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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 ?

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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.

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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.

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