How to convert ppm to mole fraction? – (ppm to mole fraction)

ppm is the abbreviation for parts per million. Parts per million (ppm) and mole fraction are two different ways of expressing the concentration of a chemical solution.

Converting ppm to mole fraction requires understanding the relationship between the two concentration units.

Thus, in this article, we will teach you all the tips and tricks involved in converting a solution concentration from ppm to mole fraction.

But first, let’s revise a few basics. 

What is ppm?

 A solution consists of two parts, i.e., a solute and a solvent.

The solute is the minor component. It may be a solid, liquid, or gas that dissolves completely in the major component, i.e., the solvent.

The solute particles get evenly distributed in the solvent to prepare a homogenous solution. 

The concentration of a solution refers to the amount of solute dissolved in a particular amount of the solution.  

 If the concentration is expressed as parts of solute per million parts of the solution, it is thus referred to as ppm. Therefore,

The ppm unit is particularly helpful for measuring very small amounts of solute dissolved in a large amount of solvent, i.e., the concentration of extremely dilute solutions.

‘Parts’ in the above formula may denote a mass or a volume.

For instance, if 0.30 g of sugar is dissolved in 600 g of an aqueous solution, then the concentration of the sugar solution is-

∴ Parts per million (ppm) = (0.36/600) × 10⁶  = 500 ppm

1 milligram is the thousandth of a gram, while a thousand mL makes 1 liter.  1000 x 1000 = 10⁶. Hence, 1 ppm is approximately equal to 1 mg/L for aqueous solutions.

What is mole fraction?

The mole fraction helps determine the proportion of a specific substance in a mixture of substances.

It is calculated by dividing the moles of one substance by the total number of moles of all the substances in the mixture.

In a homogenous solution containing a solute and a solvent;

ppm and parts per million are both ratios and, therefore, unitless.

How to convert ppm to mole fraction?

The following simple steps can be used to convert a concentration given in ppm to a mole fraction.

Example – A chemist prepared a 500 ppm glucose solution using water. Given that the total mass of the solution is 1000 g, what is the mole fraction of glucose in this solution?

Solution:

Step I: Find the mass of the solute by applying the ppm formula (in terms of mass) and substituting the known values.

Step II: Find the mass of the solvent by subtracting the answer obtained in Step 1 from the total mass of the solution.

∴ Mass of solvent (water) = 1000 – 0.5 = 999.5 g

Step III: Find the number of moles of both the solute and the solvent, dividing each mass by the respective molar mass.

⇒ Moles = Mass/Molar mass

∴ Moles of solute = (0.5/180.156) = 0.00278

∴ Moles of solvent = (999.5/18.02)  = 55.5

Step IV: Find the required mole fraction.

Result: The mole fraction of glucose in the given solution is 0.00005.   

Let’s consider another example- Find the mole fraction of 4000 ppm methane (CH₄) dissolved in 1500 mL of water. (Density of water = 1 g/mL).

Solution:

Finding the mass of solvent (water) using its density and the given volume:

∴ Density = Mass/Volume

∴ Mass of water = 1 x 1500 = 1500 g

⇒ 1 ppm = 1 mg/L, 4000 ppm = 4000 mg methane dissolved per litre (1000 mL) of water.

Thus, the mass of methane dissolved per 1500 mL of water = (4000/1000) × 1500 = 6000 mg.

Converting mg to g:

⇒ 1 mg = 10^-3 g

∴ 6000 mg = 6000 x 10^-3 = 6 g

Result: The mole fraction of methane is 0.0045. 

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