Question

At what condition among the following density of nitrogen gas will be highest:
A.STP
B.$273K$ and $2$atm
C.$546K$ and $1$ atm
D.$546K$ and $2$atm

Answer 1

Hint:The density is determined by utilizing a variation of the ideal gas law where density and molar mass replace moles and volume. The original ideal gas law uses the formula \[PV = nRT\;\;\]. We know that $density = \dfrac{{mass}}{{volume}}$ . So the ideal gas equation can be rearranged as $PM = dRT$. Units of density will be $\dfrac{g}{L}$ or gram per litre.

Complete step by step answer:
We know that the density version of the ideal gas law is $PM = dRT$, where P is pressure measured in atmospheres (atm), T is temperature measured in kelvin, R is the ideal gas law constant atm(L)mol(K) even as within the original formula, M is now the molar mass (g mol) and d is that the density ($\dfrac{g}{L}$ ).
Ideal gas equation
\[PV = nRT\;\;\]
Here, n is the number of moles. $n = \dfrac{{given{{ }}mass(m)}}{{molar{{ }}mass(M)}}$
, \[n = \dfrac{m}{M}\]$PV = \dfrac{m}{M}RT$
On rearranging the given equation, by taking M and V to the opposite sides, we get
\[PM = \left( {\dfrac{m}{V}} \right)RT = dRT\] , Because we know that $\dfrac{m}{V} = d$ (density).
This can be written concerning density as $d = \dfrac{{PM}}{{RT}}$
Here we could see that density is directly proportional to Pressure ($d \propto P$)and inversely proportional to Temperature ( $d \propto \dfrac{1}{T}$ ), we can conclude that At higher pressure and lower temperature, gases have higher density. Thus, at ${O^0}C$ ($273K$ ) – lowest temperature and $2$ atm pressure – high pressure, Nitrogen will have the highest density.
The correct answer is option B.

Note:
• Nitrogen is very important to the industry. It's used to make fertilizers, acids, nylon, dyes, and explosives. To create these products, nitrogen must first be reacted with hydrogen to provide ammonia. This can be done by the Haber-Bosch process.
• The Universal Gas constant R is independent of the actual gas and is the same for all "perfect" gases. At STP, the pressure is $1$ atm and the temperature is $273K$
• The gas Law is accurate only at relatively low pressures and high temperatures. To account for deviation from the ideal situation another factor is included. It is called the Gas Compressibility Factor.