# Practical Application: Calculating Solution Concentrations

Instructor: Amanda Robb
In this practical application lesson, you'll be learning how to calculate different measures of solution concentrations including the molarity, mole fraction, molality, mass percent, and volume percent of solutions.

## What Are Solution Concentrations?

Even though solution concentrations might sound a bit intimidating, chances are you're already quite familiar with solutions. A solution is any homogenous mixture of two or more substances. The substance of greater quantity is called the solvent and the substance being dissolved is called the solute.

If you've ever made lemonade from a package, instant hot chocolate, or Gatorade from a mix, then you already know about solvents and solutes. The ratio of solute to solvent is the concentration of a solution. Today, we're going to look at examples of problems in which we calculate the concentration of solutions using different methods.

## Example Problem #1: Molarity

Calculate the molarity of a solution of two liters of water mixed with 30 grams of sodium chloride (NaCl).

To calculate molarity, we first have to recall that molarity is equal to the moles of solute per liter of solution.

### Step 1: Calculate Liters

First, make sure you have your solution volume in liters. This problem gives you the quantity in liters, but if you are given milliliters or gallons, you must convert first.

### Step 2: Calculate Moles

Next, calculate the number of moles in solution. To do this, you must find the molar mass of your compound. Find your nearest periodic table and then locate the molar mass of each element in the compound. For sodium chloride, we add the molar mass of sodium (22 g/mol) with the molar mass of chloride (35 g/mol) to get the total molar mass of 57 g/mol.

Next, set up a conversion to find out how many moles are in the total mass of solute you have. Flip your molar mass upside down so you have a fraction of 1 mole over the mass in grams. Then, multiply that by the number of grams total.

For our example we get:

30g NaCl x (1 mol / 57g) = 0.52 moles NaCl

### Step 3: Calculate Molarity

Now, you can simply divide the number of moles by the liters of solution and get molarity.

0.52 moles NaCl / 2L water = 0.26M

## Examples Problem #2: Mole Fraction

Calculate the mole fraction of a solution of two liters of water mixed with 30g of sodium chloride.

Another way to calculate concentration is the mole fraction. Here, we calculate the ratio of the moles of solute to the moles of the entire solution.

### Step 1: Calculate moles of each substance

First, calculate the moles of each substance in the solution. Here, we would do this just as we did to calculate molarity using the molar masses of sodium and chloride. The molar mass of 30g of sodium chloride is 57 g/mol, giving us 0.52 moles sodium chloride.

Similarly, for water, the periodic table can be used to find the molar mass (18 g/mol). Then, we can use the density of water to find the mass from the volume given, which is 1g/mL. So, we have 2,000g of water. Using our formula to calculate moles we get:

2,000g water / (1 mole / 18g) = 111.1 moles water

### Step 2: Add up the moles

Next, add up all the moles to get total moles. For our example, 0.52 moles NaCl + 111.1 moles water = 111.62 moles total.

### Step 3: Divide

Now, divide the moles of solute by the total number of moles in solution to get the mole fraction.

0.52 moles NaCl / 111.62 moles total = 0.004

## Example Problem #3: Molality

Molality might sound a lot like molarity, but it's actually different. Molality is the moles of solvent divided by the mass of the solvent in kilograms. Let's calculate molality for this example.

### Step 1: Calculate moles of solute

Again, use the molar mass and then convert the mass given in a problem to moles. For our example, we have 0.52 moles of sodium chloride.

### Step 2: Calculate kilograms of solvent

Again, we can convert a volume of water to mass by using the density of water, 1g/mL. Since we have 2,000 mL of water, this is equal to 2,000g of water, or 2kg.

### Step 3: Divide

Now, divide your moles of solute by the kilograms of solvent. In our example we get:

0.52 moles NaCl / 2kg water = 0.26m

## Example Problem #4: Mass Percent

Now, let's calculate the mass percent of 30g of NaCl in 2L of water. Mass percent is the mass of the solute divided by the mass of the solution.

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