Question

An ideal gas will have maximum density when ____.
${A}.P=1atm,T=300K$
${B}.P=2atm,{ }T=150K$
${C}.P=0.5atm,T=600K$
${D}.P=1atm,T=500K$

Answer 1

First we will rearrange the ideal gas equation according to our convenience and question’s requirement then using a hit and trial method or by putting the values given in each question we will find the correct option.

Complete step-by-step answer: From ideal gas equation,
$PV=nRT$
Now we will rearrange the above ideal gas equation:
$P=\dfrac{wRT}{MV}$
$\dfrac{w}{V}=\dfrac{PM}{RT}$
$\rho =\dfrac{PM}{RT}$
From the above equation we can see that by increasing the value of P and decreasing the value of T, density increases.
When we will put the values given in each option one by one in the rearranged ideal gas equation we will come to know the desired option.

So the correct option will be option (B) i.e. $P=2atm;T=150K$

Additional information: The ideal gas law is also called the general gas equation.
The state of a gas is determined by its pressure, temperature and volume according to following equation:
$PV=nRT$
Here P = pressure
V = volume
R = Universal gas constant
T = temperature
n = number of moles of gas
This ideal gas equation is applicable to gases only not on liquids. Ideal gas is nothing but just a hypothetical concept made by scientists to make calculations and results easier.
An ideal gas can be defined as one in which all collisions between atoms or molecules are perfectly elastic and in which there are no intermolecular attractive forces.

Note: in case of real gas non elastic collisions occur and also present intermolecular force. real gas has definite volume and it is present in the environment whereas the ideal gas is not found in our environment . real gas does not follow the ideal gas equation .