Finding density of the gas mixture [closed]








**Closed.** This question is [off-topic](/help/closed-questions). It is not currently accepting answers.
 
 






---








 **Homework questions** must demonstrate some effort to understand the underlying concepts. For help asking a good homework question, see: [How do I ask homework questions on Chemistry Stack Exchange?](https://chemistry.meta.stackexchange.com/questions/141/how-do-i-ask-homework-questions-on-chemistry-stack-exchange)




Closed 5 years ago.








[Improve this question](/posts/91120/edit) 




> 
> 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?




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 $M\_\text{avg}$.


 0