The Mass-mole Conversion

Most beginner chemical thermodynamists find unit conversions difficult. The most used conversion is where the mass, m_i, of a substance, i, weighed in say a laboratory is converted into the number of moles, n_i, that this substance represents.

The relationship between the mass of a substance and the number of moles is a linear one. This means that for each unit increase in the mass the number of moles of that compound increases by the same amount. The relationship is as follows:

m_i = M_i n_i

The number of moles is thus discovered by dividing the constant of proportionality in this case the molar mass, Mi, by the mass of the substance.

How to Use Molar Mass

Say if we want to find out how many moles of a substance is in 3.5 grams of sodium chloride. We might first look at sodium chloride and find that its molar mass is 58.44 g/mol.

The important thing here is that for EVERY mol of sodium chloride there is 58.44 g of sodium chloride. An apple weighs approximately 100 g so you may think that a mol of sodium chloride weighs about a half of an apple. To most, this may be quite a big quantity, and is much bigger than 3.5 grams.

The thing is we don`t want to know what half of an apple is& instead, we want to know what a small chunk of an apple is. This small chunk only weighs 3.5 g.

One way to understand this is to look at a grid system:

The grid system shows that 1 mol of sodium chloride is equivalent to 58.44 grids, however, 3.5 g of sodium chloride is only 3.5 grids! To work out how many moles are in 3.5 g of sodium chloride, all we need to do is find out what proportion 3.5 grids is to 58.44 grids. To do this we divide 3.5 by 58.44. This means there is 0.06 moles of sodium chloride in 3.5 g.

Why do the Conversion?

Chemists always list their chemical properties in respect to how one mole of a substance effects a certain system. For example, a chemist may want to know how the temperature of a closed solution changes when they add sodium chloride to water. When sodium chloride is added to water, sodium chloride actually absorbs energy from the water in order to break the ionic bonds sodium chloride has.

The chemist may list this property as the energy absorbed per mole of substance dissolved.

This way other chemists can take this property from a textbook (for example, Lange`s Chemistry Handbook& a very complex and well-known chemist textbook) and covert it to a quantity that is more useful for their experiments. So in the case of 3.5 grams of sodium chloride, we know there is 0.06 moles of sodium chloride. We know there is 58.44 grams of sodium chloride for every 1 mole of sodium chloride. So, all we have to do is divide 1 by 0.06 to get 16.666.

This 16.666 can be divided by the energy absorbed per mole of substance in order to work out how much energy would be taken from the water when 3.5 grams of sodium chloride is dissolved.

Why not just use Mass?

As we will later see with the difference between molarity and molality, the truth is some chemists do only use mass is their calculations. This is a huge source of confusion and can led to many competent chemists making unfortunate mistakes in their calculations. We will investigate this more in a future article.

I recommend the use of moles, because in terms of measuring the amount of a substance the mole is a more fundamental unit of measurement than the mass is.

The mass of a substance is equal the to number of moles of a substance times by the molar mass, while the number of particles of a substance is equal to the number of moles of a substance times by the Avogadro constant (A).

Unlike the molar mass the Avogadro`s constant is constant for every chemical species. This leads to interesting results when each equation is depicted graphically.

As can be seen graphically, it is not possible to represent each species as a single curve when measuring the mass, but it is when considering the number of moles.

The importance of the result comes when thinking about how chemicals react with each-other. The mass would be a good unit of measurement if when chemicals react, they were always of the same mass, but most of the time this is not true.

Usually, 1 chemical of 1 size reacts with another chemical of a different size. When they react, the mass of each chemical does not effect the proportion in which they react with each-other.

This ensures that, when considering the proportions in which things react with eachother, the mole is a much better unit of measurement than the mass.

Conclusions

In this article we have considering mole-to-mass conversions because they are very important to chemists in general. We have explained that the moles of a substance is related to the mass of a substance via the molar mass. We have also done some basic molar mass calculations and shown why the number of moles should be used rather than mass when considering the amount of a substance.