In this post, I want to share you a simple calculation that may be useful in the future of your process engineering career 😊. This post explains how to convert composition expressed in weight fraction to mol fraction.

Before we jump into the calculation method, let’s first understand that it is important to state the basis of percentage, whether it is expressed in weight basis, molar basis, or volume basis. The abbreviations w/w and v/v are used to designate weight basis and volume basis.

Let’s use examples on how to convert composition expressed in weight fraction to mol fraction.

In this example, we want to express in mol fraction a technical grade hydrochloric acid which has strength of 28% w/w.

__Solution__

When the known concentration is expressed in weight basis, we need to assume basis of calculation in weight basis also.

For example, basis of calculation is 100 gr of 28% w/w HCl

- Molecular weight of water = 18
- Molecular weight of HCl = 36.5
- Mass of HCl = 28% x 100 gr = 28 gr
- Mass of water = (100% – 28%) x 100 gr = 72 gr
- Mol HCl = 28 / 36.5 = 0.77
- Mol water = 72 / 18 = 4
- Total mol = 0.77 + 4 = 4.77

Therefore,

- Mol fraction of HCl = mol HCl / total mol = 0.77 / 4.77 = 0.16
- Mol fraction of water = mol water / total mol = 4 / 4.77 = 0.84
- Check, total mol fraction = 0.16 + 0.84 = 1

**Additional Notes **

Within the accuracy needed for technical calculation, volume fraction can be taken as equivalent to mol fraction for gases up to moderate pressure, about 25 bar.

Trace quantities are often expressed as part per million (ppm). The basis need to be stated, whether weight basis (ppmw) or volume basis (ppmv).

1 ppm = 0.0001 percent