# Finding density of the gas mixture [closed]

A gas in a vessel is under pressure of $$\pu{1800kPa}$$. The design temperature of the tank is $$\pu{423K}$$. The gas consists of (by volume) $$20\ \%$$ of $$\ce{CH4}$$ and $$80\ \%$$ $$\ce{N2}$$. Estimate the density (in $$\pu{kg/m^3}$$) of the gas.

I can't just use the ideal gas law to find out the density of the mixture as there are two components, right?

$$\rho=\frac{pM_\mathrm r}{RT}$$

From the ideal gas law, I can also predict that vol% equals mol%. But with this, am I supposed to find the average value of $$M_\mathrm r$$ and then substitute it into the equation above?

• Hi, welcome to Chem.SE! Is the last line actually "...of the gas mixture" in your question? Feb 22, 2018 at 9:17
• @GaurangTandon nope. Feb 22, 2018 at 9:27
• Yes. What is the molar average molecular weight? (Hint: when we say 20% by volume, we mean that the mole fraction is 0.2) Feb 22, 2018 at 13:27

You originally said that:

The gas consists of 20vol%,CH4 and 80% N2...

This is a fault in the question. A gas cannot consist of two other gases and still remain a gas. Instead, it is now a gas mixture. (hence I had added the term "mixture" into your question, which I've now removed to retain the original meaning)

Once this is out of the way, you can think of density as: \begin{align} \text{density}&=\frac{\text{total mass}}{\text{total volume}}\\\\\ &=\frac{n_1M_1+n_2M_2}{(n_1+n_2)RT/P}\\\\ &=\frac{P(n_1M_1+n_2M_2)}{(n_1+n_2)RT}\\\\ &=\frac{PM_{\text{avg}}}{RT} \end{align}

and recall that volume percent is equivalent to mole percent, as you correctly did already. Substitute the correct values into this equation and you're good to go.

PS: I do not understand what you're denoting by $M_\mathrm r$. But, the formula you were using is identical to mine if you swap $M_\mathrm r$ with $M_\text{avg}$.

• I think there is a mistake in 2nd equation, where you took $P$. You should have taken individual pressure of the gases. Hence the equation should be $\frac{n_1M_1+n_2M_3}{RT/P}$.
– user84047
Jun 25, 2021 at 13:59