# 16.4: Vapor Pressure and Boiling

Difficulty Level: At Grade Created by: CK-12

## Lesson Objectives

The student will:

• describe the processes of evaporation and condensation.
• describe equilibrium vapor pressure.
• express the relationship between boiling point, vapor pressure, and ambient pressure.
• given a vapor pressure table for water, and the ambient pressure, determine the boiling point of water for those conditions.

## Vocabulary

• condensation
• equilibrium vapor pressure
• evaporation
• heat of condensation
• heat of vaporization
• vapor
• vapor pressure

## Introduction

The phase of a substance is essentially the result of two competing forces acting on the molecules. The molecules of a substance are pulled together by intermolecular forces of attraction, which could be either weak or strong. The molecules of a substance are also in constant random motion so that they are almost constantly colliding with each other. Without any intermolecular forces of attraction, the molecules of all substances would move away from each other, and there would be no condensed phases (liquids and solids).

If the forces caused by molecular motion are much greater than the intermolecular forces of attraction, the molecules will separate and the substance will be in the gaseous state. If the intermolecular forces of attraction are stronger than the molecular motion, the molecules will be pulled into a closely packed pattern and the substance will be in the solid state. If there is some balance between molecular motion and intermolecular forces of attraction, the substance will be in the liquid state.

When substances are heated (or cooled), their average kinetic energy will increase (or decrease) due to the increase (or decrease) in molecular motion and may result in a phase change. A substance in the solid phase can be heated until the molecular motion balances the intermolecular forces, causing the solid to melt into a liquid. The liquid may be heated until the molecular motion completely overcomes the intermolecular forces, causing the liquid to vaporize into the gaseous state.

## Evaporation and Condensation

### Evaporation

The temperature in a beaker of water is a measure of the average kinetic energy of the molecules in the beaker. This does not mean that all the molecules in the beaker have the same amount of kinetic energy. Most of the molecules will be within a few degrees of the average, but a few molecules may be considerably hotter or colder than the average. The kinetic energy of the molecules in the breaker will have a distribution curve similar to a standard distribution curve for most naturally occurring phenomena. For most naturally occurring phenomena, most instances of the phenomena will occur near the average. Instances that occur further away from the average are increasingly rare, as seen in the image below.

In the case of a beaker of water, some of the molecules will have an average temperature below the boiling point, while some of the molecules will have a temperature above the boiling point (see figure below). The dashed yellow line is the average temperature of the molecules and would be the temperature shown on a thermometer inserted into the liquid. The red line represents the boiling point of water (\begin{align*}100^\circ\mathrm{C}\end{align*} at \begin{align*}1.0 \ \mathrm{atm}\end{align*} pressure), and the area under the curve to the right of the red line represents the number of molecules that are above the boiling point. In order for a molecule above the boiling temperature to escape from the liquid, it must either be on the surface, or it must be adjacent to many other molecules that are above the boiling point so that the molecules can form a bubble and rise to the surface.

Water boils only when a sufficient number of adjacent molecules are above the boiling point and can form bubbles of gaseous water, as seen below. The process of molecules escaping from the surface of a liquid when the average temperature of the liquid is below the boiling point is called evaporation.

The phase change process is a little more complicated than just having the molecules reach the boiling point. Gaseous molecules have a force of attraction between them due to the separation between the molecules. Recall two oppositely charged objects that are separated have potential energy, and the amount of potential energy can be calculated by multiplying the force of attraction times the distance of separation. At the same temperature, the same molecules in the liquid state and the gaseous state do not have the same total energy. If they are at the same temperature, they have the same kinetic energy, but the gaseous molecules have additional potential energy that the liquid molecules do not have. As a result, molecules in the liquid state hot enough to exist in the gaseous state must absorb energy from their surroundings to gain the potential energy needed to change phase. This potential energy is called the heat of vaporization.

