The vapor pressures of ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) and 1 -propanol \(\left(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}\right)\) at \(35^{\circ} \mathrm{C}\) are \(100 \mathrm{mmHg}\) and \(37.6 \mathrm{mmHg},\) respectively. Assume ideal behavior and calculate the partial pressures of ethanol and 1-propanol at \(35^{\circ} \mathrm{C}\) over a solution of ethanol in 1-propanol, in which the mole fraction of ethanol is \(0.300 .\)

Partial pressure is a fundamental concept in chemistry, particularly when studying mixtures of gases. It refers to the pressure that a single component of a gas mixture would exert if it were alone in the entire volume occupied by the gas mixture at the same temperature. In essence, each gas in a mixture behaves independently and contributes to the total pressure of the system according to its mole fraction. This concept is critical for understanding the behavior of gas mixtures, whether in environmental science, respiratory physiology, or industrial processes.

When two or more volatile substances are mixed, the partial pressure of each component is a crucial factor in determining the system's overall pressure. Raoult's Law allows us to calculate these individual pressures, assuming ideal behavior, which suggests that the interactions between molecules of different components are similar to those between the molecules of the pure components.

Vapor pressure is an intrinsic property of a liquid that describes its tendency to evaporate. It depends on the substance's temperature, and it's vital to understand that it represents the pressure exerted by a vapor in equilibrium with its liquid phase at a given temperature. This means that at the equilibrium point, the rate of evaporation of the liquid equals the rate of condensation from the vapor.

The vapor pressure of a substance can provide insights into its volatility—the higher the vapor pressure, the more volatile the substance. This characteristic plays a pivotal role in Raoult's Law, where the vapor pressure of a pure substance is used in conjunction with the mole fraction to determine the partial pressure of each component in a solution.

The mole fraction is a dimensionless quantity that represents the ratio of the number of moles of a particular component to the total number of moles of all substances present in the mixture. It's symbolized by 'X' and provides a way to express concentrations in mixtures without the need for specific units.

To calculate the mole fraction, simply divide the number of moles of the substance of interest by the total number of moles in the mixture. As it scales from 0 to 1, it can be easily converted to percentages for practical use. The concept of mole fraction is important for computations in solutions, including those involving Raoult's Law and various other thermodynamic equations.

Ethanol \( \mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH} \) is a ubiquitous organic compound thanks to its use in beverages, as a biofuel, and in a wide variety of industrial applications. It is a volatile, colorless liquid at room temperature with a characteristic odor. Ethanol's physical properties, such as its boiling point, melting point, and vapor pressure, play significant roles in its behavior in mixtures.

When discussing vapor-liquid equilibrium, ethanol's properties become essential for understanding and predicting how it will perform within a solution. Notably, ethanol's relatively high vapor pressure compared to many other liquids indicates its high volatility and ease of evaporation. Ethanol also has strong hydrogen bonding due to its hydroxyl (-OH) group, impacting its interactions with other substances when mixed.

1-propanol \( \mathrm{C}_{3}\mathrm{H}_{7}\mathrm{OH} \) is a slightly larger alcohol compared to ethanol, with three carbon atoms in its structure. It's also a colorless liquid and exhibits strong intermolecular hydrogen bonding due to the presence of a hydroxyl group. The properties of 1-propanol, like melting and boiling points, density, and especially vapor pressure, are crucial when examining its behavior in mixtures.

For instance, its vapor pressure at a given temperature is lower than that of ethanol, which indicates that it's less volatile and has a lower tendency to evaporate. Understanding the properties of 1-propanol is essential when calculating its partial pressure in a mixture using Raoult’s Law, as was done in the example problem. The behavior of 1-propanol when mixed with other substances sheds light on the fundamentals of solution dynamics and contributes to the rich tapestry of chemistry.