Question

Under what conditions will the denisty of Neon be highest?

• A. STP
• B. $0°,2\mathrm{atm}$
• C. $273°,1\mathrm{atm}$
• D. $273°,2\mathrm{atm}$

Answer 1

The correct option is B

$0°,2\mathrm{atm}$

Explanation for correct option:

(B) $0°,2\mathrm{atm}$

Ideal Gas Equation:

• According to ideal gas equation,

$\mathrm{PV}=\mathrm{nRT}$

where, $\mathrm{P}=$Pressure of Ideal Gas

$\mathrm{V}=$Volume of Ideal Gas

$\mathrm{n}=$Number of moles of Ideal Gas

$\mathrm{R}=$Universal Gas Constant

$\mathrm{T}=$Temperature

• Now, Number of moles, $\mathrm{n}=\frac{\mathrm{Given}\mathrm{Mass}\left(W\right)}{\mathrm{Molar}\mathrm{Mass}\left(M\right)}$
• Hence, weight, $\mathrm{W}=\mathrm{Density}\left(\mathrm{\rho }\right)\times \mathrm{Volume}\left(\mathrm{V}\right)$
• Therefore rearranging Ideal Gas Equation

$$\begin{gathered} \mathrm{PV}=\mathrm{nRT} \\ \mathrm{PV}=\frac{\mathrm{W}}{\mathrm{M}}\mathrm{RT} \\ \mathrm{PM}=\frac{\mathrm{W}}{\mathrm{V}}\mathrm{RT} \\ \mathrm{PM}=\mathrm{\rho RT} \end{gathered}$$

• Therefore, Density is directly proportional to Pressure hence if we increase the pressure, the density will increase.
• Density is inversely proportional to Temperature therefore if we increase the temperature, density will decrease.
• Now for the given options, for the density to be maximum, the temperature should be minimum and the pressure should be maximum.

Explanation for incorrect option:

(A) $\mathrm{STP}$

• At STP condition, the pressure is $1\mathrm{atm}$ and temperature is $0°C$.
• Hence the pressure is less therefore density is not maximum.

(C) $273°,1\mathrm{atm}$

• For density to be maximum, the temperature needs to be minimum while in this case it is maximum.
• Hence the density will reduce due to the increase in temperature.

(D) $273°,2\mathrm{atm}$

• In this case, the temperature, as well as pressure both, are maximum.
• But for density to be maximum, the temperature should be minimum and pressure must be maximum.

Hence, option (B) is correct.