If a saucer of water is sitting out on the countertop, the water will slowly disappear – yet, at no time is the temperature of the water ever at the boiling point. When molecules of a liquid are evaporating, it is clear that it is the hottest molecules that are evaporating. It might seem that once the hottest molecules are gone, evaporation would no longer continue. This is not true, as the water in an open container continues to evaporate until it is all in the vapor state. When a substance is a vapor, the substance is in the gaseous phase even though the substance is at a temperature below its boiling point. Note that a substance in the gaseous phase at temperatures above the boiling point of its liquid is called a gas, not vapor. Evaporation continues because the temperature of the liquid is the average temperature of all the molecules. When the hottest molecules evaporate, the average temperature of those molecules left behind is lower, so the molecules left behind also contribute to the heat of vaporization to the evaporating molecules. The process of evaporation causes the remaining liquid to cool significantly. Heat flows from warmer objects to colder objects, so when the liquid cools due to evaporation, the surroundings will give heat to the liquid. The temperature of the liquid is raised so that it matches the temperature of the surroundings, thus producing more hot molecules. This process can continue in an open container until the liquid is all evaporated.

The rate of evaporation is related to the strength of the intermolecular forces of attraction, to the surface area of the liquid, and to the temperature of the liquid. As the temperature of a liquid gets closer to the boiling point, more of the molecules will have temperatures above the boiling point, resulting in faster evaporation. Substances with weak intermolecular forces of attraction evaporate more quickly than those with strong intermolecular forces of attraction. Substances that evaporate readily are called volatile, while those that hardly evaporate at all are called non-volatile.

### Condensation

Liquids in an open container will usually evaporate completely. What happens, however, if the container is closed? When a lid is placed over the container, the molecules that have evaporated are now kept in the space above the liquid. This makes it possible for a gaseous molecule to condense back to a liquid after colliding with another molecule or a wall, as seen in the figure below. This process where a gas or vapor is changed into a liquid is called condensation. Molecules at the boiling point can exist in either the liquid phase or gaseous phase – the only difference between them is the amount of potential energy they hold. See below figure.

For a liquid molecule with adequate temperature to exist in the gaseous phase, it needs to gain the heat of vaporization. It does this by colliding with adjacent molecules. For a gaseous molecule to return to the liquid phase, it must give up the same amount of potential energy that it gained. This amount of potential energy is called the heat of vaporization when it is being gained and the heat of condensation when it is being lost, but the amount of energy gained or lost is the same amount.

As more and more molecules evaporate in a closed container, the partial pressure of the gas in the space above the liquid increases. The rate at which the gas condenses is determined by the partial pressure of the gas, the surface area, and the substance involved. Once these factors are established, the rate of condensation will only vary depending on the partial pressure of the gas. As the partial pressure of the gas in the space above the liquid increases, the rate of condensation will increase.

It was pointed out that as a liquid evaporates, the remaining liquid cools because the hottest molecules are leaving, so the average temperature decreases and the heat of vaporization is absorbed from the remaining molecules. For similar reasons, when a gas is undergoing condensation, the temperature of the remaining gas increases because the coolest molecules are condensing, thus raising the average of those left behind. The condensing molecules must then give up the heat of condensation.

## Vapor Pressure

You can follow the progress of evaporation and condensation in a thought experiment. Suppose we place some liquid water in an Erlenmeyer flask and seal it. No water has evaporated yet, so the partial pressure of water vapor in the space above the liquid is zero. As a result, no condensation is taking place. As the water evaporates (at a constant rate since the temperature and surface area are constant), the partial pressure of the water vapor increases. Now that some vapor exists, condensation can begin. Since the partial pressure of the water vapor is low, the rate of condensation will be low. Over time, more and more water evaporates, causing the partial pressure of the water vapor to increase. Since the partial pressure has increased, the rate of condensation also increases.

