Concentration calculator
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
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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.
How to recompute concentration?
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Choose your substance. Let's assume that it is sodium chloride (NaCl).
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Find the molar mass of sodium chloride. It is equal to 58.5 g/mol.
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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.
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Convert concentrations by using mathematical expression (2). Substitute the known values to calculate mass percentage concentration:
wt% = 3 * 100% * 58.5/1116 = 15.7% -
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 -
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 -
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.
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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).
