PPM to Molarity Calculator

Created by Jasmine J Mah
Reviewed by Dominik Czernia, PhD and Jack Bowater
Last updated: Sep 27, 2022

The PPM to Molarity Calculator (parts per million) will convert ppm to molarity for any element or molecule dissolved in water.

The conversion from ppm to molarity, or back from molarity to ppm, is quite simple. Just read on below to learn more!

What is ppm and molarity?

Both ppm (parts per million) and molarity are measures of concentration. Did you know that ppm is used in different ways depending on the context? When dealing with dilute solutions, 1 ppm can be approximated as 1 mg1\ \text{mg} of substance per liter of water, or 1 mg/L1\ \text{mg}/\text{L}.

On the other hand, molarity is molar concentration, meaning that it tells you how many moles of molecules are in one L of water. Many concentration calculations use the mole units because we're dealing with a great number of molecules. There are 6.0221409×10236.0221409 \times 10^{23} molecules or particles in one mole.

If you want to know more about ppm and molarity, visit our dedicated calculators, the ppm calculator and the molarity calculator

Some situations where you may need to convert ppm to molarity include:

  • Measurements of drinking water quality;
  • Maintenance of chemical levels in aquariums;
  • Mixing fertilizer solutions for horticulture; and
  • Producing chemical solutions.

You will need a different ppm calculation if you are using it in other contexts, such as:

  • ppm of a nutrient in soil (which uses mg\text{mg} nutrient per kg\text{kg} of soil); and
  • ppm of pollutants in air (which uses μL\text{μL} of pollutant per L\text{L} of air).

A technical definition of ppm

So, what is ppm? And how can something called "parts per million" be represented by mg/L\text{mg}/\text{L}? Parts per million indicates the number of "parts" of something in a million "parts" of something else. The "part" can be any unit, but when mixing solutions, ppm will usually represent weight units. In this context, ppm tells you how many grams of a solute are for each million grams of solvent (e.g., water).

1 g solute1,000,000 g solvent\footnotesize\frac{1\ \text{g solute}}{1,\!000,\!000\ \text{g solvent}}

When dealing with water at room temperature, it is common to assume that the density of water is 1 g/mL1\ \text{g}/\text{mL}. Therefore, we can rewrite the relationship as follows:

1 g solute1,000,000 mL water\footnotesize\frac{1\ \text{g solute}}{1,\!000,\!000\ \text{mL water}}

Then we divide mL\text{mL} by 10001000 to convert mL to L: the easiest volume conversion!

1 g solute1,000 L water\footnotesize\frac{1\ \text{g solute}}{1,\!000\ \text{L water}}

By dividing both units by 10001000, the ratio becomes:

1 mg solute1 L water\footnotesize\frac{1\ \text{mg solute}}{1\ \text{L water}}

Therefore, you can say that 1 mg1\ \text{mg} in 1 L1\ \text{L} water is the same as 1 mg1\ \text{mg} in 1,000,000 mg1,000,000\ \text{mg} water, or 1 part per million (assuming both room temperature and an atmospheric pressure of 1 atm1\ \text{atm}).

If your solvent is not water, you should use the Advanced mode in the ppm to molarity calculator to adjust the solvent's density.

How to convert ppm to molarity? - the ppm to molarity calculator

To convert ppm to molarity, or molarity to ppm, you only need to know one thing: the molar mass of the dissolved element or molecule.

If you take molarity (with units mol/L\text{mol}/\text{L}), and multiply it by the molar mass (with units g/mol\text{g}/\text{mol}), you get g/L\text{g}/\text{L}. Just multiply g/L\text{g}/\text{L} by 10001000 to **convert g\text{g} to mg\text{mg}, and you have ppm (in mg/L\text{mg}/\text{L} of water).

This ppm to molarity formula for dilute solutions is:

ppm=molesLmmol1000\footnotesize\text{ppm} = \frac{\text{moles}}{\text{L}}\cdot m_\text{mol}\cdot 1000

Example 1 - Seawater vs. Drinking water

The average salt content in seawater is equivalent to 0.599 M0.599\ \text{M} NaCl\text{NaCl} (although sea salts are not entirely made up of NaCl\text{NaCl}). If the EPA recommends that drinking water should not exceed 20 mg/L20\ \text{mg}/\text{L} (or 20 ppm20\ \text{ppm}), how many times more salty is seawater compared to drinking water?

