Question

Calculate the density of $C{O_2}$ at ${100^ \circ }C$ and $800mm$ $Hg$ pressure.

Answer 1

In this we use the ideal gas equation to calculate the density of $C{O_2}$ . ideal gas equation is the correlations between pressure, volume, temperature and quantity of gas. It is an approximation of the behavior of many gases under many conditions, although it has several limitations.

Complete answer:
The ideal gas equation is the state of an amount of gas determined by its pressure, volume, and temperature. The modern form of the equation relates these simply in two main forms. The temperature used in the equation of state is an absolute temperature; the appropriate $SI$ unit is the kelvin.
The ideal gas law allows us to calculate the value of the fourth quantity needed to describe a gaseous sample when the others are known and also predict the value of these quantities following a change in conditions if the original conditions are known.
$PV = nRT$
Where, $P =$ Pressure
$V =$ Volume
$n =$ Amount of substance
$R =$ Ideal gas constant
$T =$ Temperature.
We know that density is a measure of mass per volume. The average density of an object equals its total mass divided by its total volume.
$\rho = \dfrac{m}{V}$
Where, $\rho =$ density
$m =$ mass
$V =$ volume.
Now, we know the density version of ideal gas law is,
$PM = dRT$
$d = \dfrac{{PM}}{{RT}}$
Where $P = \dfrac{{800}}{{760}}atm$
$T = 272 + 100 = 373K$
$R = 0.0821Latm{K^{ - 1}}mo{l^{ - 1}}$
${m_{c{o_2}}} = 44$
Therefore, $d = \dfrac{{800 \times 44}}{{760 \times 0.821 \times 373}}$
$d = 1.5124glitr{e^{ - 1}}$
So, the density of $C{O_2}$ is $1.5124 glitr {e^{ - 1}}$ .

Note:
The ideal gas law can be used in stoichiometry problems in which chemical reactions involve gases. Standard temperature and pressure are a useful set of benchmark conditions to compare other properties of gases. The ideal gas law can be used to determine densities of gases.