Question

An ideal gas exerts a pressure of $1.52MPa$ when its temperatures is $298.15K$ and its volume is ${10}^{-2}{m}^3$. $\left(a\right)$ How many moles of gas are there? $\left(b\right)$ What is the mass density if the gas in molecular hydrogen? $\left(c\right)$ What is the mass density if the gas is oxygen?

Answer 1

$\left(a\right)$

$\begin{array}{c}p=1.25mpa=1.5\times {10}^6\\ T=298.15k\\ v={10}^{-2}{m}^3\\ R=8.31Jmo{l}^{-1}{k}^{-1}\\ pv=nrt\end{array}$

where $n=$ number of mole of gas

$\begin{array}{c}n=\frac{pv}{Rt}=\frac{1.52\times {10}^6\times {10}^{-2}}{8.31\times 298.15}\\ n=6.10mol\end{array}$

$\left(b\right)$

Mass density of hydrogen $\begin{array}{c}=\frac{2}{{10}^{-2}}\\ =2\times {10}^{2}kg{m}^{-3}\end{array}$

$\left(c\right)$

Mass density of oxygen $\begin{array}{c}=\frac{16}{{10}^{-2}}\\ =16\times {10}^{2}kg{m}^{-3}\end{array}$