To solve this problem we use the combined gas law:

Use the given values for the temperature and volume, as well as the initial pressure, to solve for the final pressure.

According to Graham's law, the rate of effusion of a gas is inversely proportional to the square root of the mass:  .

The gas with the lowest molecular weight will effuse the fastest. has the lowest molecular weight of the given gasses, with a value of  .

Since both molecules are at the same temperature, the value of the temperature is irrelevant. The difference in velocity between the two molecules depends on the difference in their molar masses. The molar mass of a helium atom is , and the molar mass of a carbon monoxide molecule is .  

Graham's Law describes the relationship between gas particle mass and velocity:

Using the molar masses of the particles in question, we can determine their relationship.

This question asks you how the velocity of the molecules changes with increasing temperature. From molecular kinteics, we know that temperature is proportional to kinetic energy.

We can see that as temperature rises, the kinetic energy rises, however, the question asks us how the velocity changes. Now, we need to know how kinetic energy and velocity are related. We can pull this relationship from Newtonian mechanics.

If we simplify, we can see that . Velocity increases with increasing temperature, but in an indirectly proportional manner.

Ideal gases are assumed to have no intermolecular forces and to be composed of particles with no volume. Under high pressure, gas particles are forced closer together and intermolecular forces become a factor. In low temperatures intermolecular forces also increase, since molecules move more slowly, similar to what would occur in a liquid state. Just remember that ideal gas behavior is most closely approximated in conditions that favor gas formation in the first place—heat and low pressure.

Under the ideal gas law, we assume that the interactions between the molecules are very brief and that the forces involved are negligible. The assumption that the molecules obey Coulomb's law when interacting with each other is not necessary; rather, an ideal gas must disregard Coulomb's law.

The ideal gas law assumes only Newtonian mechanics, disregarding any intermolecular or electromagnetic forces.

Measurements of real gases deviate from ideal gas predictions because intermolecular forces and the volume of the particles themselves are not taken into consideration for ideal gases. The volume of the space between particles is considered for ideal gases and does not contribute to deviation from ideal gas behavior.

Attraction between molecules causes real pressure to be slightly less than ideal pressure, while the volume of gas particles causes real volume to be slightly greater than ideal volume.

The question wants you to pick a molecule that will have a negative attraction coefficient, . The question states that the molecules that repel each other will have a negative . Recall that similar charges repel each other; therefore, you are looking for an ionized molecule (molecule with a positive or negative charge). In a closed container, these molecules will be force into contact with each other and generate repulsion forces.

Dichloromethane  is a neutral molecule. This means that the dichloromethane molecules won’t repel each other. Similarly, sodium chloride is a neutral molecule and will not experience repulsion. Oxygen, with an electron configuration of , is also a neutral molecule. If you look at the periodic table, the neutral state of oxygen occurs when there are six valence electrons. The outermost shell of oxygen in this electron configuration  has a total of six electrons; therefore, the oxygen has six valence electrons and is neutral.

On the other hand, magnesium, with an electron configuration of , is not neutral. Recall that a neutral magnesium atom has two valence electrons and an electron configuration of . The magnesium atom in this question, however, has lost two electrons (from the  orbital) and became positively charged with a charge of ; therefore, the magnesium atoms are ionized, will repel each other, and will have a negative .

This question can be solved using either Charles's law or the ideal gas law (converted into the combined gas law).

Charles's Law:

Ideal Gas Law: 

The question states that the pressure and moles  are held constant; therefore, the volume and temperature are directly proportional. If the question were asking about an ideal gas, the volume would double when you double the temperature

The volume would double for an ideal gas; however, the question is asking about a real gas. To find the correct relationship between volume and temperature we need to look at the equation for real gas volume. Remember that the volume we are concerned with is the volume of the free space in the container, given by the container volume minus the volume of the gas particles. The equation for real gas volume accounts for the volume of the container and the volume of the gas particles. For a real gas, the volume is given as follows:

In this equation,  is the number of moles of gas particles and  is the bigness coefficient. This equation implies that the volume of free space for a real gas is always less than the volume for an ideal gas; therefore, doubling the temperature will produce a volume that is less than the predicted volume for an ideal gas. Our answer, then, must be less than double the initial volume.

Note that for an ideal gas the bigness coefficient, , would be zero and the volume of free space  would be equal to the volume of the container . This occurs because the volume of the gas particles is negligible for an ideal gas.

For a gas to behave ideally, is should have a low mass and/or weak intermolecular forces. Contrastingly, non-ideal gasses should have very large masses and/or have strong intermolecular forces. Therefore, the correct answer is  which has very strong intermolecular forces, hydrogen bonds. Nonpolar gasses such as oxygen, and other diatomic gasses have very weak intermolecular forces and thus behave ideally.