# PPM to Molarity Calculator

## 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 mg of substance per liter of water, or 1 mg/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 * 10^{23} molecules or particles in one mole.

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 nutrient per kg of soil); and
- ppm of pollutants in air (which uses μL of pollutant per 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? 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 solute / 1,000,000 g solvent`

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

`1 g solute / 1,000,000 mL water`

Then we divide mL by 1000 to convert mL to L:

`1 g solute / 1000 L water`

By dividing both units by 1000, the ratio becomes:

`1 mg solute / 1 L water`

Therefore, you can say that 1 mg in 1 L water is the same as 1 mg in 1,000,000 mg water, or 1 part per million (assuming both room temperature and an atmospheric pressure of 1 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**), and multiply it by the molar mass (with units **g/mol**), you get **g/L**. Just multiply g/L by 1000 to **convert g to mg**, and you have ppm (in **mg/L of water**).

This ppm to molarity formula for dilute solutions is:

`ppm = moles/L * molar mass * 1000`

## Example 1 - Seawater vs. Drinking water

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

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

` 0.599 mol/L * 58.44 g/mol = 35.0556 g/L`

Next, multiply by 1000 to get mg/L:

`35.0556 g/L * 1000 mg/g = 35,055.6 mg/L`

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

`35,055.6 / 20 = 1750`

Rounding to 3 significant figures, 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 NaOH. How do you go about creating a 1 L solution of 200 ppm NaOH? NaOH has a molar mass of 39.997 g/mol.

**1. Convert 200 ppm to molarity.**

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

`200 mg/L divided by 1000 mg/g = 0.2 g/L`

Next, divide 0.2 g/L by the molar mass of NaOH to get the molarity:

`0.2 g/L divided by 39.997 g/mol = 0.005 mol/L`

**2. Calculate the dilution recipe.**

From step 1, we know the target molarity is **0.005 mol/L**. To calculate the dilution, we use the dilution equation:

`m₁ * V₁ = m₂ * V₂`

where:

- m₁ is the concentration of stock solution;
- m₂ is the concentration of diluted solution;
- V₁ is the volume of stock solution; and
- V₂ is the volume of diluted solution.

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

`1 M * V₁ = 0.005 M * 1 L`

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

`V₁ = (0.005 M / 1 M) * 1 L`

`V₁ = 0.005 L`

Therefore, we need to dilute **0.005 L** (or 5 mL) of stock solution to a final volume of 1 L to get a 200 ppm NaOH solution.

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