Question

The density of neon is highest at

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

Answer 1

The correct option is B

$0°\mathrm{C},2\mathrm{ATM}$

The explanation for the correct answer:-

Option (B)$0°\mathrm{C},2\mathrm{ATM}$

• Neon is reddish-orange coloured in neon lamps and vacuum discharge tubes and is the second-lightest noble gas.
• It is a less costly refrigerant than helium in many applications.
• The cooling power is forty times greater than liquid helium and on a unit volume basis, three times more than liquid hydrogen.
• It is a rare gas and its molecules are made up of a single atom of Neon.

Step 1: Formula used

The ideal gas equation is,

$\mathrm{PV}=\mathrm{nRT}$ , where $\mathrm{P}\mathrm{and}\mathrm{V}$are pressure and volume of gas

$\mathrm{n}-$ number of moles of gas, $R–$ universal gas constant, $T$– temperature

$\mathrm{PV}=(\mathrm{w}/\mathrm{m})\mathrm{RT}$

Step 2: Rearranging equation

Rearranging the above equation we get,

$\mathrm{PM}=(\mathrm{w}/\mathrm{V})\mathrm{RT}$

Step 3: Deriving density

As,$\mathrm{w}/\mathrm{V}$= density, and substituting value in the above equation we get

$$\begin{gathered} \mathrm{PM}=\mathrm{dRT} \\ \mathrm{d}=\mathrm{PM}/\mathrm{RT} \end{gathered}$$

Thus, density is directly proportional to the pressure and inversely proportional to temperature.

Thus, higher density results in low temperature and high pressure. Therefore, the neon density would be the highest at $0°\mathrm{C},2\mathrm{ATM}.$

Hence, option (B) is the correct answer.