Eventually, the rate of condensation will become high enough that it is equal to the rate of evaporation. Once this happens, the rate of water molecules entering the vapor phase and the rate of water molecules condensing back into liquid are exactly the same, so the partial pressure no longer increases. When the partial pressure of the water vapor becomes constant, the rate of condensation is constant and is exactly equal to the rate of evaporation. As a result, the pressure exerted by the vapor of a solid or liquid in equilibrium with the vapor is known as the equilibrium vapor pressure. As time goes on from this point, neither the amount of liquid or the amount of gas can change; consequently, neither the rate of evaporation nor the rate of condensation can change. Everything remains exactly the same, and evaporation and condensation will continue at exactly the same rate. As seen in Table below, a liquid will establish an equilibrium vapor pressure at all temperatures. The pressure of the vapor in the space above the liquid is called the vapor pressure of that liquid at that temperature.

Vapor Pressure of Water at Various Temperatures
Temperature in \begin{align*}^\circ\mathbf{C}\end{align*} Vapor Pressure in Torr
\begin{align*}4.6\end{align*}
\begin{align*}10\end{align*} \begin{align*}9.2\end{align*}
\begin{align*}20\end{align*} \begin{align*}17.5\end{align*}
\begin{align*}30\end{align*} \begin{align*}31.8\end{align*}
\begin{align*}40\end{align*} \begin{align*}55.3\end{align*}
\begin{align*}50\end{align*} \begin{align*}92.5\end{align*}
\begin{align*}60\end{align*} \begin{align*}149.4\end{align*}
\begin{align*}70\end{align*} \begin{align*}233.7\end{align*}
\begin{align*}80\end{align*} \begin{align*}355.1\end{align*}
\begin{align*}90\end{align*} \begin{align*}525.8\end{align*}
\begin{align*}100\end{align*} \begin{align*}760.0\end{align*}

Volatile liquids would have higher vapor pressures than water at the same temperature, and non-volatile liquids would have lower vapor pressures at the same temperature. The amount of volume for the space above the liquid makes no difference. If the space is small, it will take little gas to produce the pressure, and if the space is large, it will take much more gas to produce the pressure. As long as you introduce enough liquid into the container so that vapor pressure equilibrium will be reached, then the precise vapor pressure will be attained.

Note that the equilibrium vapor pressure of a liquid is the same regardless of whether or not another gas is present in the space above the liquid. If the space above liquid water contains air at \begin{align*}760 \ \mathrm{torr}\end{align*} and the liquid water evaporates until its equilibrium vapor pressure \begin{align*}(25 \ \mathrm{torr})\end{align*} is reached, then the total pressure in the space above the liquid will be\begin{align*}785 \ \mathrm{torr}\end{align*}. The presence of the air in no way affects the vapor pressure.

When gaseous substances are produced from chemical reactions and collected in the laboratory, they are usually collected over water. The “collection over water” technique is inexpensive and allows gaseous substances to be collected without having air mixed in. The process involves filling a collecting jar with water and inverting the jar in a pan of water without letting any water out or air in, as illustrated below.

In the sketch above, the picture on the far left represents the collecting jar full of water and inverted in a pan of water. A tube runs from the reaction vessel where the gas is produced and is tucked under the edge of the collecting jar. As the gas is produced and comes out the end of the tube, it bubbles up through the water and pushes the water out of the jar. When the water in the collecting jar and the pan are exactly level, as in the picture at the far right, the pressure inside the collecting jar and the atmospheric pressure in the lab are equal. Using the pressure and temperature in the lab, as well as the volume of the jar to the water level, you can calculate how much gas you produced. (Plug \begin{align*}P \ \mathrm{and} \ R\end{align*} into \begin{align*}PV=nRT\end{align*} and solve for \begin{align*}n\end{align*}). It turns out, however, that you must make a correction before you plug in the pressure value. Since the collecting jar is a closed container and it has liquid water in the bottom of it, it will contain the vapor pressure of water at this temperature. Consequently, the pressure in the lab tells you the pressure inside the collecting jar, but it doesn’t tell you how much of that pressure is due to the gas collected and how much is due to water vapor. You must get a table of the vapor pressure of water at each temperature and look up the vapor pressure of water at the temperature of your lab and then subtract that pressure from the total pressure in the collecting jar. The result will be the actual pressure of the gas collected.

