0.225 L}$ = $\text{1.67 mol NaOH/L}$

The container for this solution would be labeled "1.67 M NaOH".We would say that this is a 1.67 molar solution of NaOH or sodium hydroxide.

The following diagram can help you remember how to calculate moles from given mass and molar mass, and how to calculate molarity from moles and volume in liters.

Here is a video which discusses how to complete a calculation of molarity.

video from: Noel Pauller