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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 beaker of salt water sitting open in a room will decrease over time. This is due to the evaporation of the solvent (water) and the increasing concentration of the solute (salt), which decreases the fraction of water molecules at the surface available for evaporation, resulting in a reduced vapor pressure.

Step by step solution

01

Understanding Vapor Pressure

Vapor pressure is defined as the pressure exerted by a vapor that is in equilibrium with its associated liquid in a closed system. It depends on the temperature and the liquid's volatility, which is its tendency to evaporate. The higher the temperature, the higher the vapor pressure.
02

Understanding Raoult's Law

Raoult's law is used to explain the relationship between vapor pressure and the presence of solutes in a solution. According to Raoult's law, the vapor pressure of a solution is equal to the mole fraction of the solvent multiplied by the vapor pressure of the pure solvent. In other words, adding a non-volatile solute to a solvent will decrease the vapor pressure of the solution, as the fraction of solvent molecules at the surface is decreased.
03

Considering the Beaker of Salt Water

In our given exercise, we have a beaker of salt water, which is a solution of a non-volatile solute (salt) in a volatile solvent (water). Since the beaker is open, the closed system constraint is not fulfilled which means Raoult's law is not strictly applicable, but we can still use the idea behind it. The presence of the salt decreases the vapor pressure of the water due to the reduced fraction of water molecules at the surface available for evaporation.
04

Analyzing Evaporation

The process of evaporation is the conversion of a liquid into a vapor. As time passes, the solvent molecules (water) at the surface will evaporate, leaving behind the solute (salt). This process will continue until an equilibrium is reached between the rate of evaporation and the rate of condensation. However, in an open container, there is no constraint on the maximum amount of vapor that can build-up, hence no equilibrium will be reached.
05

Vapor Pressure Behavior Over Time

As time goes on, the amount of water in the beaker decreases, while the concentration of salt increases. This means that the fraction of water molecules at the surface of the solution decreases, resulting in a further decrease in the vapor pressure of the system. Therefore, the vapor pressure of the saltwater in the beaker will decrease over time. In conclusion, the vapor pressure of the beaker of salt water sitting open in a room will decrease over time due to the evaporation of the solvent and the increasing concentration of the solute.

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Most popular questions from this chapter

From the following: pure water solution of \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}(m=0.01)\) in water solution of \(\mathrm{NaCl}(m=0.01)\) in water solution of \(\mathrm{CaCl}_{2}(m=0.01)\) in water Choose the one with the a. highest freezing point. b. lowest freezing point. c. highest boiling point. d. lowest boiling point. e. highest osmotic pressure.

Calculate the freezing point and the boiling point of each of the following aqueous solutions. (Assume complete dissociation.) a. \(0.050 \mathrm{~m} \mathrm{MgCl}_{2}\) b. \(0.050 \mathrm{~m} \mathrm{FeCl}_{3}\)

An aqueous solution is \(1.00 \% \mathrm{NaCl}\) by mass and has a density of \(1.071 \mathrm{~g} / \mathrm{cm}^{3}\) at \(25^{\circ} \mathrm{C}\). The observed osmotic pressure of this solution is \(7.83\) atm at \(25^{\circ} \mathrm{C}\).

How does \(\Delta H_{\text {soln }}\) relate to deviations from Raoult's law? Explain.

Which ion in each of the following pairs would you expect to be more strongly hydrated? Why? a. \(\mathrm{Na}^{+}\) or \(\mathrm{Mg}^{2+}\) d. \(\mathrm{F}^{-}\) or \(\mathrm{Br}^{-}\) b. \(\mathrm{Mg}^{2+}\) or \(\mathrm{Be}^{2+}\) e. \(\mathrm{Cl}^{-}\) or \(\mathrm{ClO}_{4}^{-}\) c. \(\mathrm{Fe}^{2+}\) or \(\mathrm{Fe}^{3+}\) f. \(\mathrm{ClO}_{4}^{-}\) or \(\mathrm{SO}_{4}^{2-}\)
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