Question

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

Answer 1

Hint: As we all know that the ideal gas equation is valid for all the ideal gases. Ideal gas equation shows relation between temperature, pressure, moles and volume, from ideal gas equation we can derive a relation between the density, pressure and temperature.

Complete step by step answer:
Density is the measurement of closeness of particles present in a solid, liquid or gas. Basically it is the ratio of mass per unit volume. From this definition we can say that if a substance has high density then its volume will be less, the whole mass will be packed closely in a small volume and if the density of a material is low then we can say that the volume is large, the whole mass will be distributed in a large volume.
Formula of density, ${\text{density = }}\dfrac{{{\text{mass}}}}{{{\text{volume}}}}$
But here we are talking about neon so the ideal gas equation will be applicable here and from that equation we will find out the relation between temperature, pressure and density.
As we all know that,
${\text{PV = nRT}}$ where,
${\text{n}}$is the number of moles
${\text{P}}$ is the pressure
${\text{V}}$ is the volume
${\text{R}}$ is gas constant and
${\text{T}}$ is temperature
Now we will convert the moles in the ratio of mass and molar mass
So, ${\text{PV = }}\dfrac{w}{M}{\text{RT}}$ where $w$ is weight and $M$ is molecular weight.
Now by rearranging the equation we get
${\text{PM = }}\dfrac{w}{V}{\text{RT}}$
And we know that ratio of mass and molar mass is density ($d$)
So, ${\text{PM = }}d{\text{RT}}$
$ \Rightarrow d = \dfrac{{{\text{PM}}}}{{{\text{RT}}}}$
From the above derived formula we can predict the values of temperature and pressure.
We have to make our density highest, to do so we can maximize our pressure and minimize our temperature.
Hence we can conclude that temperature is $0^\circ C$ and pressure is $2atm$.

So, the correct answer is Option B .

Note:
 Density is the measure of closeness of particles of a solid, liquid or a gas. The density of gases mostly depends on the temperature and pressure of surroundings, if pressure is increased the particles will come closer and the density will increase and if the temperature is increased the particles will move away from each other and the density will decrease.