# PPM to Molarity Calculator

Created by Jasmine J Mah
Reviewed by Dominik Czernia, PhD and Jack Bowater
Last updated: Nov 20, 2023

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 $1\ \text{mg}$ of substance per liter of water, or $1\ \text{mg}/\text{L}$.

On the other hand, molarity is molar concentration, meaning that it tells you how many moles of molecules are in one L of solution. Many concentration calculations use the mole units because we're dealing with a great number of molecules. There are $6.0221409 \times 10^{23}$ 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 $\text{mg}$ nutrient per $\text{kg}$ of soil); and
• ppm of pollutants in air (which uses $\text{μL}$ of pollutant per $\text{L}$ of air).

## A technical definition of ppm

So, what is ppm? And how can something called "parts per million" be represented by $\text{mg}/\text{L}$? 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 solution.

$\footnotesize\frac{1\ \text{g solute}}{1,\!000,\!000\ \text{g solution}}$

When dealing with a diluted solution in water at room temperature, we can approximate the mass of the solvent to the total mass of the solution and assume the density of water to be $1\ \text{g}/\text{mL}$. Therefore, we can rewrite the relationship as follows:

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

Then we divide $\text{mL}$ by $1000$ to convert mL to L: the easiest volume conversion!

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

By dividing both units by $1000$, the ratio becomes:

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

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

If your solvent is not water, you should adjust the solvent's density in the calculator.

## 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 $\text{mol}/\text{L}$) and multiply it by the molar mass (with units $\text{g}/\text{mol}$), you get $\text{g}/\text{L}$. Just multiply $\text{g}/\text{L}$ by $1000$ to convert $\text{g}$ to $\text{mg}$, and you have ppm (in $\text{mg}/\text{L}$ of water).

This ppm to molarity formula for dilute solutions is:

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

## Example 1 – Seawater vs. Drinking water

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

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

$\scriptsize 0.599\ \text{mol}/\text{L} \cdot 58.44\ \text{g}/\text{mol} = 35.0556\ \text{g}/\text{L}$

Next, multiply by $1000$ to get $\text{mg}/\text{L}$:

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

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

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

The significant figures we calculated are too many: reduce them to 3. Then, we can say that seawater is approximately $1750$ times saltier than drinking water!

## Example 2 – Prepare a NaOH solution

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

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

Let's first assume $200\ \text{ppm} = 200\ \text{mg}/\text{L}$. Then, divide the result by $1000$ to get $\text{g}/\text{L}$:

$200\ \text{mg}/\text{L}$ divided by $1000\ \text{mg}/\text{g}$ is equal to $0.2\ \text{g}/\text{L}$.

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

$0.2\ \text{g}/\text{L}$ divided by $39.997\ \text{g}/\text{mol}$ is equal to $0.005\ \text{mol}/\text{L}$.

2. Calculate the dilution recipe.

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

$\footnotesize m_1\cdot V_1=m_2\cdot V_2$

where:

• $m_1$ — The concentration of stock solution;
• $m_2$ — The concentration of diluted solution;
• $V_1$ — The volume of stock solution; and
• $V_2$ — The volume of diluted solution.

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

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

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

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

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