Consider the following gases, all at STP: $\mathrm{Ne}, \mathrm{SF}_{6}, \mathrm{~N}_{2}, \mathrm{CH}_{4}$. (a) Which gas is most likely to depart from the assumption of the kinetic- molecular theory that says there are no attractive or repulsive forces between molecules? (b) Which one is closest to an ideal gas in its behavior? (c) Which one has the highest root-mean-square molecular speed at a given temperature? (d) Which one has the highest total molecular volume relative to the space occupied by the gas? (e) Which has the highest average kinetic- molecular energy? (f) Which one would effuse more rapidly than $\mathrm{N}_{2} ?\( (g) Which one would have the largest van der Waals \)b$ parameter?

Step by step solution

01

(a) Gas with most significant attractive or repulsive forces

To determine which gas is most likely to depart from the assumption that there are no attractive or repulsive forces between molecules, we need to consider the intermolecular forces of the gases. SF6 has a more massive molecular weight and a more complex structure compared to the other molecules. It is more likely to have stronger van der Waals forces (London dispersion forces) between the molecules. So SF6 is most likely to depart from the assumption of the kinetic-molecular theory.

02

(b) Gas closest to an ideal one

An ideal gas is one with no intermolecular forces and occupies no volume. Ne (neon) is an inert noble gas with weak van der Waals forces and a small molecular size compared to other molecules. Thus, Ne is the closest to an ideal gas in its behavior.

03

(c) Gas with the highest RMS molecular speed

The root-mean-square molecular speed (υrms) is given by the formula: \[υrms = \sqrt{\frac{3RT}{M}}\] where R is the gas constant, T is the temperature, and M is the molar mass of the gas. At a given temperature, the gas with the lowest molecular mass will have the highest υrms. The molecular masses of the gases are: Ne-20, SF6-146, N2-28, and CH4-16. CH4 has the lowest molecular mass, so it has the highest root-mean-square molecular speed at a given temperature.

04

(d) Gas with the highest molecular volume

In a real gas, molecular volume is related to the van der Waals parameter "b." Higher values of "b" indicate larger molecular size and therefore greater molecular volume. For the given gases, the van der Waals parameter "b" increases in this order: Ne < N2 < CH4 < SF6. Therefore, SF6 has the highest total molecular volume relative to the space occupied by the gas.

05

(e) Gas with the highest average kinetic energy

The average kinetic energy of a gas is given by the formula: \[KE_{avg} = \frac{3}{2} RT\] This formula shows that the average kinetic energy is only dependent on the temperature and not the mass of the gas molecules. Since all gases are at STP, they all have the same temperature and thus the same average kinetic-molecular energy.

06

(f) Gas that would effuse more rapidly than N2

The effusion rate of a gas is given by Graham's law: \[\frac{Rate_{1}}{Rate_{2}}=\sqrt{\frac{M_{2}}{M_{1}}}\], where Rate1 and Rate2 are the effusion rates of gas 1 and gas 2, and M1 and M2 are their respective molar masses. We want to find a gas that would effuse more rapidly than N2 (M2 = 28). A gas with a lower molar mass will effuse faster. CH4 has a molar mass of 16, which is lower than N2, so it would effuse more rapidly than N2.

07

(g) Gas with the largest van der Waals b parameter

The van der Waals parameter "b" relates to the effective molecular volume of a gas, and higher values of "b" indicate larger molecular size. As mentioned earlier, for the given gases, the van der Waals parameter "b" increases in the order: Ne < N2 < CH4 < SF6. Thus, SF6 has the largest van der Waals b parameter.

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