This molarity calculator is a tool for converting the mass concentration of any solution to molar concentration (or, otherwise speaking, recalculating grams per ml to moles). You can also calculate what is the required mass of the substance to achieve a desired molarity. This article will provide you with the molarity definition and molarity formula. To understand the topic as a whole, you will find the mole definition, a paragraph about molarity units and the comparison of two misleading terms: molarity vs molality. What is more, we prepared for you some interesting examples of molar solutions and a short step-by-step tutorial of how to calculate molarity of a concentrated solution. In the end, you can learn the titration definition and discover how to find the molar concentration using the titration process.
Molar concentration - introduction
When you look around yourself, even when sitting at home, you can notice many different substances. Majority of these substances don't exist as pure materials but are, in fact, mixtures.
Mixtures consist of different compounds, and sometimes the number of elements may be quite high. Orange juice in your glass, a cup of tea, detergents in the bathroom or milk - all these substances are mixtures. Even biological organisms are very complex mixtures of molecules, gases, and ions dissolved in water.
In chemistry, we can consider two types of mixtures:
Homogeneous mixtures - components are uniformly distributed throughout the mixture, and there is only one phase of matter observed. They are also known as solutions and might occur in solid, liquid or gas state. It is not possible to simply separate the mixture components. Examples: sugar water, dishwashing detergent, steel, vine, windscreen washer fluid, air.
Heterogeneous mixtures - components of the mixture are not uniform and may have regions with different properties. Different samples of the mixture are not identical. At least two phases are always present in the mixture, and it's usually possible to physically separate them. A few examples of such substances: blood, concrete, ice cubes in cola, pizza, the Pacific Ocean.
Concentration is one of the most known and important parameters for anybody who works with any chemical substances or reactions. It measures how much of a substance is dissolved in a given volume of solution.
Chemists use many different units for describing the concentration. However, the term molarity, also known as molar concentration, is the most common way of expressing the concentration. When the reactants (compounds) are expressed in mole units, it allows writing them in chemical reactions with integers. That helps to easily combine their amounts. First, let's take a closer look at what is the mole, so we can move on later to find what is molarity.
The mole is the SI unit of measurement for the amount of substance. The current definition was adopted in the year 1971 and bases on carbon substance assumptions. It says:
"The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilograms of carbon 12; its symbol is "mol". When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles."
It follows that the molar mass of carbon 12 is exactly 12 grams per mole, M(¹²C) = 12 g/mol. The word "substance" in the definition should specify (be replaced with the name of) the substance concerned in a particular application, e.g. amount of chloride (HCl) or amount of carbon dioxide CO₂. It is crucial to always give a precise specification of the entity involved (as noted in the second part of the mole definition). This should be done by providing the empirical chemical formula of the material involved.
According to the newest conventions (effective since 20 May 2019), mole definition states that a mole is the amount of a chemical substance that contains exactly
6.02214076*10²³particles like atoms, molecules, etc. That number equals to the Avogadro's constant. It's symbol is NA or L. The Avogadro number provides the convenience while considering the substances weighs and chemical reactions, thanks to the values that you can directly read from periodic table (e.g. 1 mole of N₂ is 28 g or 1 mole of NaCl is 58.5 g).
We can link the number of entities X in a specified sample - N(X), and the amount of substance of entities X in the same sample - n(X), with the relation:
n(X) = N(X)/NA. N(X) is dimensionless, and n(X) has the SI unit mole.
What is molarity?
Not to be confused with all similar chemical terms, keep in mind that molarity means exactly the same as molar concentration (M). Molarity expresses the concentration of a solution. It is defined as the number of moles of a substance or solute, dissolved per liter of solution (not per liter of solvent!).
concentration = number of moles / volume
The following equation will allow you to find the molarity of a solution:
molarity = concentration / molar mass
The concentration denotes the mass concentration of the solution, expressed in the units of density(usuallyg/l or g/ml).
Molar mass is the mass of 1 mole of the solute. It is expressed in grams per mole. It is a constant property of each substance - for example, the molar mass of water is approximately equal to 18 g/mol.
Our calculator can also find the mass of substance you need to add to your solution to obtain a desired molar concentration, according to the formula
mass / volume = concentration = molarity * molar mass
where mass is the mass of solute (substance) in grams, and volume is the total volume of the solution in liters.
Molarity has many applications. One of them is the calculating the solution dilution.
The units of molar concentration are moles per cubic decimeter. They are noted as mol/dm³ as well as M (pronounced "molar"). The molar concentration of solute is sometimes abbreviated by putting square brackets around the chemical formula of the solute. E.g., the concentration of hydroxide anions can be written as [OH⁻]. In many older books or articles, you can find different units of molar solutions - moles per liter (mol/l). Remember that one cubic decimeter equals to one liter, so these two notations express the same numeric values.
