Question

At what temperature will the total kinetic energy (KE) of 0.30 mole of He be the same as the total KE of 0.40 mole of Ar at 400K:
A.400K
B.373K
C.533K
D.300K

Answer 1

Hint: The kinetic theory of gases is a basic, historically significant classical model of gas thermodynamic behaviour that laid the groundwork for many fundamental thermodynamic ideas. A gas is described by the model as a huge number of identical submicroscopic particles (atoms or molecules) moving in a random, continuous motion. Their size is thought to be significantly less than the typical particle distance. The particles collide with one other and with the container's surrounding walls at random elastic collisions. The simplest form of the model represents an ideal gas and ignores all additional particle interactions.

Complete answer:
The mean kinetic energy of a gas is measured by its temperature. The molecules are in continual random motion, and that motion has an energy associated with them (mass x square of velocity). The more the motion, the higher the temperature. The position of the molecules relative to each other in a solid is nearly constant. The molecules in a gas, on the other hand, may move around and interact with each other and their environment in a variety of ways. As previously stated, molecular motion contains a random component. The entire fluid may be made to move in a controlled manner. The ordered motion is placed on top of the molecules' usual random motion.
We know that
${\text{KE}} = \dfrac{{3{\text{nRT}}}}{2}$
$\dfrac{{({\text{KE}}){\text{He}}}}{{({\text{KE}}){\text{Ar}}}} = \dfrac{{({\text{ moles of He}}) \times ({\text{ temp of He}})}}{{({\text{ moles of Ar}}) \times ({\text{ temperature of Ar}})}}$
$1 = \dfrac{{0.3 \times {\text{T}}}}{{0.4 \times 400}}$
${\text{T}} = 400 \times \dfrac{4}{3}$
$ \Rightarrow {\mathbf{T}} = {\mathbf{533K}}$
So, option C is correct.

Note:
One of the four basic states of matter is gas (the others being solid, liquid, and plasma). A pure gas can be made up of individual atoms (such as a noble gas like neon), elemental molecules (such as oxygen), or complex molecules (composed of a variety of atoms) (e.g. carbon dioxide). A gas mixture, such as air, consists of a number of different pure gases. The enormous separation of individual gas particles differentiates a gas from liquids and solids. A colourless gas is generally undetectable to a human observer due to this gap.