### How to calculate solution concentration

Solution concentration can be expressed in many ways. However, here, we will discuss two ways in which solution concentration can be calculated. The two ways are:

• Percent by mass

• Molarity

### What’s solution concentration?

Solution concentration is the amount of solute dissolved in a given amount of solution or solvent. Generally, we can express solution concentration mathematically as:

Solution concentration = amount of solute/amount of solution or solvent

The solute is the chemical in lesser amounts, while the solvent is the chemical in larger amounts.

### What’s solution concentration in percent by mass?

Percent by mass (% m) is the mass of solute divided by the mass of solution multiplied by 100. Mathematically, % by mass = (mass of solute in grams/mass of solution in grams) x 100.

Notice! Mass of solution = mass of solute in grams **plus** mass of solvent in grams.

Since the grams cancel out, the final unit will be in percent. For example, a 20.0 percent sodium chloride (NaCl) solution will contain 20.0 g of NaCl in 100 g of solution (20 g/100 g). Since mass of solution is equal to 100 g, we can get the mass of solvent by subtracting 20 g of solute from the 100 g of solution (100 g – 20 g = 80 g of solvent). So, if water was used as our solvent, our mass of water will be 80 g. This means that the 20 g of NaCl/80 g of water can be used as a conversion factor to convert from mass of solute to mass of solvent and vice versa.

*For example,** How many grams of NaCl must be added to 1000 g** of water to prepare a 20.0 percent NaCl solution.*

**Answer**

The 20 percent NaCl solution means 20 g of NaCl/100 g of solution (read as 20 g of NaCl in a 100 g of solution). Since the question demands how many grams of NaCl must be added to 1000 g of water, we have to figure out the amount of water in the 20 percent of solution so that we can set up the correct conversion factor. To get that, we simply subtract 20 g of NaCl from the 100 g of solution (100 g – 20 g = 80 g of water).

Now, our conversion factor is: 20 g NaCl/80 g water.

To figure out how many grams of NaCl must be added to 1000 g, we simply multiply the 1000 g of water by 20 g NaCl/80 g water. If this calculation confuses you, click here to read more about conversion factors.

Thus, 1000 g H_{2}O x 20 g NaCl/80 g H_{2}O = 250 g. Therefore, 250 g of NaCl must be dissolved in 1000 g of water to make a 20 % NaCl solution.

Here is a summary of the calculation:

### What’s Molarity?

Molarity, with symbol M, is defined as the number of moles of solute present in a liter of solution. Mathematically, Molarity can be expressed as: Molarity, M = moles of solute/Liter of solution.

Notice, volume of solution is in liters. If volume is not given in liters, you must convert to liters before you calculate solution concentration. Similarly, if mass of solute is given, you must convert mass to moles before you calculate solution concentration. Molarity is a derived unit (moles/Liter). Therefore, you can use it as conversion factor to convert from moles to liters and vice versa. Chemists like reporting concentration in Molarity because it ties well with the mole concept and can be used to determine the number of ions or molecules in a solution.

*For example,** You made a 200mL solution of glucose** that contains 0.3 mol of glucose. What’s the** solution concentration?*

**Answer**

First, we must convert the 200 mL to liters: Since 1000 mL = 1 L

We can write that, 200 mL x 1L/1000 mL = .20 L

Therefore, Molarity = mol/L = .3 mol glucose/.20L = 1.5 mol/L = 1.5 M glucose.

*Now, if we modify the above example by changing the moles of glucose to grams of glucose, we will get the following question:*

*You made a 200mL solution of glucose**that contains 54 g of glucose. What’s the**solution concentration in Molarity?*

To solve this question, we will recall that: Molarity (M) = moles of solute/Liter of solution

But since we are given grams of glucose not moles of glucose, then it follows that we must convert the 54 g of glucose into moles of glucose. To do this, we will need the molar mass of glucose. But to calculate molar mass, we will need the chemical formula of glucose. This formula is : C_{6}H_{12}O_{6}. Next, we will then look on the periodic table for the molar mass of each atom, and then multiply this value by the corresponding number of each atom in the formula.

If we do, we will get:

Therefore, the molar mass of glucose is 180.12 g/mol. Next, to get the moles of glucose, we must multiply 54 g by the inverse of 180.12 g/mol, which is— 1 mol/180.12 g— to get our answer in moles. If we do, we will get:

Now, just like the previous example, we must divide moles of glucose by the volume of the solution in liters to get Molarity. If we do, we will get:

Molarity of glucose = 0.30/0.20L = 1.5 M

As you can see, this answer is the same as the answer we got in the previous example. Therefore, regardless of whether you are starting from mass or moles of a particular chemical, you will always arrive at the same answer.

To learn how to prepare a chemical solution from scratch, click here.