| Solubility The definition of solubility is the maximum quantity of solute that can dissolve in a certain quantity of solvent or quantity of solution at a specified temperature or pressure (in the case of gaseous solutes). In CHM1045 we discussed solubility as a yes or no quality. But the reality is that almost every solute is somewhat soluble in every solvent to some measurable degree. As stated in the definition, temperature and pressure play an important role in determining the degree to which a solute is soluble. Let's start with temperature: For Gases, solubility decreases as temperature increases (duh...you have seen water boil, right?) The physical reason for this is that when most gases dissolve in solution, the process is exothermic. This means that heat is released as the gas dissolves. This is very similar to the reason that vapor pressure increases with temperature. Increased temperature causes an increase in kinetic energy. The higher kinetic energy causes more motion in the gas molecules which break intermolecular bonds and escape from solution. Check out the graph below:  As the temperature increases, the solubility of a gas decreases as shown by the downward trend in the graph. For solid or liquid solutes: CASE I: Decrease in solubility with temperature: If the heat given off in the dissolving process is greater than the heat required to break apart the solid, the net dissolving reaction is exothermic (See the solution process). The addition of more heat (increases temperature) inhibits the dissolving reaction since excess heat is already being produced by the reaction. This situation is not very common where an increase in temperature produces a decrease in solubility. But is the case for sodium sulfate and calcium hydroxide. CASE II: Increase in solubility with temperature: If the heat given off in the dissolving reaction is less than the heat required to break apart the solid, the net dissolving reaction is endothermic. The addition of more heat facilitates the dissolving reaction by providing energy to break bonds in the solid. This is the most common situation where an increase in temperature produces an increase in solubility for solids. The use of first-aid instant cold packs is an application of this solubility principle. A salt such as ammonium nitrate is dissolved in water after a sharp blow breaks the containers for each. The dissolving reaction is endothermic - requires heat. Therefore the heat is drawn from the surroundings, the pack feels cold. The effect of temperature on solubility can be explained on the basis of Le Chatelier's Principle. Le Chatelier's Principle states that if a stress (for example, heat, pressure, concentration of one reactant) is applied to an equilibrium, the system will adjust, if possible, to minimize the effect of the stress. This principle is of value in predicting how much a system will respond to a change in external conditions. Consider the case where the solubility process is endothermic (heat added). An increase in temperature puts a stress on the equilibrium condition and causes it to shift to the right. The stress is relieved because the dissolving process consumes some of the heat. Therefore, the solubility (concentration) increases with an increase in temperature. If the process is exothermic (heat given off). A temperature rise will decrease the solubility by shifting the equilibrium to the left. Now let's look at pressure: Solids and liquids show almost no change in solubility with changes in pressure. But gases are very dependent on the pressure of the system. Gases dissolve in liquids to form solutions. This dissolution is an equilibrium process for which an equilibrium constant can be written. For example, the equilibrium between oxygen gas and dissolved oxygen in water is O2(aq) <=> O2(g). The equilibrium constant for this equilibrium is K = p(O2)/c(O2). The form of the equilibrium constant shows that the concentration of a solute gas in a solution is directly proportional to the partial pressure of that gas above the solution. This statement, known as Henry's law, was first proposed in 1800 by J.W. Henry as an empirical law well before the development of our modern ideas of chemical equilibrium. Henry's Law: Sg stands for the gas solubility, kH is the Henry's Law constant and Pg is the partial pressure of the gaseous solute. Table: Molar Henry's Law Constants for Aqueous Solutions at 25oC
The inverse of the Henry's law constant, multiplied by the partial pressure of the gas above the solution, is the molar solubility of the gas. Thus oxygen at one atmosphere would have a molar solubility of (1/756.7)mol/dm3 or 1.32 mmol/dm3. Values in this table are calculated from tables of molar thermodynamic properties of pure substances and aqueous solutes
Summary of Factors Affecting Solubility Normally, solutes become more soluble in a given solvent at higher temperatures. One way to predict that trend is to use Le Chatelier's principle. Because DHsoln is positive for most solutions, the solution formation reaction is usually endothermic. Therefore, when the temperature is increased, the solubility of the solute should also increase. However, there are solutes that do not follow the normal trend of increasing solubility with increasing temperature. One class of solutes that becomes less soluble with increasing temperature is the gasses. Nearly every gas becomes less soluble with increasing temperature. Another property of gaseous solutes in summarized by Henry's law which predicts that gasses become more soluble when their pressures above a liquid solution are increased. That property of gaseous solutes can be rationalized by using Le Chatelier's principle. Imagine that you have a glass of water inside of a sealed container filler with nitrogen gas. If the size of that container were suddenly halved, the pressure of nitrogen would suddenly double. To decrease the pressure of nitrogen above the solution (as is required by Le Chatelier's principle), more nitrogen gas becomes dissolved in the glass of water. In this section we will look at how the pressure and temperature effect solubility. When we look at pressure effects, we are considering the pressure of a gas over a liquid, and so the solute is necessarily a gas, and we will introduce Henry's law to describe this. When we look at the temperature effect, the solute can be a solid or a gas, and the temperature effects can often be very different. We will introduce solubility curves to describe the temperature effects, noting that gas solubilities go down as temperature goes up, but solid solubilities usually, but not always increase upon heating.
