Question

What is the density at STP of the gas sulfur hexafluoride $S{{F}_{6}}$?

Answer 1

Hint: Density is defined as the mass per unit area or mass per unit volume. Density of any substance is represented by the symbol $\rho $. Whereas specific volume is the ratio of volume of any material to its mass and this is the same as the reciprocal of its density.

Complete answer:
STP stands for standard temperature and pressure and it can be defined as a temperature 273.15 K and an absolute pressure exactly equal to 100 kpa or 1 bar where temperature units K implies kelvin and pressure unit kpa represents kilo Pascal.
Now to calculate the density we can use ideal gas equation which can be represented as
$PV=nRT$
Where P is pressure exerted by the gas, Volume occupied, n is number of moles, R is gas constant and T is temperature.
Now number of moles can be calculated by $n=\dfrac{Given\ mass}{Molar\ \text{mass}}=\dfrac{m}{M}$
From this the ideal gas equation becomes $PV=\dfrac{mRT}{M}$
This can be rearranged as
$PM=\dfrac{mRT}{V}$
Now we know that density can be shown as:
\[Density(\rho )=\dfrac{Mass}{Volume}=\dfrac{m}{V}\]
\[\therefore PM=\rho RT\]
Now the density will be equal to
\[\rho =\dfrac{PM}{RT}\]
Now at STP the pressure is 1 bar and temperature is 273.15 K and the molar mass of sulfur hexafluoride is 146.06 \[gmo{{l}^{-1}}\]and the value of gas constant is 0.08314 bar. By putting all the values in the equation we find that
\[\rho =\dfrac{1\times 146.06}{0.08314\times 273.15}=6.43g/L\]
Hence density at STP of the gas sulfur hexafluoride is \[6.43g/L\].

Note:
The density of any substance varies with temperature and pressure, molecules which are of gaseous nature show greater change in density while solid and liquid will not show much change. By increasing the pressure on an object it decreases the volume of the object and thus increases its density or by increasing the temperature it decreases its density by increasing its volume.