Question

Indicate whether each statement is true or false: (a) The critical pressure of a substance is the pressure at which it turns into a solid at room temperature. (b) The critical temperature of a substance is the highest temperature at which the liquid phase can form. (c) Generally speaking, the higher the critical temperature of a substance, the lower its critical pressure. (\boldsymbol{d} ) In general the more intermolecular forces there are in a substance, the higher its critical temperature and pressure.

Short answer

(a) False: The critical pressure is related to the gas-liquid equilibrium, not the solid-liquid equilibrium, and it depends on the critical temperature, not room temperature. (b) True: The critical temperature is the threshold temperature above which the liquid phase cannot exist even if the pressure is increased. (c) False: Critical temperature and critical pressure are not inversely related. A substance may exhibit a high or low critical pressure and a high or low critical temperature depending on its particular properties. (d) True: A substance with stronger intermolecular forces will require more energy (high temperature) and pressure to overcome these forces, giving it a higher critical temperature and pressure.

Step-by-step solution

Understanding Critical Temperature and Critical Pressure

The critical temperature (\(T_c\)) is the temperature above which a substance cannot remain in a liquid state, regardless of the pressure applied. Above its critical temperature, the substance will exist solely as a gas. The critical pressure (\(P_c\)) is the pressure required to force a gas to liquefy when it is at its critical temperature. The critical point is when the substance reaches both its critical temperature and pressure simultaneously. Now, we will analyze each statement and determine whether it is true or false.

Evaluating Statement (a)

Statement (a): "The critical pressure of a substance is the pressure at which it turns into a solid at room temperature." This statement is false. The critical pressure is related to the gas-liquid equilibrium, not the solid-liquid equilibrium, and it depends on the critical temperature, not room temperature.

Evaluating Statement (b)

Statement (b): "The critical temperature of a substance is the highest temperature at which the liquid phase can form." This statement is true. The critical temperature is the threshold temperature above which the liquid phase cannot exist even if the pressure is increased.

Evaluating Statement (c)

Statement (c): "Generally speaking, the higher the critical temperature of a substance, the lower its critical pressure." This statement is false. Critical temperature and critical pressure are not inversely related. A substance may exhibit a high or low critical pressure and a high or low critical temperature depending on its particular properties.

Evaluating Statement (d)

Statement (d): "In general, the more intermolecular forces there are in a substance, the higher its critical temperature and pressure." This statement is true. Intermolecular forces affect the substance's properties, including its critical temperature and pressure. A substance with stronger intermolecular forces will require more energy (high temperature) and pressure to overcome these forces, giving it a higher critical temperature and pressure.

Key concepts

Phase Equilibrium

Understanding the concept of phase equilibrium is central to many areas of chemistry, especially when we consider the transformation of matter from one state to another. Phase equilibrium occurs when two phases of a substance—such as solid and liquid, liquid and gas, or solid and gas—are present simultaneously and exchange particles at the same rate they are returned. This means there's a balance, with no net change in the amount of each phase.

Let's take water as an example. At 0°C and 1 atm pressure, ice and liquid water coexist. This is the melting point of ice and, simultaneously, the freezing point of water. In thermodynamic terms, the chemical potential of ice equals the chemical potential of water. If the temperature or pressure changes, the equilibrium would shift, favoring one phase over the other. Phase equilibrium is dynamic and responsive to external conditions, such as temperature and pressure changes.

Intermolecular Forces

Intermolecular forces are the attractive and repulsive forces between molecules that dictate how they interact and bind with each other. These forces are weaker than the intramolecular forces that hold a molecule itself together, like covalent and ionic bonds but are critical in determining the physical properties of substances.

There are several types of intermolecular forces including dipole-dipole interactions, hydrogen bonding, and London dispersion forces. These forces have a significant impact on a substance's phase, boiling point, melting point, and as you now know, critical temperature and pressure. Substances with stronger intermolecular forces require more energy to change phases because these forces need to be overcome. For example, hydrogen bonds in water result in a higher boiling point compared to other molecules of similar size.

Gas-Liquid Equilibrium

Gas-liquid equilibrium is a type of phase equilibrium specific to the coexistence of a substance in both its gas and liquid states. Distinctive from solid-liquid equilibrium (like melting ice), gas-liquid equilibrium is particularly influenced by changes in pressure and temperature.

One classic example is the carbonation in soft drinks. When sealed, the carbon dioxide is dissolved in the liquid due to high pressure, maintaining equilibrium. Once the bottle is opened and pressure decreases, the equilibrium shifts, and the carbon dioxide escapes as bubbles (gas).

In relation to the critical temperature and pressure of a substance, the gas-liquid equilibrium can exist only below the critical temperature. Above this temperature, the distinction between gas and liquid phases disappears and the substance becomes a supercritical fluid.