Question

The density of oxygen at 2 atm and ${27^ \circ }$ C is:
A. 0.13 g/l
B. 0.6 g/l
C. 2.6 g/l
D. 1.3 g/l

Answer 1

Hint: The general gas law is PV = nRT. It follows that no matter how we change the state of the given amount of gas the ratio PV/T always remains constant. An ideal gas is a gas that follows the general gas law at all the conditions. Real gases obey this law only under conditions of low temperature and high pressure which is the given condition.

Complete step by step answer:
R is a Rydberg constant which is independent of all variables and popularly known as universal constant.
R=0.0821 litre atm /k mol=8.314 J/k mol
We know that Density = ${\dfrac{Mass}{Volume}}$
$\rho = \dfrac{{Mass}}{{Volume}} \\
V = \dfrac{{nRT}}{P} \\$
Substituting the value of volume from the gas law equation in the formula of density we get $\rho = \dfrac{{P \times m}}{{R \times T \times n}}$ , m/n =M (molar mass of oxygen=32 g/mol), T=300 K
$\rho = \dfrac{{32\times 2}}{{0.0821\times 300}} = 2.6$ g/l

Hence the correct option is option C.

Additional information: the general gas law has been derived out of so many laws such as
Boyle's law states at constant temperature, the volume of a fixed mass of gas is inversely proportional to its pressure.
Charles law which states that at constant pressure, the volume of a fixed mass of a gas is proportional to its temperature.
Gay lussacs law which states that at constant volume, the pressure of a fixed mass of gas is proportional to the temperature.
Avogadro’s law states that the amount of gas in moles is proportional to the volume of the gas.

Note: Use the value of R after observing the values of pressure you are given with. When a gas follows all the above listed laws, it is said to be ideal or perfect gas.