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Solubility Product
The term solubility product is generally applicable for sparingly soluble salts. It is the maximum product of the molar concentration of the ions (raised to their appropriate powers) which are produced due to dissociation of the compound.
At a given temperature the solubility product is constant. Lesser the value of solubility product indicates lower solubility and higher value of solubility product indicates greater solubility.
On the basis of solubility, the factors affecting solubility vary on the state of the solute:
Liquids In Liquids
Solids In Liquids
Gases In Liquids
Temperature and Solubility
Although the solubility of a solid generally increases with increasing temperature, there is no simple relationship between the structure of a substance and the temperature dependence of its solubility. Many compounds (such as glucose and CH3CO2Na) exhibit a dramatic increase in solubility with increasing temperature. Others (such as NaCl and K2SO4) exhibit little variation, and still others (such as Li2SO4) become less soluble with increasing temperature.
Solubilities of Several Inorganic and Organic Solids in Water as a Function of Temperature. Solubility may increase or decrease with temperature; the magnitude of this temperature dependence varies widely among compounds.
The variation of solubility with temperature has been measured for a wide range of compounds, and the results are published in many standard reference books. Chemists are often able to use this information to separate the components of a mixture by fractional crystallization, the separation of compounds on the basis of their solubilities in a given solvent.
For example, if we have a mixture of 150 g of sodium acetate (CH3CO2Na) and 50 g of KBr, we can separate the two compounds by dissolving the mixture in 100 g of water at 80°C and then cooling the solution slowly to 0°C.
According to the temperature curves, shown in the graph above, both compounds dissolve in water at 80°C, and all 50 g of KBr remains in solution at 0°C. Only about 36 g of CH3CO2Na are soluble in 100 g of water at 0°C, however, so approximately 114 g (150 g − 36 g) of CH3CO2Na crystallizes out on cooling. The crystals can then be separated by filtration.
Thus fractional crystallization allows us to recover about 75% of the original CH3CO2Na in essentially pure form in only one step.
Fractional crystallization is a common technique for purifying compounds . For the technique to work properly, the compound of interest must be more soluble at high temperature than at low temperature, so that lowering the temperature causes it to crystallize out of solution. In addition, the impurities must be more soluble than the compound of interest (as was KBr in this example) and preferably present in relatively small amounts.
The solubility of gases in liquids is much more predictable. The solubility of gases in liquids decreases with increasing temperature.
Attractive intermolecular interactions in the gas phase are essentially zero for most substances, because the molecules are so far apart when in the gaseous form. When a gas dissolves, it does so because its molecules interact with solvent molecules. Heat is released when these new attractive forces form.
Thus, if external heat is added to the system, it overcomes the attractive forces between the gas and the solvent molecules and decreases the solubility of the gas.
Solubilities of Several Common Gases in Water is a Function of Temperature at Partial Pressure of 1 atm. The solubilities of gases decrease with increasing temperature.
The decrease in the solubilities of gases at higher temperatures has both practical and environmental implications. The same phenomenon occurs on a much larger scale in the giant boilers used to supply hot water or steam for industrial applications, where it is called “boiler scale,” a deposit that can seriously decrease the capacity of hot water pipes.
Hard water contains dissolved Ca2+ and HCO3− (bicarbonate) ions. Calcium bicarbonate [Ca(HCO3)2] is rather soluble in water, but calcium carbonate (CaCO3) is quite insoluble. A solution of bicarbonate ions can react to form carbon dioxide, carbonate ion, and water:
2HCO3−(aq) → CO22−(aq) + H2O(l) + CO2(aq)
Heating the solution decreases the solubility of CO2, which escapes into the gas phase above the solution. In the presence of calcium ions, the carbonate ions precipitate as insoluble calcium carbonate, the major component of boiler scale.
Calcium carbonate (CaCO3) deposits in hot water pipes can significantly reduce pipe capacity. These deposits, called boiler scale, form when dissolved CO2 is driven into the gas phase at high temperatures.
In thermal pollution, lake or river water that is used to cool an industrial reactor or a power plant is returned to the environment at a higher temperature than normal. Because of the reduced solubility of O2 at higher temperatures , the warmer water contains less dissolved oxygen than the water did when it entered the plant. Fish and other aquatic organisms that need dissolved oxygen to live can literally suffocate if the oxygen concentration of their habitat is too low.
Because the warm, oxygen-depleted water is less dense, it tends to float on top of the cooler, denser, more oxygen-rich water in the lake or river, forming a barrier that prevents atmospheric oxygen from dissolving. Eventually even deep lakes can be suffocated if the problem is not corrected.
Additionally, most fish and other nonmammalian aquatic organisms are cold-blooded, which means that their body temperature is the same as the temperature of their environment. Temperatures substantially greater than the normal range can lead to severe stress or even death.
Effects of Pressure on the Solubility of Gases:
External pressure has very little effect on the solubility of liquids and solids. In contrast, the solubility of gases increases as the partial pressure of the gas above a solution increases. Because the concentration of molecules in the gas phase increases with increasing pressure, the concentration of dissolved gas molecules in the solution at equilibrium is also higher at higher pressures.
The relationship between pressure and the solubility of a gas is described quantitatively by Henry’s law,
The solubility of gases in water is described by Henry’s law which states that at a constant temperature, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas present above the surface of liquid or solution.
These can be expressed as
C = kP
where C is the concentration of dissolved gas at equilibrium, P is the partial pressure of the gas, and k is the Henry’s law constant, which must be determined experimentally for each combination of gas, solvent, and temperature. Although the gas concentration may be expressed in any convenient units, we will use molarity exclusively. The units of the Henry’s law constant are therefore mol/(L·atm) = M/atm. Values of the Henry’s law constants for solutions of several gases in water at 20°C are listed in Table below
Henry’s Law Constants for Selected Gases in Water at 20°C
The partial pressure of a gas can be expressed as concentration by writing Henry’s Law as
Pgas = C/k.
Since partial pressure and concentration are directly proportional, if the partial pressure of a gas changes while the temperature remains constant, the new concentration of the gas within the liquid can be easily calculated using the following equation:
Where C1 and P1 are the concentration and partial pressure, respectively, of the gas at the initial condition, and C2 and P2 are the concentration and partial pressure, respectively, of the gas at the final condition. For example:
Practice Problem: The concentration of CO2 in a solution is 0.032 M at 3.0 atm. What is the concentration of CO2 at 5.0 atm of pressure?
Solution: To address this problem, first we must identify what we want to find. This is the concentration of CO2 at 5.0 atm of pressure. These two values represent C2 = ?? and P2 = 5.0 atm. At this point it will be easiest to rearrange our equation above to solve for C2. Next we need to identify the starting conditions, C1 = 0.032 M and P1 = 3.0 atm. Then we can plug that values into the equation and solve for C2 :
Gases that react chemically with water, such as HCl and the other hydrogen halides, H2S, and NH3, do not obey Henry’s law; all of these gases are much more soluble than predicted by Henry’s law. For example, HCl reacts with water to give H+(aq) and Cl−(aq), not dissolved HCl molecules, and its dissociation into ions results in a much higher solubility than expected for a neutral molecule. Overall, gases that react with water do not obey Henry’s Law.