Question

How to calculate mass fraction ratio?

Answer 1

Hint: You can simply find out the mass fraction as you calculate mole fraction. It is the ratio of mass of that component to the total mass of the mixture. This comes out to the mass fraction, for converting it in percent you have to multiply it with $100$ . On dividing note that the gram units get cancelled.

Complete step-by-step answer:
Before coming to the exact solution of the problem, let’s see what mass fraction is. Mass fraction is the fraction of that particular component from the mixture which is given. Suppose you have nitrogen, hydrogen and helium in a container, we all know these are gases so the mass fraction of let’s say hydrogen is the amount of hydrogen from that mixture.

Formula can be written as- $Mass\,fraction({H_2}) = \dfrac{{Mass\,of\,hydrogen\,gas}}{{Total\,mass\,of\,the\,mixture}}$
Or more generally we can say, $Mass\,fraction\,of\,a\,component = \dfrac{{Mass\,of\,that\,component}}{{Total\,mass\,of\,the\,mixture}}$

Now we take an example for your better understanding, we have $70\,g\,{N_2}$ , $20\,g\,{O_2}$ , $5\,g\,He$ , $5\,g\,{H_2}$ in a container. So for finding the mass fraction of each component, let’s firstly do the total mass of mixture which comes out to be- $100\,g$
Now for mass fraction of nitrogen $Mass\,fraction({N_2}) = \dfrac{{Mass\,of\,nitrogen\,gas}}{{Total\,mass\,of\,the\,mixture}}$
Putting values in the above formula, we get this type of equation $Mass\,fraction({N_2}) = \dfrac{{70\,g}}{{100\,g}}$
$Mass\,fraction({N_2}) = 0.70\,g$
Similarly let’s take the mass fraction for oxygen which is also present in the container,
$Mass\,fraction({O_2}) = \dfrac{{Mass\,of\,oxygen\,gas}}{{Total\,mass\,of\,the\,mixture}}$
$Mass\,fraction({O_2}) = \dfrac{{20\,g}}{{100\,g}}$ = $0.20\,g$
Now if we calculate for other remaining gases like helium and hydrogen, they also have the same calculations-
For helium gas, $Mass\,fraction(He) = \dfrac{{5\,g}}{{100\,g}}$ = $0.05\,g$
For $5\,g$ of hydrogen, $Mass\,fraction({H_2}) = \dfrac{{5\,g}}{{100\,g}}$

Now an interesting fact about the mass fraction by which you can easily check your mistakes is that the total mass fraction of all the gases present in the container is equal to $1$ . This total is just the same as the mole fraction that we usually study in our books that the total mole fraction of all the components is equal to $1$ . If we have a two component system where we have two gases then the mole fraction of one component is equal to $(1 - \,mole\,fraction\,of\,other\,component)$ .


Note: Don’t multiply with $100$ as we want only mass fraction and not mass percent. Check your mistakes by summing up the mass fraction of all the components by adding them, if you are getting $1$ , it means your calculation is right. Make sure that both masses are in the same unit, they both can be in grams or in kilograms.