Question

Calculate the mass density of a pure sample of oxygen gas at a pressure of $ 1.0atm $ , a volume of $ 7.8L $ at $ {197.2^ \circ }C $ ?

Answer 1

Hint: An object's mass density is defined as its mass per unit volume. This value can be stated in a variety of ways, including kilograms per square metre and pounds per square foot. The lower-case Greek symbol rho ( $ \rho $ ), represents mass density.
 $ PV = nRT $
 $ P = $ Pressure
 $ V = $ Volume
 $ n = $ Number of moles
 $ R = $ Gas constant
 $ T = $ Temperature.

Complete Step By Step Answer:
Given:
 $ P = 1.0atm $
 $ V = 7.8L $
 $ T = {197.2^ \circ }C = 470.35K $
Mass of oxygen $ = 32g $
To find: Mass density
Using the ideal gas formula,
 $ PV = nRT $
Since, $ mass = \dfrac{mass}{molar\;mass} $
As we know,
 $ n = \dfrac{m}{M} $
 $ PM = \dfrac{m}{V}RT $
 $ Density = \dfrac{mass}{Volume} $
 $ \rho = \dfrac{m}{V} $
 $ PM = \rho RT $
 $ \rho = \dfrac{{PM}}{{RT}} $
Substituting the given values in above equation,
 $ \rho = \dfrac{{1.0 \times 32}}{{0.08206 \times 470.35}} $
On solving the above equation, we get,
 $ \rho \Rightarrow 0.83{\text{ }}g{L^{ - 1}} $
Hence, the mass density of a pure sample of oxygen gas at a pressure of $ 1.0atm $ is $ 0.83g{L^{ - 1}} $ .

Additional Information:
The mass density of a substance, material, or item is a measure of how much mass (or how many particles) it has in relation to the amount of space it takes up. This measurement, however, is not always accurate; mass density is affected by a variety of parameters, including temperature and pressure. When gases are heated, for example, they expand. In other words, as the temperature rises, their volume rises as well. If the volume of a gas expands, its density decreases.

Note:
The level of corrosion on an object can also be determined by its mass density. When iron corrodes, it oxidises and turns into rust, which takes up more space than the original metal. Concrete cracking and spalling can occur as a result of this expansion and decreasing density.