When a gas phase molecule hits the surface of a liquid it may be deflected back into the gas or dissolved into the solution, in the latter case becoming a solute particle. If a dissolved molecule reaches the surface of the liquid, a fraction will have enough kinetic energy to escape, and so particles are being exchanged across the liquid/gas boundary all the time. When the rate at which the gas phase particles enter and leave are equal you have a dynamic equilibrium, where the concentration in each phase becomes a constant value. The solubility is a measure of the concentration of the dissolved gas particles in the liquid and is a function of the gas pressure. As you increase the pressure of a gas, the collision frequency increases and thus the solubility goes up, as you decrease the pressure, the solubility goes down.. Figure \(\PageIndex{1}\): This figure shows how the solubility of a gas can be understood as a dynamic process where gaseous particles are transitioning across the boundary between the two phases. Figure 13.3.1 shows a system at equilibrium (a) where the rate across the suface/vapor boundary is constant (red arrows equal black arrows). In (b) the pressure is increased (by decreasing the volume). This increases the concentration in the vapor phase, and so the collision frequency with the liquid increases, causing more to be dissolved. As the concentration in the liquid increases the rate of escape equals, and the concentration rises until the rate of escape equals the rate at which they are entering the liquid, when a new equilbrium occurs (c).
Exercise \(\PageIndex{1}\) What would be the effect if the gas in figure 13.3.1 was reduced in pressure? AnswerThe solubility would decrease because there would be less molecules hitting the surface. The relationship between the solubility of a gas and its pressure is a linear one, and can be described by Henry's law. Video \(\PageIndex{1}\): 0:27 professional animation uploaded by kwesiamoa showing how the solubility of a gas is a function of pressure
Henry's law states that the concentration of a gaseous solute in a liquid is proportional to the absolute pressure. This explains commonly observed phenomena like the degassing of a can of carbonated beverage upon opening. While sealed, there was no room for gas to expand and so the pressure would be high, resulting in a high dissolved concentration. This system was at equilibrium, but once it was opened, the gas pressure dropped and created a state of disequilibrium, with the gas leaving the fluid far mor rapidly than it was entering. Overtime, the system reached a new equilibrium, and the carbonated beverage became "flat".
\[\underbrace{C=kP}_{\text{ Henry's Law }}\] In the above equation, C= concentration, k= Henry's Law constant and P is the partial pressure of the gas that dissolves. Henry's law describes the solubility of a specific gas in a specific solvent and is a strong function of the temperature. So a table of Henry's law constants for various gasses must define the solvent and the temperature for which they apply, and care must be taken that these are the same when comparing constants from different sources. The point is that there is no such thing as Henry's law constant for carbon dioxide, there is one for carbon dioxide at 25oC in water, another in ethanol and another in benzene... It should be noted that there are many units for concentration and so "C" may mean different things (Molality, Molarity, ppm,...), and of course there are many units for pressure (atm, torr, bar,...), which students often find this confusing. Probably the best way to write out Henry's law is to look at the units of the constant. So for: k(CO2) in water at 20oC = 0.034 \(\frac{mol}{kg\cdot bar}\), I would use, m=kP, where m=molality, for k(CO2) in water at 25oC = 3.92x10-2 \(\frac{mol}{L\cdot atm}\), I would use M=kP, where M=molarity. (The important thing is to always look at the units of k)
Exercise \(\PageIndex{1}\) What is Henry's Law constant if the solubility of oxygen is 40mg/L water at 1 bar. Express in the given units, and convert to \(\frac{mol}{L\cdot atm}\) Answer\(C=kP\; k=\frac{C}{P}\;=\frac{40mg\, O_{2}}{L\cdot bar}\). To convert to \(\frac{mol}{L\cdot atm}\): \(\frac{40mg\, O_{2}}{L\cdot bar}\left ( \frac{g\, O_{2}}{10^{3}\, mg\, O_{2}} \right )\left ( \frac{molO_{2}}{32g} \right )\left ( \frac{bar}{0.987atm} \right )=1.27x10^{-3}\frac{mol}{l\cdot atm}\)
