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11.3 Solubility  (Page 2/13)

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Other factors also affect the solubility of a given substance in a given solvent. Temperature is one such factor, with gas solubility typically decreasing as temperature increases ( [link] ). This is one of the major impacts resulting from the thermal pollution of natural bodies of water.

This graph shows solubilities of methane, oxygen, carbon monoxide, nitrogen, and helium in 10 superscript negative 3 mol L superscript negative 1 at temperatures ranging from 0 to 30 degrees Celsius. Solubilities as indicated on the graph in decreasing order are methane, oxygen, carbon monoxide, nitrogen, and helium. At ten degrees, solubilities in 10 superscript negative 3mol L superscript negative 1 are approximately as follows; methane 1.9, oxygen 1.8, carbon monoxide 1.2, nitrogen 0.7, and helium 0.4. At twenty degrees, solubilities in 10 superscript negative 3 mol L superscript negative 1 are approximately as follows; methane 1.2, oxygen 1.1, carbon monoxide 0.9, nitrogen 0.5, and helium 0.35.
The solubilities of these gases in water decrease as the temperature increases. All solubilities were measured with a constant pressure of 101.3 kPa (1 atm) of gas above the solutions.

When the temperature of a river, lake, or stream is raised abnormally high, usually due to the discharge of hot water from some industrial process, the solubility of oxygen in the water is decreased. Decreased levels of dissolved oxygen may have serious consequences for the health of the water’s ecosystems and, in severe cases, can result in large-scale fish kills ( [link] ).

Two photos are shown. The first shows the top portion of a transparent colorless glass of a clear colorless liquid with small bubbles near the interface of the liquid with the container. The second photo shows a portion of a partially frozen body of water with dead fish appearing on in the water and on an icy surface.
(a) The small bubbles of air in this glass of chilled water formed when the water warmed to room temperature and the solubility of its dissolved air decreased. (b) The decreased solubility of oxygen in natural waters subjected to thermal pollution can result in large-scale fish kills. (credit a: modification of work by Liz West; credit b: modification of work by U.S. Fish and Wildlife Service)

The solubility of a gaseous solute is also affected by the partial pressure of solute in the gas to which the solution is exposed. Gas solubility increases as the pressure of the gas increases. Carbonated beverages provide a nice illustration of this relationship. The carbonation process involves exposing the beverage to a relatively high pressure of carbon dioxide gas and then sealing the beverage container, thus saturating the beverage with CO 2 at this pressure. When the beverage container is opened, a familiar hiss is heard as the carbon dioxide gas pressure is released, and some of the dissolved carbon dioxide is typically seen leaving solution in the form of small bubbles ( [link] ). At this point, the beverage is supersaturated with carbon dioxide and, with time, the dissolved carbon dioxide concentration will decrease to its equilibrium value and the beverage will become “flat.”

A dark brown liquid is shown in a clear, colorless container. A thick layer of beige bubbles appear at the surface of the liquid. In the liquid, thirteen small clusters of single black spheres with two red spheres attached to the left and right are shown. Red spheres represent oxygen atoms and black represent carbon atoms. Seven white arrows point upward in the container from these clusters to the bubble layer at the top of the liquid.
Opening the bottle of carbonated beverage reduces the pressure of the gaseous carbon dioxide above the beverage. The solubility of CO 2 is thus lowered, and some dissolved carbon dioxide may be seen leaving the solution as small gas bubbles. (credit: modification of work by Derrick Coetzee)

For many gaseous solutes, the relation between solubility, C g , and partial pressure, P g , is a proportional one:

C g = k P g

where k is a proportionality constant that depends on the identities of the gaseous solute and solvent, and on the solution temperature. This is a mathematical statement of Henry’s law    : The quantity of an ideal gas that dissolves in a definite volume of liquid is directly proportional to the pressure of the gas.

Application of henry’s law

At 20 °C, the concentration of dissolved oxygen in water exposed to gaseous oxygen at a partial pressure of 101.3 kPa (760 torr) is 1.38 × 10 −3 mol L −1 . Use Henry’s law to determine the solubility of oxygen when its partial pressure is 20.7 kPa (155 torr), the approximate pressure of oxygen in earth’s atmosphere.

Solution

According to Henry’s law, for an ideal solution the solubility, C g , of a gas (1.38 × 10 −3 mol L −1 , in this case) is directly proportional to the pressure, P g , of the undissolved gas above the solution (101.3 kPa, or 760 torr, in this case). Because we know both C g and P g , we can rearrange this expression to solve for k .

C g = k P g k = C g P g = 1.38 × 10 −3 mol L −1 101.3 kPa = 1.36 × 10 −5 mol L −1 kPa −1 ( 1.82 × 10 −6 mol L −1 torr −1 )

Now we can use k to find the solubility at the lower pressure.

C g = k P g
1.36 × 10 −5 mol L −1 kPa −1 × 20.7 kPa ( or 1.82 × 10 −6 mol L −1 torr −1 × 155 torr ) = 2.82 × 10 −4 mol L −1

Note that various units may be used to express the quantities involved in these sorts of computations. Any combination of units that yield to the constraints of dimensional analysis are acceptable.

Check your learning

Exposing a 100.0 mL sample of water at 0 °C to an atmosphere containing a gaseous solute at 20.26 kPa (152 torr) resulted in the dissolution of 1.45 × 10 −3 g of the solute. Use Henry’s law to determine the solubility of this gaseous solute when its pressure is 101.3 kPa (760 torr).

Answer:

7.25 × 10 −3 in 100.0 mL or 0.0725 g/L

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Source:  OpenStax, Chemistry. OpenStax CNX. May 20, 2015 Download for free at http://legacy.cnx.org/content/col11760/1.9
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