In a process in which benzene is used as a solvent, it is...

In a process in which benzene is used as a solvent, it is evaporated into dry nitrogen. The resulting mixture at a temperature of 297 K and a pressure of $101.3 \mathrm{kN} / \mathrm{m}^2$ has a relative humidity of $60 \%$. It is required to recover $80 \%$ of the benzene present by cooling to 283 K and compressing to a suitable pressure. What must this pressure be? Vapour pressures of benzene: at $297 \mathrm{~K}=12.2 \mathrm{kN} / \mathrm{m}^2$ : at $283 \mathrm{~K}=6.0 \mathrm{kN} / \mathrm{m}^2$.

Key Concepts

Gas Compression

Gas compression increases the total pressure of a gas mixture, thereby proportionally raising the partial pressures of all components. In systems where one component is condensable, compressing the mixture can help achieve the required equilibrium conditions for condensation. The relationship between compression, temperature, and vapor-liquid equilibrium is key in designing an effective recovery process.

Cooling and Condensation

Cooling a gas mixture lowers the temperature, which decreases the saturation vapor pressure of the condensable component. When the partial pressure of the vapor exceeds its reduced saturation vapor pressure, condensation occurs. This principle is exploited in recovery processes where the objective is to condense a specific fraction of a vapor from a gas stream, thus separating and collecting a valuable component.

Vapor Pressure

Vapor pressure is the equilibrium pressure exerted by a vapor above its liquid (or solid) phase at a given temperature. This property is essential when studying phase equilibria because it indicates the tendency of a substance to evaporate or condense. In solvent recovery processes, knowing the vapor pressures at different temperatures is crucial for determining the conditions under which the vapor will begin to condense and can be separated or recovered.

Relative Humidity

Relative humidity is a measure of how close a vapor in a gas mixture is to its saturation level at a specific temperature, typically expressed as a percentage of the maximum vapor pressure. Although commonly used for water, the concept applies to any condensable vapor in a system. It is key in understanding the initial state of the vapor phase and in predicting the amount of vapor that might condense when the temperature changes.

Partial Pressure

Partial pressure refers to the pressure contributed by an individual gas in a mixture, proportional to its mole fraction according to Dalton’s Law. This concept is fundamental in gas mixtures, particularly when one component is undergoing phase change. Accurate knowledge of partial pressures is vital when determining the conditions required for condensation, such as in the recovery of a vapor by cooling and compression.

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