Question

What is the average kinetic energy of \[1{\text{ }}mole\] of \[S{O_2}\] at \[300k\] ?
A. $4578\,J/mol$
B. $3741\,J/mol$
C. $3741\,J/mol$
D. $4173\,J/mol$

Answer 1

Hint: Temperature of a material is proportional to total kinetic energy of its particles, according to the kinetic-molecular theory. When a substance is heated, some of the absorbed energy is stored in the particles, while the rest is used to improve particle motion.

Complete answer: The state equation for a hypothetical ideal gas is known as the ideal gas law. Although it has a number of flaws, it is a good approximation of the behaviour of several gases in a variety of situations. The ideal gas equation is the following:
$PV = nRT$
Where,
The ideal gas's pressure is ‘P’.
The volume of the ideal gas is ‘V’.
‘n' is the volume of ideal gas measured in moles.
The universal gas constant is ‘R’.
The letter ‘T’ stands for temperature.
Using the well-known equation \[\dfrac{3}{2}{\text{ }}nRT\] , you can easily figure it out.
We know that the average kinetic energy of a mole of any gas is: \[\dfrac{3}{2}{\text{ }}nRT\] .
"n" denotes the gas mole, which is \[1{\text{ }}mole\] of \[S{O_2}\] .
The letter "T" stands for temperature, which is given as \[300k\]
R stands for gas constant and is equivalent to $8.314J\,{K^{ - 1}}mol{e^{ - 1}}$
$
  K.E = \dfrac{3}{2} \times 1 \times 8.314{K^{ - 1}}mol{e^{ - 1}} \times 300K \\
   = 3741Jmol{e^{ - 1}} \\
 $
So, the correct option is: (C) $3741Jmol{e^{ - 1}}$

Note:
Gas particles are drawn to one another in the real world. When a gas cools, its kinetic energy decreases, causing the particles to travel slowly enough to condense due to attractive forces. Since the product is no longer a gas, the gas rule no longer applies.