Molarity Calculator

Molarity is the concentration of a solution in terms of the number of moles of the solute in 1 dm³ (1 liter) of the solution.

The units of molarity are M or mol/L. A 1 M solution is said to be “one molar”.

A mole is the quantity of anything that has the same number of particles as 12 g of carbon-12. This equates to roughly 6.02x10²³, also referred to as Avogadro's Number. So, 1 mole of hydrogen gas (H₂) contains 6.02x10²³ molecules, and 1 mole of glucose (C₆H₁₂O₆.) also contains 6.02x10²³ molecules, but as H₂ is a much simpler molecule, 1 mole of H₂ will have a much smaller mass (the molar mass) than 1 mole of C₆H₁₂O₆.

The molar mass is the mass in grams of 1 mole of a particular molecule.

One mole of sodium (Na) is 22.99 g, and 1 mole of chlorine is 35.45 g. For sodium chloride (NaCl) they are in a ratio of 1:1 so the molar mass of NaCl is 22.99 + 35.45 = 58.44 g/mol.
For a compound like water (H₂O), 1 mole of hydrogen (H) is 1.008 g/mol and 1 mole of oxygen (O) is 15.9994 g/mol. So, the molar mass of H₂O is (2 x 1.008) + 15.9994 = 18.0154 g/mol.

Two solutions that have the same molarity will have the same number of molecules of the chemical per liter but are likely to contain differing masses of that chemical per liter to achieve this. Whereas two solutions at the same concentration will have the same mass of the chemical per liter of solution but are therefore likely to have differing numbers of molecules of that chemical per liter. Provided some additional information is known, one value can be deduced from the other using the equations below.

To calculate molarity or to calculate related values (including volume, mass, molar mass and concentration) from molarity, the following equations are utilized.

The scenario in which most lab scientists will encounter this type of calculation is when making up solutions following a standard operating procedure (SOP) or a scientific paper. Here, the solution being used is typically defined by its molar concentration (M). For example;
You need to make a 0.5 M solution of NaCl, having decided you want 2 liters how much NaCl should you add?

1. First you must calculate the number of moles in this solution, by rearranging the equation
   No. Moles (mol) = Molarity (M) x Volume (L)
   = 0.5 x 2
   = 1 mol
   
2. For NaCl, the molar mass is 58.44 g/mol
   Now we can use the rearranged equation
   Mass (g) = No. Moles (mol) x Molar Mass (g/mol)
   = 1 x 58.44
   = 58.44 g
   So, to make 2 liters of a 0.5 M solution of NaCl, you would need to add 58.44 g of NaCl.
   

Atomic mass (m_a) – mass of one atom of that element which typically reflects the mass of the nucleus (protons plus neutrons). For example, hydrogen is 1. This used to be measured in atomic mass units (AMU) but is now typically expressed in Daltons (Da).

Molecular mass (also called molecular weight) - sum of the atomic weights of all atoms appearing in a given molecular formula. For example, glucose has a molecular formula of C₆H₁₂O₆, the molecular weight of C is 12 Da, H is 1 Da and O is 16 Da. Therefore, the molecular mass of glucose is = (6 x 12) + (12 x 1) + (6 x 16)
= 72 + 12 + 96
= 180 Da
Numerically this is the same as molar mass differing only in the units in which they are expressed.

Relative atomic mass and relative molecular mass (M_R) – values for atomic and therefore molecular masses are normally obtained relative to the mass of the isotope ¹²C (carbon-12), however “relative” is generally omitted from the title. Written correctly, the relative values have no units.

Formula mass (also called formula weight) - sum of the atomic weights of all atoms appearing in a given empirical formula. The empirical formula indicates the ratio of atoms of each element in a molecule rather than the actual number. For example, glucose (molecular formula C₆H₁₂O₆) would therefore have the empirical formula CH₂O, the molecular weight of C is 12 g, H is 1 g and O is 16 g. Therefore, the formula mass of glucose is
= (1 x 12) + (2 x 1) + (1 x 16)
= 12 + 2 +16
= 30 g
For molecules like H₂O, where the formula is already in its simplest form, the formula mass and molecular mass are the same.

Normality – similar to molarity, however calculation of normality uses the number of mole equivalents rather than the number of moles. Units are N or eq/L. Normality is generally only used when a substance has more than one sub-species that can participate in a specified reaction such as a proton for acid/base reactions, an electron for oxidation/reduction reactions, or in precipitation reactions. For example, sulfuric acid (H₂SO₄) has two ionizable protons (H⁺) which can participate in the neutralization of a base such as sodium hydroxide (NaOH)
H₂SO₄(aq) + 2 NaOH → 2 Na⁺(aq) + 2 H₂O + SO₄²⁺(aq)
If a sulfuric acid solution is 1 M, then it is 2 N expressed as normality. A 2 N solution is said to be “two normal”.

Molality – similar to molarity, however calculation of molality uses the mass rather than volume of the solvent used, making it temperature independent unlike molarity. Units are m or mol/kg.