Even without knowing Henry's Law constant, if you know the solubility at one pressure, you can determine it at another. \[C_1=kP_1 \\ \; \\ \text{dividing both sides by the concentration at a different pressure} \\ \; \\\frac{C_{1}}{C_{2}}=\frac{kP_{1}}{C_{2}} \\ \; \\ substituting \;\; C_2=kP_2 \\ \; \\ \frac{C_{1}}{C_{2}}=\frac{\cancel{k}P_{1}}{\cancel{k}P_{2}}=\frac{P_{1}}{P_{2}}\\ C_{2}=C_{1}\frac{P_{2}}{P_{1}}\] Where the subscripts 1 indicates the concentration at one pressure and the subscript 2 indicates the concentration at a different pressure
Exercise \(\PageIndex{2}\) If the solubility of carbon dioxide is 1.45g/L at 25oC and 100 kPa, what is it at 50 kPa? And give answer in units of Molarity. Ok, if you think about it, you halved the pressure, so you are going to halve the concentration and it will be 0.725g/L. This is the same as asking what is the volume of 10 grams of a solid of constant density if 20 grams is 10mL. We simply take the two state approach for Henry's Law. \[\frac{C_{1}}{C_{2}}=\frac{kP_{1}}{kP_{2}}=\frac{P_{1}}{P_{2}}\\ C_{2}=C_{1}\frac{P_{2}}{P_{1}}\\ =1.45(\frac{g}{L})\frac{50kPa}{100kPa}\\ =0.725\frac{g}{L} \nonumber\] In units of molarity \[M=0.725\frac{g}{L} \left ( \frac{molCO_{2}}{44.01g} \right )=0.0165M \; CO_{2} \nonumber\] or 16.5mM CO2
The temperature effect depends on the nature of the solute and the solvent, and their interactions. These are completely different between solid solutes and gaseous ones. The propensity of a solid is to become more soluble as temperature goes up, and for a gas to become less soluble. We will revisit this in chapter 18 when we cover entropy and the second law of thermodynamics, which essentially says that a process goes in the direction that increases the entropy of the universe, that is, how dispersed the universe is. Spontaneous process tend to occur when reactions are exothermic and particles become more dispersed, but sometimes solvation can get real tricky, as dissolving an ion can induce order in the solvent, as when ion-dipole interactions cause the polar molecules to align around the ions. The "Rule of Thumb" is that with increasing temperature gas solubility goes down solid solubility goes up, but there are cases where this is not true.
In chapter 11 we saw that increasing the temperature increased the vapor pressure above the surface of a pure volatile liquid. This was because more molecules had enough kinetic energy to escape the liquid and enter the vapor phase (figure 11.6.5) . In that chapter we were talking about a pure substance, but if a solution with a gas dissolved in it is heated, it too gains kinetic energy, increases the fraction of collisions at the surface that have enough energy to escape the surfaces forces of the solution, and so the concentration of those remaining dissolved goes down. Figure 13.3.2 shows how the solubility of a gas in water goes down as the temperature is raised. This decrease in the solubility of oxygen as temperature goes up is one of the reasons cold water fish like trout can not live in warm water. Figure \(\PageIndex{2}\): Solubility of several gasses in water
Figure 13.3.3 shows the solubility of many ionic and covalent compounds in water. There are a wide range of dependencies on the temperature and although most compounds increase their solubility as heated, some actually show a decrease. We will revisit this material when we get to chapter 18 and cover entropy and Gibb's free energy. Figure \(\PageIndex{3}\): Solubility of various covalent and ionic solids in water Some of the molecules in the gas phase condense when they contact the liquid and some in the liquid evaporate into the gas. Thus the molecules can be considered to be partioned across both phases, with some in the liquid and some in the gas phase. For a system at equilibrium the rate they enter the gas phase equals the rate at which they enter the liquid, and so the concentration in both phases is constant.
Robert E. Belford (University of Arkansas Little Rock; Department of Chemistry). The breadth, depth and veracity of this work is the responsibility of Robert E. Belford, . You should contact him if you have any concerns. This material has both original contributions, and content built upon prior contributions of the LibreTexts Community and other resources, including but not limited to: |
What states that the solubility of a gas in a liquid is proportional to the pressure of the gas over the solution a entropy B Henrys Law C dissolution D Vapor pressure?
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