Calculate Molarity of Each of The Following Solutions

What is Molarity?

Molarity (M) is defined as the number of moles of solute dissolved in one liter of solution. It's one of the most common ways to express the concentration of a solution in chemistry. Molarity is particularly useful in stoichiometric calculations, where knowing the exact amount of solute in a given volume of solution is crucial.

The molarity scale is dimensionless, meaning it doesn't have units. However, it's important to note that the units for moles and liters must be consistent when calculating molarity. For example, if you're using grams of solute, you must first convert them to moles using the solute's molar mass.

Molarity Formula

The basic formula for calculating molarity is:

Where:

• M = Molarity (moles per liter)
• n = Number of moles of solute
• V = Volume of solution in liters

To use this formula, you need to know the mass of the solute and its molar mass, as well as the volume of the solution. The calculation typically involves several steps:

1. Convert the mass of the solute to moles using its molar mass
2. Convert the volume of the solution to liters
3. Divide the number of moles by the volume in liters to get molarity

How to Calculate Molarity

Step 1: Determine the Moles of Solute

To find the number of moles of solute, you need to know the mass of the solute and its molar mass. The formula is:

For example, if you have 25 grams of sodium chloride (NaCl) with a molar mass of 58.44 g/mol:

Step 2: Determine the Volume of Solution

The volume of the solution should be in liters. If you're given milliliters, convert them to liters by dividing by 1000. For example, 500 mL would be 0.5 L.

Step 3: Calculate Molarity

Once you have the number of moles and the volume in liters, you can calculate molarity using the formula:

Using our previous example with 0.428 moles of NaCl dissolved in 0.5 L of solution:

Example Calculations

Let's look at a few more examples to solidify your understanding of molarity calculations.

Example 1: Diluting a Solution

You have 100 mL of a 2.0 M hydrochloric acid (HCl) solution. You need to prepare 500 mL of a 0.5 M HCl solution. What volume of the original solution should you use?

First, calculate the moles of HCl in the original solution:

Now, determine the volume needed to make 0.5 M solution:

You need to use 400 mL of the original solution to prepare 500 mL of 0.5 M HCl solution.

Example 2: Preparing a Solution from Solid Solute

You need to prepare 250 mL of a 0.10 M potassium chloride (KCl) solution. The molar mass of KCl is 74.55 g/mol. How many grams of KCl should you dissolve?

First, calculate the moles needed:

Now, convert moles to grams:

You need to dissolve approximately 1.86 grams of KCl to prepare 250 mL of 0.10 M KCl solution.

Common Mistakes

When calculating molarity, several common mistakes can lead to incorrect results. Being aware of these pitfalls can help you avoid them:

1. Using incorrect units: Always ensure that the volume is in liters and the mass is in grams before performing calculations.
2. Incorrect molar mass: Using the wrong molar mass for the solute will lead to incorrect mole calculations.
3. Volume miscalculation: Forgetting to convert milliliters to liters or vice versa can significantly affect the final molarity.
4. Precision errors: Rounding intermediate results too early can lead to less accurate final answers.
5. Confusing molarity with molality: Remember that molarity is based on the volume of the solution, while molality is based on the mass of the solvent.