The concentration calculator is a tool for converting the molarity into percentage concentration (or vice versa) with a known molar mass of the dissolved substance and the 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 following:
- The definition of concentration;
- The mass percentage concentration;
- The concentration formula; and
- A short step-by-step tutorial on how to recompute concentration.
What is concentration?
Concentration describes the composition of a solution. It is a phrase we typically use when discussing water-based solutions, but we can use it to refer to any mixture.
It is also the amount of a constituent (expressed with mass, moles, etc.) divided by the total mass or volume of a solution.
There are several mathematical descriptions, such as molarity or mass percentage concentration. Moreover, it is possible to describe a solution by the ratio of solute in a solvent solution.
A solution can be described in a qualitative way by using the words concentrated and dilute. Concentrated refers to a solution with a higher amount of solute, while a diluted solution has a smaller amount of dissolved substance. If you know the concentration of a solution and dilute it, you can use the solution dilution calculator to calculate the concentration of a diluted solution. We also have a tool to help you calculate the concentration of an unknown sample with the calibration curve!
What is mass percentage concentration formula?
Mass percent concentration (wt%) is one of the types of percentage concentration. It is defined as the ratio of the solute's mass to the solution's total mass. Then it's multiplied by 100% to arrive at a percentage. Written as a formula, that's:
wt% = m₁ / m₂ × 100%
- m₁ – Mass of solute [g]; and
- m₂ – Total mass of solution [g].
How to calculate concentration – other useful equations
If you know the density (d [g/dm³]) and molarity (c [mol/dm³]) of the solution and molar mass (M [g/mol]) of the solute, you can calculate mass percentage concentration by a given mathematical equation (1):
wt% = c × 100% × M/d
Alternatively, if you know the density (d) and mass percentage concentration (wt% [%]) of the solution and molar mass (M) of the solute, you can calculate molarity by this mathematical equation (2):
c = wt% × d / 100% × M
Knowing the mass percentage concentration (wt%), you can easily calculate the mass of solute (m₁) (equation (3)):
m₁ = wt% × m₂ / 100%
If you want to calculate of mass of solute per 100 g of water (H₂O), you can use this equation:
m = m₁ × 100/(m₂ - m₁)
where m is the mass of solute per 100 g of water [g/100 g H₂O], m₁ – the mass of solute, calculated from equation (4) [g], m₂ – total mass of solution [g]. To make calculations easier, assume 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 a 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.
Knowing the concentration of fluids is very useful in everyday life, and one such application of it lies in adjusting the salinity of your swimming pool water! See our pool salt calculator for more.
The reconstitution process also requires solution preparation with accurate concentrations of diluent and a dry ingredient. Check out our reconstitution calculator.
The mass percentage calculation represents the concentration of a component of a mixture or compound.
How to recompute concentration?
Here is how to recompute the concentration:
Choose your substance. Let's assume that it is sodium chloride (NaCl).
Find the molar mass of sodium chloride. It is equal to 58.5 g/mol.
Find the molarity of your solution and its density. Let's assume that you have 3M NaCl with a density equal to 1.116 g/cm³ = 1116 g/dm³ = 1116 g/L.
Convert concentrations by using mathematical expression (1). Substitute the known values to calculate mass percentage concentration:
wt% = 3 × 100% × 58.5/1116 = 15.7%
Let's assume that the total mass of the solution (m₂) is 100 g. Using equation (3), the mass of the dissolved substance is calculated by:
m₁ = 15.7% × 100/100% = 15.7
Then, substitute the known values to calculate the amount of substance per 100 g of water (equation (4)):
m = 15.7 × 100 /(100 – 15.7) = 1570/84.3 = 18.66 g/100 g H₂O
You can also use this concentration calculator to calculate 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 the work for you.
Alternatively, you can calculate molarity (c) by using this calculation. If you know mass percentage concentration (wt%), density (d), and molar mass (M), this calculator calculates molarity (c) and the amount of substance per 100 g of water (m).
How do I compute mass percentage concentration given molarity?
To calculate mass percentage concentration from the molarity of the solution, you need to:
- Determine the density (g/dm³) of the solute.
- Find the solute's molar mass (g/mol).
- Multiply the molar mass by the molarity.
- Divide the result from Step 3 by the density of your solute.
- Multiply the result by 100% to obtain percentages.
How do I find the mass of solute given mass percentage concentration?
The mass of solute can be easily derived from mass percentage concentration (wt%) on the condition that you also know the total mass of solution (M). You need to multiply these two values and divide the product by 100%. That is, the mass of solute is equal to
wt% × M / 100%.
What is mass percentage concentration if I have 10 g of solute?
The answer depends on the total mass of the solution. You need to divide
10 g by the total mass and multiply by
100% to get your answer. For example, if you have 1 kg in total, then mass percentage concentration is 1 % because
10 g / 1000 g × 100% = 1%.