# Week 36 – Molarity

If you’ve ever made ice tea and decided it needs more sugar, you understand the importance of solution concentration.  Add too little sugar and the sugar concentration is too low to make the ice tea pleasantly sweet.  Add too much sugar and the ice tea just tastes like sugar water because the sugar concentration is too high.  Somewhere in there is the ice tea Goldilocks zone – just the right amount of sweet.  If you have access to water, a measuring cup, a glass, some tea, some sugar, and a teaspoon: fill a glass with one cup (8 ounces) of cold water, add one bag of tea, and let it steep while you continue working.

Back to our lesson: we need to understand the concept of molarity which is defined as the concentration of dissolved substances in a solution, expressed in moles of solute per liter of solution.  We use M as the unit of molarity (M = mol/L).  We already know how to calculate moles from grams, so just take moles and divide by volume (in liters) to calculate molarity.  Here’s an easy example question: glucose has a molar mass of 180 g/mol.  If 90 g of glucose is added to 1 L of water, calculate the molarity of the solution.  Answer: 90 g x 1 mol / 180 g = 0.5 mol, 0.5 mol / 1 L = 0.5 M.  The molarity of the solution is 0.5 M.

Here’s a harder example question: A 20 fluid ounce bottle of Dr. Pepper contains 64 grams of sugar (high fructose corn syrup).  Determine the molarity of sugar Dr. Pepper.

To approach this question, we need to know some additional pieces of information.  Ultimately, we need our answer in units of M, or mol/L.  So we need to convert ounces to liters and we need the molar mass of high fructose corn syrup.

Key information:

• 1 L = 33.814 fluid ounces
• High fructose corn syrup consists of glucose and fructose, both of which have a molar mass of 180 g/mol.

Answer: First, let’s convert 64 grams of sugar to moles: 64 g x (1 mol / 180 g) = 0.36 mol of sugar.  Next, let’s convert 20 ounces to liters: 20 ounce x (1 L / 33.814 ounces) = 0.59 L.  Finally, we just need to divide moles by liters to calculate molarity: 0.36 mol / 0.59 L = 0.61 M.

Let’s turn our attention back to the tea we started making at the beginning of this lesson and wrap this up with a more challenging practice problem.  Question: If we add one teaspoon of table sugar to our 8 ounce glass of tea, what is the molarity of the solution?

Key information:

• 1 L = 33.814 fluid ounces
• molar mass of table sugar (sucrose) = 342 g/mol
• 1 teaspoon of table sugar = 4.2 grams

Answer: Let’s begin by calculating the number of moles of sucrose (table sugar) added to the tea.  One teaspoon = 4.2 grams of sucrose.  4.2 grams x (1 mole / 342 g) = 0.0123 mol of sucrose.  Next, let’s convert 8 ounces to liters: 8 ounces x (1 L / 33.814 ounces) = 0.237 L.  Finally, to calculate molarity (M), divide moles by liters: 0.0123 mol / 0.237 L = 0.052 M.

Time to show what you know!  Complete the Week 36 – Molarity Google Form assignment and then return to Week 36 – Solution Concentration and continue working.