# Chemical engineering calculations - basis

You have a gas of the following compositions : 40% N2, 30% CO2, 30%,CH4 in a tank . What is the Average Molecular Weight of the gas if your compositions is based on molar ?

I found that the AMR with basis set at $100$kg-Mol = $29.2$kg/kg-mol

As Im still learning , I tried to give a basis of $100$kg ... but I don't get the same AMR.

Why is this the case ?

## 2 Answers

Since the composition is given in mole % then your calculation basis must be in moles or kilo moles.

If you start with a Kg basis then you need to know the weight composition then calculate the mole composition.

As @user307640 said, if you use a mass basis, you can obtain the average molecular weight using the mass percentage composition.

As an alternative approach, you can do:

\begin{align} M&=\sum n_iMW_i\\ &=n_T\sum y_iMW_i \end{align}

Where $$M$$ is total mass, $$n_T$$ is total number of moles, $$n_i$$ is the number of moles of species $$i$$, $$y_i$$ is the mole fraction of species $$i$$ and $$MW_i$$ is the molecular weight of species $$i$$.

But:

$$n_T = M/MW_{avg}$$

so:

\begin{align} M&=\frac{M}{MW_{avg}}\sum y_iMW_i\\ 1&=\frac{1}{MW_{avg}}\sum y_iMW_i\\ MW_{avg}&=\sum y_iMW_i \end{align}

Which is 29.2 as you pointed out previously, the average molecular weight doesn't depend on the mass basis used, which is perfectly correct.