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Chapter 11: Problem 10

Consider a beaker of salt water sitting open in a room. Over time, does the vapor pressure increase, decrease, or stay the same? Explain.

Short Answer

Expert verified
The vapor pressure of the saltwater in the open beaker decreases over time. This is due to the combined effects of Raoult's Law, evaporation, and the open nature of the beaker. As water evaporates, the salt concentration increases, which lowers the vapor pressure according to Raoult's Law. The inability to maintain equilibrium in an open system further contributes to the decrease in vapor pressure.

Step by step solution

01

Understand the concept of vapor pressure

Vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system. When a liquid (in this case, water mixed with salt) is in a container, some molecules gain enough energy to escape from the liquid's surface and enter the gas phase. Conversely, some gas molecules return to the liquid phase. When the rate at which molecules enter and exit the liquid is equal, we achieve equilibrium, and the pressure above the liquid is called the vapor pressure.
02

Examine the factors that influence vapor pressure

Several factors can affect the vapor pressure of a liquid, such as temperature, the presence of solutes, and the surface area exposed to the atmosphere. In this exercise, we focus on two specific factors: the presence of salt (which affects vapor pressure due to Raoult's Law) and the fact that the beaker is open to the atmosphere.
03

Apply Raoult's Law to the system

Raoult's Law states that the vapor pressure of a component in a solution is equal to the product of the vapor pressure of the pure component and its mole fraction in the solution. In simpler terms, when a solute (in this case, salt) is dissolved in a solvent (water), the vapor pressure of the solvent is reduced. This is because the solute particles dilute the number of solvent particles at the surface, reducing the number of solvent particles available to enter the vapor phase.
04

Consider the open nature of the beaker

Since the beaker is open to the atmosphere, there is no closed system, and a proper equilibrium between the liquid and vapor phases cannot be established and maintained. The vapor pressure will continue to change over time as the water evaporates until there is no more liquid left. Also, the room temperature can impact evaporation and vapor pressure over time.
05

Analyze the effect of salt on vapor pressure and conclude

As the water evaporates from the saltwater solution, it leaves the salt behind. The salt concentration in the solution gradually increases, further reducing the vapor pressure according to Raoult's Law. Therefore, over time, the vapor pressure will decrease. This can be concluded from the combined effects of Raoult's Law, evaporation, and the open nature of the beaker leading to changes in vapor pressure, concentration of salt, and inability to maintain equilibrium.

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