Density
g/cm³
Molar mass
g/mol
Molarity
M
Percentage concentration
wt/wt %
Mass per 100 g H2O
g
/100 g H2O

# Concentration Calculator

By Anna Pawlik, PhD candidate

The concentration calculator is a tool for converting the molarity into percentage concentration (or vice versa) with a known molar mass of dissolved substance and density of the solution. In addition, you can calculate the mass of the substance per 100 g of water if the percentage concentration is known. This article will provide you with the definition of concentration and mass percentage concentration, as well as with a short step-by-step tutorial of how to recompute concentration.

## What is concentration?

Concentration is used to describe the composition of a solution, mainly water solution, but it can be used for any mixtures. Otherwise speaking, it is the amount of a constituent (expressed with mass, moles etc) divided by total mass or volume of a solution. There are several types of mathematical description such as molarity or mass percentage concentration. Moreover, it is possible to describe a solution by the ratio of solute in a solution to solvent. Molarity can be calculated with molarity calculator.

The solution can be described in a qualitative way by using words concentrated and dilute. Concentrated refers to a solution with a higher amount of solute, while a dilute solution has a smaller amount of dissolved substance. If you know the concentration of a solution and you dilute it, you can use the solution dilution calculator in order to calculate the concentration of a diluted solution .

## Mass percentage concentration, concentration formula

One of the types of percentage concentration is mass percent concentration (wt%). It is expressed by mass of solute divided by total mass of the solution and multiplied by 100% (equation (1))

`wt% = m₁/m₂ × 100%` (1)

where m₁ is mass of solute [g], m₂ - total mass of solution [g].

## How to calculate concentration - other useful equations

• If you know density (d [g/dm³]) and molarity (c [mol/dm³]) of the solution and molar mass (M [g/mol]) of solute, you can calculate mass percentage concentration by a given mathematical equation (2):

`wt% = c * 100% * M/d` (2)

• Alternatively, if you know density (d) and mass percentage concentration (wt% [%]) of the solution and molar mass (M) of solute, you can calculate molarity by a given mathematical equation (3):

`c = wt% * d / 100% * M` (3)

• Knowing the mass percentage concentration (wt%), you can easily calculate mass of solute (m₁) (equation (4)):

`m₁ = wt% * m₂ / 100%` (4)

• If you want to calculate of mass of solute per 100 g of water (H₂O), you can use equation (5):

`m = m₁ * 100/(m₂ - m₁)` (5)

where m is mass of solute per 100 g of water [g/100 g H₂O], m₁ - mass of solute, calculated from equation (4) [g], m₂ - total mass of solution [g]. In order to make calculations easier, it can be assumed that m₂ = 100 g.

Did you know that we can also approach this problem by using proportions?

`a / b = c / d`

We can put the mass of your substance as a numerator (`a`) and the volume of the solution as denominator (`b`) on the left side of the equation. Then, we can set the denominator (`d`) on the right side of the equation as `1`. By calculating this proportion, we will get the concentration - mass of the substance per 1 unit of volume. You can do it by using our proportion calculator. Remember to perform the calculations using the same units!

## How to recompute concentration?

1. Choose your substance. Let's assume that it is sodium chloride (NaCl).

2. Find the molar mass of sodium chloride. It is equal to 58.5 g/mol.

3. Find molarity of your solution and its density. Let's assume that you have 3M NaCl with density equal to 1.116 g/cm³ = 1116 g/dm³ = 1116 g/L.

4. Convert concentrations by using mathematical expression (2). Substitute the known values to calculate mass percentage concentration: `wt% = 3 * 100% * 58.5/1116 = 15.7%`

5. Let's assume that total mass of solution (m₂) is 100 g. Using equation (4) mass of dissolved substance is calculated: `m₁ = 15.7% * 100/100% = 15.7`

6. Then, substitute the known values to calculate the amount of substance per 100 g of water (equation (5)): `m = 15.7 * 100 /(100 – 15.7) = 1570/84.3 = 18.66 g/100 g H₂O`

7. You can also use this concentration calculator to mass percentage concentration or molarity and the amount of substance per 100 g of water. Simply type in the remaining values and watch it do all work for you.

8. Alternatively, you can also calculate molarity (c) by using this calculation. If you know mass percentage concentration (wt%), density (d) and molar mass (M), this calculator calculate molarity (c) and the amount of substance per 100 g of water (m).

Anna Pawlik, PhD candidate