Question

The density of neon gas will be highest at:
A.STP
B.$0^\circ {\text{C}}$, 2 atm
C.$273^\circ {\text{C}}$, 1 atm
D.$273^\circ {\text{C}}$, 2 atm

Answer 1

Hint: Density mainly depends upon two factors. These two factors are pressure and temperature. Density varies when these factors change. At higher pressure and lower temperature, density of the gas will be the highest.
Formula used: $d = \dfrac{{PM}}{{RT}}$

Step-by-step answer:
Density of any particular gas is related to pressure and temperature by the following equation.
$d = \dfrac{{PM}}{{RT}} \cdot \cdot \cdot \cdot \cdot \cdot \left( {\text{I}} \right)$

Where,
d is the density.
P is the pressure.
M is the molar mass of gas.
R is the universal gas constant.
T is the temperature.

The equation (I) shows that density of gas is directly proportional to pressure and inversely proportional to temperature as shown below.
$d \propto P$ and $d \propto \dfrac{1}{T}$

We know that pressure is mainly responsible for expansion or contraction of gas. On increasing the pressure, compression increases. This increases the close packing between molecules. This ultimately increases the density of the gas. In contrast, when temperature of the gas increases, the dispersion of molecules increases which ultimately reduces the density of the gas and when temperature decreases, density increases.

Thus when pressure increases and temperature decreases, density becomes highest at such conditions. Therefore, among the given options, the density of the neon will be highest at a temperature of $0^\circ {\text{C}}$(lowest temperature) and pressure of 2 atm (highest pressure).

Note: The density of the gas always depends upon two factors which are pressure and temperature. At STP (standard temperature and pressure), the temperature is $0^\circ {\text{C}}$ and pressure is equivalent to 1 atmospheric pressure.