Is the mole fraction equal to the weight fraction?

Whenever there is a reaction is excess of air it is customary to assume mole ratio of $$\ce{N2}$$ to $$\ce{O2}$$ as $$79/21$$. However, in another reaction which states that it will contain $$\pu{1 wt\%}$$ of $$\ce{C}$$ in iron, I am absolutely confused whether weight ratio will suffice just like I did it for air. Is it absolutely necessary to convert mass to amount of substance and then take ratio or are they equal?

• Yes $\vphantom{ghhh}$ Commented Oct 1, 2018 at 12:27

Ratios can be quoted either as mass ratios or molar ratios

The trouble with the example you use is that, for air, the weight and mass ratios are close (oxygen and nitrogen molecule masses are only 14% different) so the ratio will similar either way. And you quote the ratio as a molar ratio but later describe it as a "weight ratio". The molar and mass ratios will not be remotely as close for carbon in iron. So you need to know which is which.

If you are trying to interpret a ratio don't overthink it, look at what the ratio claims to be. 1 wt% C in Fe claims to be a mass ratio (that's what wt% or weight percent means, if the ratio has been mol% it would have meant a molar ratio).

If you are given a wt% you don't need to work out the molar ratios, you can simply directly measure the relative weights of the components and be done. If you do convert to a molar ratio you will (usually) find that that is very different to the mass ratio.

Is the mole fraction equal to the weight fraction?

If you had a mixture of two compounds then typically the mole fraction and weight fraction would be different quantities.

The odd exception would be mixtures of isomers. So a mixture of n-hexane and 2-methylpentane would have the same weight fraction and mole fraction since the two different molecules have the same molecular weight.

Is it absolutely necessary to convert mass to amount of substance and then take ratio...?

Typically a problem is posed so that you need to use either the weight fraction or the mole fraction. However some problems could require you to use both.