# Which of the following statements are true and supported by kinetic molecular theory?

## Which of the following statements are true and supported by kinetic molecular theory? I. Ideal gas behavior is better achieved at low pressure and high temperature. II. The kinetic energy of a molecule is directly proportional to its temperature. III. Instantaneous dipoles are most prominent in gases that are non-polar. IV. As the temperature of a gas increases, the system pressure decreases. I, II and IV I I and II I, II and III II

Jun 28, 2018

Likely the intended answer was $\left(4\right)$, $\text{I", "II", "and III}$, but I would say $\left(6\right)$, $\text{I}$ and $\text{III}$... Choice $\text{II}$ is only completely true if the system contains ONE molecule, which almost never happens.

...While it is true that SINGLE-MOLECULE kinetic energy is proportional to ITS speed squared, any typical measure of temperature is given as an ensemble average, which means that temperature is directly proportional to average kinetic energy, NOT SINGLE-MOLECULE kinetic energy...

$\text{I.}$ Ideal gas behavior is better achieved at low pressure and high temperature.

Yes.

• Low pressure reduces attractive intermolecular forces that cause nonideality, otherwise known at a high-school level as "sticky particles".
• Low temperature reduces nonideal interactions by reducing frequency of collisions, which promotes conservation of energy.

$\text{II.}$ The kinetic energy of a molecule is directly proportional to its temperature.

Not quite true.

A requirement of real life is that what we measure contains multiple particles 99.9% of the time...

Hence, the best measure of molecular speed is the most probable speed (as opposed to average speed or root-mean-square speed):

${\upsilon}_{m p} = \sqrt{\frac{2 R T}{M}}$

This requires that a gas sample contains a large number of molecules, not just one.

Hence, while ${v}_{m p}^{2} \propto T$, it is NOT true that $K = \frac{1}{2} m {v}^{2}$ for one molecule is directly proportional to ${v}_{m p}^{2}$, which is for a collection of molecules. What we measure is an ensemble, and $K$ as-given is for a single molecule.

$\text{III.}$ Instantaneous dipoles are most prominent in gases that are non-polar.

Yes.

Polar gases contain stronger intermolecular forces from reliable, measurable partial charges, which implies that they are more permanent, long-lasting, and therefore more prominent forces.

London dispersion forces, which form instantaneous dipoles, are evidently short-lived and temporary, forming every so often but certainly not permanently.

Every molecule has these instantaneous, but polar forces dominate such nonpolar forces over time.

$\text{IV.}$ As the temperature of a gas increases, the system pressure decreases.

Absolutely not.

As implied in $\left(\text{I}\right)$, higher temperatures increase the frequency of collision, which means the gases collide with the walls more often as well.

Hence, pressure increases by definition.