To find out, let's convert 0.599 M0.599\ \text{M} NaCl\text{NaCl} into ppm\text{ppm}. We need to know the molar mass of NaCl\text{NaCl}, which is 58.44 g/mol58.44\ \text{g}/\text{mol}. Multiply the molarity by molar mass to get g/L\text{g}/\text{L}:

0.599 mol/L58.44 g/mol=35.0556 g/L\footnotesize0.599\ \text{mol}/\text{L} \cdot 58.44\ \text{g}/\text{mol} = 35.0556\ \text{g}/\text{L}

Next, multiply by 10001000 to get mg/L\text{mg}/\text{L}:

35.0556 g/L1,000 mg/g=35,055.6 mg/L\footnotesize 35.0556\ \text{g}/\text{L} \cdot 1,\!000\ \text{mg}/\text{g}=35,\!055.6\ \text{mg}/\text{L}

Finally, divide the salt concentration of sea water by the drinking water guideline to find their ratio:

35,055.620=1,750\footnotesize \frac{35,\!055.6}{20} = 1,\!750

The significant figures we calculated are too many: reduce them to 3. Then, we can say that seawater is approximately 17501750 times saltier than drinking water!

Example 2 - Prepare a NaOH solution

You have a stock solution of 1 molar NaOH\text{NaOH}. How do you go about creating a 1 L1\ \text{L} solution of 200 ppm200\ \text{ppm} NaOH\text{NaOH}? NaOH\text{NaOH} has a molar mass of 39.997 g/mol39.997\ \text{g}/\text{mol}.

1. Convert 200 ppm200\ \text{ppm} to molarity.

Let's first assume 200 ppm=200 mg/L200\ \text{ppm} = 200\ \text{mg}/\text{L}. Then, divide the result by 10001000 to get g/L\text{g}/\text{L}:

200 mg/L200\ \text{mg}/\text{L} divided by 1000 mg/g1000\ \text{mg}/\text{g} is equal to 0.2 g/L0.2\ \text{g}/\text{L}.

Next, divide 0.2 g/L0.2\ \text{g}/\text{L} by the molar mass of NaOH\text{NaOH} to get the molarity:

0.2 g/L0.2\ \text{g}/\text{L} divided by 39.997 g/mol39.997\ \text{g}/\text{mol} is equal to 0.005 mol/L0.005\ \text{mol}/\text{L}.

2. Calculate the dilution recipe.

From step 1, we know the target molarity is 0.005 mol/L0.005\ \text{mol}/\text{L}. To calculate the dilution, we use the dilution equation:

m1V1=m2V2\footnotesize m_1\cdot V_1=m_2\cdot V_2

where:

  • m1m_1 — The concentration of stock solution;
  • m2m_2 — The concentration of diluted solution;
  • V1V_1 — The volume of stock solution; and
  • V2V_2 — The volume of diluted solution.

We can fill in the numbers for all the variables except for the volume of stock solution:

1 MV1=0.005 M1 L\footnotesize 1\ \text{M} \cdot V_1 = 0.005\ \text{M} \cdot 1\ \text{L}

By rearranging the equation, we will find the volume of stock solution required:

V1=0.005 M1 M1 L=0.005 L\footnotesize V_1 = \frac{0.005\ \text{M}}{1\ \text{M}}\cdot 1\ \text{L}=0.005\ \text{L}

Therefore, we need to dilute 0.005 L0.005\ \text{L} (or 5 mL5\ \text{mL}) of stock solution to a final volume of 1 L1\ \text{L} to get a 200 ppm200\ \text{ppm} NaOH\text{NaOH} solution.

You can check Step 1 with this ppm to molarity calculator, and check Step 2 with the solution dilution calculator!$$

FAQ

How do I calculate molarity given density and ppm?

To estimate the molarity of any water solution:

  1. Take the solution's density in g/L.
  2. Divide it by the solute's molar mass in g/mol.
  3. The resulting quotient is the solution molarity in mol/L.
  4. In case you have the ppm value, repeat all the steps but substitute the density with the ppm and multiplying everything by 1000 mg/g.

How many ppms are in a gram?

There is 1000 ppm of particles/molecules assuming we have one gram of the substance in a one-liter solution. That's because 1 L of water weighs 1000 g, so there is one solute particle per thousand total particles, and thus one thousand per every million.

How do I calculate ppm from the volume concentration?

To get ppm by volume:

  1. Take the solutions' molar concentration in mol/L.
  2. Multiply it by the molar mass in g/mol.
  3. Divide it by the solute's density in g/cm³.
  4. Multiply everything by 1000 mg/g.
  5. The resulting ppm unit by volume is typically μL/L.

What is the concentration in ppm when 0.5 moles of CH₄ are dissolved in 1500 ml of water?

The concentration is 5,333 ppm. To get the result:

  1. Estimate the molar concentration of CH₄, which is 0.5 mol / 1.5 L = 0.3333 M.
  2. Multiply it by the methane molar mass (16 g/mol).
  3. Multiply everything by 1000 mg/g.
  4. As a result, we obtain: 0.3333 M * 16 g/mol * 1000 mg/g = 5,333 ppm
Jasmine J Mah
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