Example:

Some hydrogen gas was collected over water in the lab on a day that the atmospheric pressure was \begin{align*}755 \ \mathrm{torr}\end{align*} and the lab temperature was \begin{align*}20^\circ\mathrm{C}\end{align*}. Hydrogen gas was collected in the collecting jar until the water levels inside and outside the jar was equal. What was the partial pressure of the hydrogen in the collecting jar?

Solution:

The total pressure in the collecting jar is \begin{align*}755 \ \mathrm{torr}\end{align*} and is equal to the sum of the partial pressure of hydrogen in the jar and the vapor pressure of water at \begin{align*}20^\circ\mathrm{C}\end{align*}. From the table, the vapor pressure of water at \begin{align*}20^\circ\mathrm{C}\end{align*} is \begin{align*}17.5 \ \mathrm{torr}\end{align*}.

Partial pressure of \begin{align*}\mathrm{H}_2 = 755 \ \mathrm{torr} - 17.5 \ \mathrm{torr} = 737 \ \mathrm{torr}\end{align*}

## The Boiling Point of a Liquid

Imagine you are boiling water in a place where the atmospheric pressure is \begin{align*}1.00 \ \mathrm{atm}\end{align*}. In the boiling water, a large bubble forms near the surface of the liquid. The bubble remains the same size as it rises to the top of the water, where the gas can escape into the air. If the pressure of the gas inside that bubble had been less than \begin{align*}1.00 \ \mathrm{atm}\end{align*}, the outside pressure of the atmosphere would have crushed the bubble. If the pressure of the gas inside that bubble had been greater than \begin{align*}1.00 \ \mathrm{atm}\end{align*}, the bubble would have expanded to a larger size, instead of remaining at the same size. The fact that the bubble remained at the same size indicates that the gas pressure inside that bubble was the same as the atmospheric pressure.

When you are heating water in an effort to boil it, gas bubbles cannot form until the water can produce a vapor pressure equal to the surrounding air pressure. The hotter the water gets, the higher its vapor pressure becomes. The liquid cannot boil, however, until its vapor pressure is equal to the pressure on the surface of the liquid. The boiling point is the temperature at which the vapor pressure of the liquid equals the surrounding pressure.

If you are measuring boiling points at the normal sea level atmospheric pressure of \begin{align*}1.00 \ \mathrm{atm}\end{align*}, a liquid more volatile than water such as chloroform will boil at \begin{align*}61.3^\circ\mathrm{C}\end{align*}. This is because the vapor pressure of chloroform is \begin{align*}1.00 \ \mathrm{atm}\end{align*} at \begin{align*}61.3^\circ\mathrm{C}\end{align*}. The vapor pressure of ethanol reaches \begin{align*}1.00 \ \mathrm{atm}\end{align*} at a temperature of \begin{align*}78.4^\circ\mathrm{C}\end{align*}, so this is the normal boiling point of ethanol.

Since liquids boil when their vapor pressures become equal to the surrounding pressure, if the surrounding pressure is lower, the liquids will boil at lower temperatures. At higher altitudes, atmospheric pressure is lower. In cities whose altitude is around \begin{align*}5,000 \ \mathrm{feet}\end{align*}, water boils at \begin{align*}95^\circ\mathrm{C}\end{align*} instead of at \begin{align*}100^\circ\mathrm{C}\end{align*}, and at \begin{align*}10,000 \ \mathrm{feet}\end{align*}, water boils around \begin{align*}90^\circ\mathrm{C}\end{align*}. The water boils in normal fashion, but its temperature is lower. As a result, cooking in boiling water takes a longer time at higher altitudes.

If a container of water is placed in a bell jar and a vacuum pump attached so that the air pressure around the water can be greatly reduced, water may be made to boil at very low temperatures. At room temperature, \begin{align*}20^\circ\mathrm{C}\end{align*}, the vapor pressure of water is \begin{align*}17.5 \ \mathrm{mm \ of \ Hg}\end{align*}, so if the pressure in the bell jar is reduced to \begin{align*}17.5 \ \mathrm{mm \ of \ Hg}\end{align*}, water will boil at \begin{align*}20^\circ\mathrm{C}\end{align*}. The appearance of the boiling water is the same as it is at \begin{align*}100^\circ\mathrm{C}\end{align*}, but the water can be removed from the bell jar and poured on your hand without burning.

