Concentration is one of the most important characteristics that defines the composition of a solution. This is an intensive property of solutions that indicates the relationship between the amount of solute and either the amount of solution (in most cases) or the amount of solvent (in the case of molality, for example). This can be expressed in different units, depending on the context in which it is going to be used, and also depending on how concentrated or diluted the solute is found in the solvent.

For the same reasons that we would not express the size of a cell in kilometers or the distance from the Earth to the planet Mars in nanometers, we must carefully select which concentration units are most appropriate in each situation and for each level of concentration.

In addition, concentrations can also be expressed in physical units, which are based on magnitudes such as masses and volumes, or in chemical units, in which the amounts of solute and/or solvent and/or solution are expressed in terms of the number of particles, moles, equivalents or others.

Regardless of the above, a solution only has a single concentration, and knowing how to transform that concentration between the different existing units is a basic skill for any chemistry student.

In this article, we show how to transform or convert concentration from molarity to parts per million or ppm.

## What is molarity?

Molarity, represented by the symbol M, is one of the most widely used units of concentration by chemists. It is a chemical unit of concentration that indicates the number of moles of solute present per liter of solution. Mathematically, molarity is given by the following formula.

where n sto is the number of moles of solute and V sol is the volume of the solution expressed in liters. Using the relationship between moles and mass, which is n=m/MM, the above formula can be written in terms of the mass of solute in grams and its molar mass in g/mol.

where m this is the mass of the solute in grams and MM this is the molar mass of the solute expressed in g/mol.

## What are parts per million?

Unlike molarity, parts per million correspond to a physical unit of concentration. This indicates how many “parts” of solute there are for every million “parts” of the solution. In this sense, it is a similar concept to percentages, only in that it is based on a million instead of 100 parts of solution.

By “parts” of solute and solution, it is understood either the mass or the volume, so there are 3 types of ppm, which are:

- Parts per million mass/mass or ppm m/m
- Parts Per Million Mass/Volume or ppm m/V
- Parts per million volume/volume or ppm V/V

The two most commonly used and the ones that are usually transformed into molarity and vice versa are ppm m/m and ppm m/V. In both cases, it is a very small unit of concentration, ideal for expressing the concentration of very dilute solutions.

### Parts per million mass/mass

There are two different ways of expressing the formula for calculating ppm. One is similar to the percent formula but multiplying by 10 6 (one million) instead of 100, and the other is integrating the factor of 10 6 in a unit transformation:

In the first case, any unit of mass can be used for the solute and the solution, as long as they are the same. In the second case, the mass of the solute must be expressed in milligrams if the amount of solution is expressed in kilograms. To convert molarity to ppm m/m we will use the second formula, since it is the most frequently used.

This formula allows us to understand ppm m/m as the milligrams of solute present for each kilogram of solution.

### Parts per million mass/volume

In the case of ppm m/V, these are calculated with the following formula:

By virtue of this, it is usually said that ppm m/V represents the milligrams of solute present per liter of solution.

## How do you convert from molarity to ppm?

Of course, the conversion from molarity to ppm depends on whether you want to convert to ppm m/V or ppm m/m. In general, when you don’t specify which ppm it is, it’s pretty safe to assume it’s ppm m/V, so let’s start with this conversion.

Conversions between units of concentration can always be carried out in two different ways, by virtue of the fact that it is an intensive property:

- Assuming any amount of solution and determining the amount of solute and then using this data in the formula for the new unit of concentration, or
- Combining the two formulas to obtain a new formula that gives a concentration based on the other.

The first is easier to understand while the second is much easier and faster to apply, once you have the formula.

## Formula to convert from molarity to parts per million m/V

Since we want to determine ppm m/V, we first need to find the mass of solute in milligrams from molarity. To achieve this, it is enough to clear the mass of solute from the molarity formula:

But this mass is in grams, and we need it in milligrams, so we add the appropriate conversion factor :

Now we substitute this expression in the ppm m/V formula, and that’s it:

After canceling the volumes of the solution (both in L), the formula remains:

Let’s see both methods in action by way of examples.

### Example 1

*Determine the concentration in ppm m/V of a solution containing Pb 2+ ions at a concentration of 2.83.10 -5 molar.*

**Solution:** If the concentration is 2,83.10 -5 mol/L, this means that in 1L of solution, there are 2,83.10 -5 mol of Pb 2+ ions . The molar mass of lead is 207.2 g/mol, so the mass of lead present in 1 L of solution is:

Now, we apply the ppm m/V formula, knowing that the volume of the solution is 1 L (assumed) and the mass of solute is 5.86 mg (calculated from the assumed amount of solution):

### Example 2

*Convert a 0.145 mol/L concentration of sodium ions (Na + ) to parts per million m/V.*

**Solution:** In this case we will use the formula to illustrate how simple it is. The only thing we are missing is the molar mass of sodium, which is 22.99 g/mol.

## Formula to convert from molarity to parts per million m/m

As in the previous case, this conversion can be done in two ways. Next, the formula to convert molarity to ppm m/m is derived.

We will start from the expression of the milligrams of solute from molarity.

The problem in this case is that the ppm m/m is in terms of the mass of the solution, and not the volume of the solution, as appears in this formula. For this reason, before substituting this expression in the ppm m/m formula, the density of the solution must be known in order to convert its volume to mass:

The volume in molarity is in liters and we are interested in the mass of the solution in kilograms (because that is how it is in the ppm m/m formula), so the density should be in kg/L. However, most densities are reported in g/mL, so a conversion factor must also be included:

Combining this expression, that of the mass of the solute in milligrams and the formula of ppm m/m, and after canceling the masses of the solution, we obtain:

### Example 3

*Determine the concentration in milligrams of solute per kilogram of solution for a 0.050 molar solution of hydrochloric acid, knowing that the solution has a density of 1.025 g/mL.*

**Solution:** In this case, just plug the data into the formula to convert molarity to parts per million, and you’re done. The molar mass of HCl is 36.46 g/mol:

### References

https://www.quimicas.net/2015/05/ejemplos-de-ppm-partes-por-millon.html