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Chapter 12: Problem 16

A liquid is in equilibrium with its vapor in a closed vessel at a fixed temperature. The vessel is connected by a stopcock to an evacuated vessel. When the stopcock is opened, will the final pressure of the vapor be different from the initial value if (a) some liquid remains; (b) all the liquid is first removed? Explain.

Short Answer

Expert verified
If some liquid remains, the final pressure stays the same. If all the liquid is removed, the final pressure decreases.

Step by step solution

01

Understand the Problem

A closed vessel containing a liquid in equilibrium with its vapor is connected to an evacuated vessel. The task is to determine whether the final pressure of the vapor will change if the stopcock is opened and (a) some liquid remains or (b) all the liquid is removed.
02

Analyze Scenario (a)

When the stopcock is opened and some liquid remains, the system will still have liquid that can evaporate to replace the vapor that moved to the evacuated vessel. Thus, the system will reach a new equilibrium where the vapor pressure remains the same because it is determined by the temperature.
03

Analyze Scenario (b)

If all the liquid is removed before the stopcock is opened, there will be no source of additional vapor. The initial release of vapor into the previously evacuated vessel will lower the vapor pressure because the system cannot replenish the lost vapor.
04

Conclusion

In summary, when some liquid remains, the final vapor pressure does not change due to equilibrium being re-established. If all the liquid is removed, the final vapor pressure will be lower because the vapor cannot be replenished.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Vapor Pressure
Vapor pressure is a fundamental concept when discussing liquids and their vapors. It refers to the pressure exerted by the vapor that is in equilibrium with its liquid form at a given temperature.

When a liquid evaporates, molecules leave the liquid phase and enter the vapor phase. As more molecules enter the vapor phase, the vapor exerts a pressure. This pressure is known as vapor pressure.

Key points about vapor pressure:
  • It depends on temperature: Higher temperatures give molecules more energy to escape the liquid and become vapor.
  • It is specific to each substance: Different substances have different tendencies to evaporate, thus different vapor pressures.
  • When temperature remains constant, vapor pressure remains constant if there is enough liquid to replenish the vapor.

Understanding vapor pressure is crucial for analyzing how liquids behave in different environments, including closed systems.
Equilibrium
Equilibrium in a vapor-liquid system means that the rate of evaporation is equal to the rate of condensation.

In an equilibrium state:
  • The amount of liquid turning into vapor equals the amount of vapor condensing back into liquid.
  • The vapor pressure remains constant over time at a fixed temperature.
  • Any disturbance, like opening a stopcock, will lead to a new equilibrium state if there is still liquid present to evaporate.

Maintaining equilibrium depends on having both liquid and vapor in the system. If all the liquid is removed, equilibrium can no longer be maintained, affecting the vapor pressure.
Evaporation
Evaporation is the process where molecules at the surface of a liquid gain enough energy to enter the vapor phase.

Key characteristics of evaporation:
  • It occurs at any temperature, not just at the boiling point.
  • Molecules with higher energy can escape the liquid surface and become vapor.
  • Evaporation is a cooling process because it involves the escape of higher-energy molecules, leaving the lower-energy ones behind.

Evaporation continues until equilibrium is reached if the system is closed and there is enough liquid. In an open or disturbed system, evaporation can cause significant changes in the vapor pressure.
Closed System
A closed system is one where nothing can enter or leave the system, including mass and energy.

In a vapor-liquid equilibrium discussion, a closed system means:
  • The liquid and vapor are contained within a sealed environment.
  • The temperature is constant and no external air or vapor can enter or exit.
  • Equilibrium can be established without external interference.

If the closed system is disturbed (e.g., by opening a stopcock as in the original exercise), the system will seek a new equilibrium state. The presence or absence of liquid determines if the vapor pressure can be maintained or if it will decrease due to inability to replenish the evaporated molecules.

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Most popular questions from this chapter

Polonium, the Period 6 member of Group \(6 \mathrm{~A}(16),\) is a rare radioactive metal that is the only element with a crystal structure based on the simple cubic unit cell. If its density is \(9.142 \mathrm{~g} / \mathrm{cm}^{3}\), calculate an approximate atomic radius for polonium.

Diethyl ether has a \(\Delta H_{\mathrm{vap}}^{\circ}\) of \(29.1 \mathrm{~kJ} / \mathrm{mol}\) and a vapor pressure of 0.703 atm at \(25.0^{\circ} \mathrm{C}\). What is its vapor pressure at \(95.0^{\circ} \mathrm{C} ?\)

Which member of each pair of compounds forms intermolecular \(\mathrm{H}\) bonds? Draw the \(\mathrm{H}\) -bonded structures in each case: (a) \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{NH}\) or \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{~N}\) (b) \(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{OH}\) or \(\mathrm{FCH}_{2} \mathrm{CH}_{2} \mathrm{~F}\)

Describe in molecular terms what occurs when ice melts.

Distinguish between isotropic and anisotropic substances. To which category do liquid crystals belong?
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