Formerly, chemists used to give concentrations as
weight of solute/volume. Nowadays, since mole has become the most common way of quoting the quantity of a chemical substance, molarity is commonly used instead.
Note that molarity might be quite often confused with the term molality. Molality is usually written with lower case m, while molarity (what was mentioned above) with an uppercase M. We explain the difference between these two in the paragraph below.
How to calculate molarity
- Choose your substance. Let's assume that it is the hydrochloric acid (HCl).
- Find the molar mass of your substance. For the hydrochloric acid it is equal to 36.46 g/mol.
- Decide on the mass concentration of your substance - you can either input it directly or fill put the boxes for substance mass and solution volume. Let's assume that you have 5 g of HCl in a 1.2 liter solution.
- Convert the expressions above to obtain a molarity formula. As
mass / volume = molarity * molar mass, then
mass / (volume * molar mass) = molarity.
- Substitute the known values to calculate the molarity:
molarity = 5 / (1.2 * 36.46) = 0.114 mol/l = 0.114 M.
- You can also use this molarity calculator to find the mass concentration or molar mass. Simply type in the remaining values and watch it do all work for you.
Molarity vs molality
Let's consider the differences between these two similarly named chemical concepts: molarity and molality. We hope that after reading this paragraph you will have no doubts regarding this topic.
Both terms are used to express the concentration of a solution, but there is a significant difference between them. While molarity describes the amount of substance per unit volume of solution, molality defines the concentration as the amount of substance per unit mass of the solvent. In other words, molality is the number of moles of solute (dissolved material) per kilogram of solvent (where the solute is dissolved in).
It is possible to recalculate from molarity to molality and vice versa. To make this shift, use the formula below:
molarity = (molality * mass_density_of_the_solution) / (1 + (molality * molar_mass_of_the_solute))
In this molarity vs molality table, you can find all main differences between these two terms:
|Definition||Amount of substance (in moles) divided by the volume (in litres) of the solution||Amount of substance (in moles) divided by the mass (in kg) of the solvent|
|Symbol||M||m or b|
|Temperature and pressure||dependent||independent|
|Usage||more popular, practical to use in the lab, faster and easier||accurate but rarely used|
Molar solution - life examples
As you already know, mixtures and solutions surround us on all sides, and they are a consistent part of the natural environment. In the table below, you can find the list of orders of magnitude for molar concentration - examples taken from the natural environment.
|10−⁻¹⁵||fM||2 fM||bacteria in surface seawater (1×10⁹/L)|
|10⁻¹⁴||-||50–100 fM||gold in seawater|
|10⁻¹²||pM||7.51–9.80 pM||normal range for erythrocytes in blood in an adult male|
|10⁻⁷||-||101 nM||hydronium and hydroxide ions in pure water at 25 °C|
|10−4||-||180–480 µM||normal range for uric acid in blood|
|10⁻³||mM||7.8 mM||upper bound for healthy blood glucose 2 hours after eating|
|10⁻²||cM||44.6 mM||pure ideal gas at 0 °C and 101.325 kPa|
|10⁻¹||dM||140 mM||sodium ions in blood plasma|
|10²||hM||118.8 M||pure osmium at 20 °C (22.587 g/cm³)|
|10⁴||hM||24 kM||helium in the solar core (150 g/cm³ * 65%)|
Determining the molar concentration by titration
The titration is a technique thanks to which you can find the concentration of an unknown solution, based on its chemical reaction with a solution of known concentration. This process is based on adding the titrant (with a known concentration & volume) to a known quantity of the unknown solution (the analyte) till the reaction is complete. You can determine the concentration of the analyte by measuring the volume of used titrant.
Follow these steps to find the molarity with the titration method:
- Prepare the concentrations - put the analyte in an Erlenmeyer flask and the titrant in a burette.
- Mix the concentrations - add the titrant to the analyte until the endpoint is reached. You can find this moment by observing the color change. Use the acid-base indicator for this purpose; in case of using phenolphthalein, you will notice color change form pink to colorless.
- Calculate the molarity - use the titration formula. If the titrant to analyte ratio is 1:1, use the equation:
acid_molarity * acid_volume = molarity_of_base * volume_of_base.
For ratios other than 1:1, you need to modify the formula.
Example: 35 ml of 1.25 M HCl acid is needed to titrate a 25 ml solution of NaOH. In that case, you can use the 1:1 formula, because one mole of HCl reacts with one mole of NaOH. Then, multiply the molarity of the acid by the volume of the acid -
1.25 * 35 = 43.75 and the result, by the volume of the base. The molarity of the base equals
43.75 / 25 = 1.75 M.