Question

The density of ${O_2}$ is 16 at NTP. At what temperature its density will be 14? Consider that the pressure remains constant, at
A. 50 degree Celsius
B. 39 degree Celsius
C. 25 degree Celsius
D. 56 degree Celsius

Answer 1

Hint: The elements in nature exist in one of the three states, solid, liquid, or gas. The gases are the freest in their mobility while the solids are the most rigid. All these properties arise from the intermolecular forces of attraction that act between the molecules and atoms of the elements.

Complete step by step answer:
It has been given in the question that the initial density of oxygen is 16, let’s denote it as $d_1$. The temperature that we require is to be found out at the density of 14, let’s denote them as $d_2$ and the temperature as $T_2$. The temperature at which the density is 16 is NTP which will be 273 K, which can be denoted by $T_1$.
Charles law is a gas law that is derived after experimentation. It describes how gases tend to increase in volume when they are heated. The law states that, when the pressure of the gas is held constant, the kelvin temperature and the volume of the gas will be directly proportional. This law can be mathematically stated as,
$\dfrac{{{V_1}}}{{{T_1}}} = \dfrac{{{V_2}}}{{{T_2}}}$
Where ${V_1}$ is the first volume and ${V_2}$ is the second volume. Similarly, ${T_1}$ is the first temperature and ${T_2}$ is the second temperature.
It can also be noted that the density of the gas is dependent on the mass and volume of the gas. The density of the gas can be given as
$Density = \dfrac{{Mass}}{{Volume}}$
From the above equation that the volume of the gas is inversely proportional to the density of the gas thus since the mass of the gas is constant, applying this relation in Charles law we get
${d_1}{T_1} = {d_2}{T_2}$
${T_2} = \dfrac{{{d_1}{T_1}}}{{{d_2}}}$
Thus on putting the values of the variables in the above reaction we get
${T_2} = \dfrac{{16 \times 237}}{{14}}$
${T_2} = 312K$
Converting the above temperature in Celsius we get $39^\circ C$.

Thus, the correct answer is option B.

Note: The ideal gas equation is the equation that states how the gas should act in ideal conditions and what the ideal characteristics are for the gas is also defined.
The ideal gas also draws heavily from the kinetic theory of gases but actually, the ideal gas is a theoretical concept and thus doesn't exist in the real world, the gases that exist are called real gases.