When octane is mixed with methanol, the vapor pressure of the octane over the solution is higher than what we would calculate using Raoult's law. Why? Explain the discrepancy in terms of intermolecular attractions.

Vapor pressure is a critical concept when examining liquid mixtures and solutions. It refers to the pressure exerted by the vapor that is in equilibrium with its liquid at a given temperature. When a liquid is inside a closed container, molecules escape from the surface of the liquid into the vapor phase. Over time, some of these molecules return to the liquid. An equilibrium is established when the rate at which the molecules vaporize equals the rate at which they condense. The pressure of the vapor at this point is the vapor pressure.

Higher temperature leads to increased vapor pressure because more molecules have enough energy to escape into the vapor phase. The nature of the liquid itself also affects vapor pressure. Substances with strong intermolecular forces are more difficult to vaporize and thus have lower vapor pressures.

Intermolecular forces refer to the attractive forces that occur between molecules. These forces are crucial in understanding the behavior of a substance in different states, as well as when mixed with other substances. The strength and type of intermolecular forces impact melting and boiling points, viscosity, surface tension, and vapor pressure.

There are several types of intermolecular forces:

• Dispersion Forces: These occur in all molecules but are the only forces present in nonpolar compounds.
• Dipole-Dipole Interactions: These occur between polar molecules.
• Hydrogen Bonds: A strong type of dipole-dipole interaction that occurs when hydrogen is bonded to highly electronegative atoms like nitrogen, oxygen, or fluorine

. When these intermolecular forces are weak, molecules can escape more easily into the vapor phase, resulting in a higher vapor pressure.

Non-ideal solutions deviate from Raoult's Law, which describes the vapor pressures of ideal mixtures. The deviation occurs because the intermolecular interactions between different types of molecules are not the same as the interactions between molecules of the same type.

In a non-ideal solution, the presence of stronger or weaker interactions among the components compared to pure substances results in vapor pressures that are higher or lower than expected. This gives rise to two scenarios:

• Positive Deviation: Where the mixture's vapor pressure is greater than predicted by Raoult's Law. This happens when the intermolecular forces between unlike molecules are weaker than those between like molecules.
• Negative Deviation: Where the mixture's vapor pressure is less than predicted. This occurs when attractions between unlike molecules are stronger than those between like molecules.

In the case of a mixture of octane and methanol, the weaker intermolecular forces lead to a positive deviation from Raoult's Law, increasing the vapor pressure of octane in the mixture.

The mole fraction is a way of expressing the concentration of a component in a mixture. It is defined as the ratio of the number of moles of a particular substance to the total number of moles of all substances present in the mixture. Mathematically, the mole fraction of component A is given by the formula: \( x_A = \frac{n_A}{n_{total}} \) where \( n_A \) is the number of moles of A and \( n_{total} \) is the sum of the moles of all components in the mixture.

Raoult's Law uses mole fraction to determine the expected partial pressure of each component in a mixture. According to Raoult's Law, the partial vapor pressure of each component in an ideal solution is equal to the product of the mole fraction of that component and the vapor pressure of the pure substance at the same temperature. This helps in predicting the behavior of the mixture's components, provided the solution behaves ideally, which is not the case with the octane and methanol mixture.