If the surrounding pressure is less than \begin{align*}1.00 \ \mathrm{atm}\end{align*}, the boiling points of liquids will be lower. Conversely, if the surrounding pressure is greater than \begin{align*}1.00 \ \mathrm{atm}\end{align*}, the boiling points of liquids will be higher. If we use a strong container with a lid that screws on very tightly, as we boil water in the container, the gas pressure in the container will increase. As the pressure in the container increases, the boiling point of the water increases. The vapor pressure of liquid water at \begin{align*}120^\circ\mathrm{C}\end{align*} is \begin{align*}2.00 \ \mathrm{atm}\end{align*}. Therefore, if we can raise the pressure inside a sealed container to \begin{align*}2.00 \ \mathrm{atm}\end{align*}, water will not boil in the container until its temperature is \begin{align*}120^\circ\mathrm{C}\end{align*}. This is the concept that is used in pressure cookers and rice cookers. The cooking pot has a tightly sealing lid and a valve in the lid. The valve will open slightly when the pressure inside the container reaches \begin{align*}2.00 \ \mathrm{atm}\end{align*}, helping to maintain the inside pressure at \begin{align*}2.00 \ \mathrm{atm}\end{align*}. The pressure and the boiling point of water will therefore increase inside the container until the pressure reaches \begin{align*}2.00 \ \mathrm{atm}\end{align*}. The temperature of the boiling water inside will be \begin{align*}120^\circ\mathrm{C}\end{align*}. Under these conditions, any food placed inside the pressure cooker will cook in as little as one-third the normal time.

## Lesson Summary

• Molecules of liquid may evaporate from the surface of a liquid.
• When molecules of a liquid evaporate, the remaining liquid cools.
• Gas molecules in contact with their liquid may condense to liquid form.
• If a liquid is placed in a closed container, eventually vapor pressure equilibrium will be reached.
• The boiling point of a liquid is the temperature at which the vapor pressure of the liquid becomes equal to the surrounding pressure.
• The normal boiling of a liquid is the temperature at which the vapor pressure of the liquid becomes equal to \begin{align*}1.00\end{align*} atmosphere.

This video is a ChemStudy film called “Gas Pressure and Molecular Collisions.” The film is somewhat dated but the information is accurate.

## Review Questions

1. In the following groups of substances, pick the one that has the requested property and justify your answer.
1. highest boiling point: \begin{align*}\mathrm{HCl}, \mathrm{Ar}, \mathrm{F}_2\end{align*}
2. highest melting point: \begin{align*}\mathrm{H}_2\mathrm{O}, \mathrm{NaCl}, \mathrm{HF}\end{align*}
3. lowest vapor pressure at \begin{align*}20^\circ\mathrm{C}\end{align*}: \begin{align*}\mathrm{Cl}_2\end{align*},\begin{align*}\mathrm{Br}_2\end{align*}, \begin{align*}\mathrm{I}_2\end{align*}
2. A flask half-filled with water is sealed with a stopper. The space above the water contains hydrogen gas and water vapor in vapor pressure equilibrium with the liquid water. The total pressure of the two gases is \begin{align*}780. \ \mathrm{mm \ of \ Hg}\end{align*} at \begin{align*}20.^\circ\mathrm{C}\end{align*}. The vapor pressure of water at \begin{align*}20.^\circ\mathrm{C}\end{align*} is \begin{align*}19 \ \mathrm{mm \ of \ Hg}\end{align*}. What is the partial pressure of the hydrogen gas in the flask?
3. Describe all the reasons that the remaining liquid cools as evaporation occurs.
4. Describe all the reasons that the remaining gas gets hotter as condensation occurs.

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