13.42 Calculate The Molarity of The Following Aqueous Solutions

Molarity is a fundamental concept in chemistry that measures the concentration of a solute in a solution. It's expressed as moles of solute per liter of solution (mol/L). This guide will explain how to calculate molarity, provide a step-by-step example, and help you avoid common mistakes.

What is Molarity?

Molarity (M) is defined as the number of moles of solute dissolved in one liter of solution. The formula for molarity is:

Molarity (M) = Moles of Solute / Volume of Solution (L)

Where:

Moles of Solute - The amount of substance in grams divided by its molar mass
Volume of Solution - The total volume of the solution in liters

Molarity is commonly used in chemistry because it allows chemists to compare the concentration of different solutions regardless of their total volume. It's particularly useful in titrations, dilution calculations, and reaction stoichiometry.

How to Calculate Molarity

Calculating molarity involves these steps:

Determine the mass of the solute in grams
Find the molar mass of the solute (sum of atomic masses of all atoms in the molecule)
Calculate the number of moles of solute using the formula: moles = mass / molar mass
Measure the total volume of the solution in liters
Divide the number of moles by the volume in liters to get molarity

Tip: Always ensure your volume is in liters. If you have milliliters, divide by 1000 to convert to liters.

Example Calculation

Let's calculate the molarity of a solution made by dissolving 5.2 grams of sodium chloride (NaCl) in 250 milliliters of water.

Step 1: Find the molar mass of NaCl

The molar mass of NaCl is the sum of sodium (22.99 g/mol) and chlorine (35.45 g/mol):

Molar mass of NaCl = 22.99 + 35.45 = 58.44 g/mol

Step 2: Calculate moles of NaCl

Using the formula moles = mass / molar mass:

Moles of NaCl = 5.2 g / 58.44 g/mol ≈ 0.089 mol

Step 3: Convert volume to liters

250 milliliters = 0.25 liters

Step 4: Calculate molarity

Using the molarity formula:

Molarity = 0.089 mol / 0.25 L = 0.356 M

So, the molarity of this solution is approximately 0.356 M.

Common Mistakes

When calculating molarity, these common errors can occur:

Using incorrect molar mass - Always verify the molar mass of your solute
Incorrect volume units - Ensure volume is in liters, not milliliters
Mixing moles of solute and solvent - Molarity is about the solute, not the solvent
Rounding too early - Keep intermediate calculations precise until the final answer

Remember: Molarity is a concentration measure, not a measure of the total solution volume.

FAQ

What is the difference between molarity and molality?: Molarity measures moles of solute per liter of solution, while molality measures moles of solute per kilogram of solvent. Molarity changes with temperature, while molality does not.
Can molarity be greater than 1?: Yes, molarity can be greater than 1. A solution with a molarity of 2 M has 2 moles of solute per liter of solution.
How does dilution affect molarity?: Dilution decreases molarity because you're adding more solvent without adding more solute. The moles of solute stay the same, but the volume increases, lowering the concentration.
What units are used for molarity?: Molarity is expressed in moles per liter (mol/L) or molar (M).