User:Karlhahn/KarlsSandbox

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Vapor over liquid tables for Ammonia (data page) are now published to main namespace (5-Oct-2006)

Programmer's Guide to Hebrew Calender published in Hebrew calendar on 6-Oct-2006.

Rewrite on "Solubility of calcium carbonate in water" from Calcium carbonate published to that article on 11-Oct-2006.

New sections published to surface tension on 12-Oct-2006.

Translated data (from German page) published to water (data page) on 14-Oct-2006

Added sections lead#Descriptive chemistry and lead#Processing of metal from ore on 10-Dec-2006.

Working on Surface tension (supplement).

Link to archived sandbox material.

Contents 1 Descriptive chemistry (lead) 2 Water Strider Physics 3 Liquid in a Cylindrical Tube 4 Pool of Liquid on a Nonadhesive Surface 5 Rewrite Project 5.1 Original version 5.2 Current state of rewritten version 6 Future Project: Tide Prediction 7 Notes

[edit] Descriptive chemistry (lead)

Various oxidized forms of lead are easily reduced to the metal. An example is heating PbO with mild organic reducing agents such as glucose. A mixuture of the oxide and the sulfide heated together without any reducing agent will also form the metal.^[1]

2PbO + PbS   →   3 Pb + SO₂

Metallic lead is attacked only superficially by air, forming a thin layer of oxide that protects it from further oxidation. The metal is not attacked by sulfuric or hydrochloric acids. It does, however, dissovle in nitric acid with the evolution of nitric oxide gas to form dissolved Pb(NO₃)₂.

3 Pb + 8 H⁺ + 8 NO₃^–   →   3 Pb²⁺ + 6 NO₃^– + 2 NO + 4H₂O

When heated with nitrates of alkali metals, metallic lead oxidizes to form PbO (also known as litharge), leaving the corresponding alkali nitrite. PbO is representative of lead's II oxidation state. It is soluble in nitric and acetic acids, from which solutions it is possible to preciptate halide, sulfate, and basic carbonate salts of lead. The sulfide can also be precipitated from acetate solutions. These salts are all poorly soluble in water. Among the halides, the iodide is less soluble than the bromide, which, in turn, is less soluble than the chloride.^[2]

The II oxide is also soluble in alkali hydroxide solutions to form the corresponding plumbite salt.^[1]

PbO + 2OH^– + H₂O   →   Pb(OH)₄^2–

Chlorination of plumbite solutions causes the formation of lead's IV oxidation state. Lead dioxide is representative of the IV state, and is a powerful oxidizing agent. The chloride of this oxidation state is formed only with difficulty and decomposes readily into the II chloride and chlorine gas. The bromide and iodide of IV lead are not known to exist.^[2] Lead dioxide dissolves in alkali hydroxide solutions to form the corresponding plumbates.^[1]

PbO₂ + 2 OH^– + 2 H₂O   →   Pb(OH)₆^2–

[edit] Water Strider Physics

The photograph shows water striders standing on the surface of a pond. It is clearly visible that their feet cause indentations in the water's surface. It is intuitively evident that the surface with indentations has more surface area than a flat surface. If surface tension tends to minimize surface area, how is it that the water striders are increasing the surface area?

Recall that what nature really tries to minimize is potential energy. By increasing the surface area of the water, the water striders have increased the potential energy of that surface. But note also that the water striders' center of mass is lower than it would be if they were standing on a flat surface. So their potential energy is decreased. Indeed when you combine the two effects, the net potential energy is minimized. If the water striders depressed the surface any more, the increased surface energy would more than cancel the reduction in the decreased energy of lowering the insects' center of mass. If they depressed the surface any less, their higher center of mass would more than cancel the reduction in surface energy.

The photo of the water striders also illustrates the notion of surface tension being like having an elastic film over the surface of the liquid. In the surface depressions at their feet it is easy to see that the reaction of that imagined elastic film is exactly countering the weight of the insects.

[edit] Liquid in a Cylindrical Tube

An old style mercury barometer consists of a vertical glass tube about 1 cm in diameter partially filled with mercury, and with a vacuum in the unfilled volume (see diagram to the left). Notice that the mercury level at the center of the tube is higher than at the at the edges, making the upper surface of the mercury dome-shaped. The center of mass of the entire column of mercury would be slightly lower if the top surface of the mercury were flat over the entire crossection of the tube. But the dome-shaped top gives slightly less surface area to the entire mass of mercury. Again the two effects combine to minimize the total potential energy. Such a surface shape is known as a convex meniscus.

The reason we consider the surface area of the entire mass of mercury, including the part of the surface that is in contact with the glass is because mercury does not adhere at all to glass. So the surface tension of the mercury acts over its entire surface area, including where it is in contact with the glass. If instead of glass, the tube were made out of copper, the situation would be very different. Mercury aggressively adheres to copper. So in a copper tube, the level of mercury at the center of the tube will be lower rather than higher than at the edges (that is, it would be a concave meniscus). In a situation where the liquid adheres to the walls of its container, we consider the part of the fluid's surface area that is in contact with the container to have negative surface tension. The fluid then works to maximize the contact surface area. So in this case increasing the area in contact with the container decreases rather than increases the potential energy. That decrease is enough compensate for the increase potential energy associated with the lifting of the fluid near the walls of the container.

[edit] Pool of Liquid on a Nonadhesive Surface

Pouring mercury onto a horizontal flat sheet of glass results in a puddle that has a perceptible thickness (do not try this except under a fume hood. Mercury vapor is a toxic hazard). The puddle will only spread out only to the point where it is a little under a centimeter thick, and no thinner. Again this is the action of mercury's strong surface tension. The liquid mass flattens out because that brings as much of the mercury to as low a level as possible. But the surface tension, at the same time, is acting to reduce the total surface area. The result is the compromise of a puddle of a nearly fixed thickness.

The same surface tension demonstration can be done with water, but only on a surface made of a substance that the water does not adhere to. Candle wax is such a substance. Water poured onto a smooth, flat, horizontal wax surface will behave similarly to the mercury poured onto glass.

[edit] Rewrite Project

for calcium carbonate water solubility section:

[edit] Original version

Calcium carbonate is not rigorously insoluble in water. For the following equilibrium reaction

• CaC0₃(solid) ↔ Ca²⁺ + CO₃²⁻, we take a solubility product at 25°C (K_sp=3.8 x 10⁻⁹ is given in ^[3]

Considering a saturated pure CaCO₃ solution, the calculation of the Ca²⁺ concentration must take into account the equilibria between the three different carbonate forms (H₂CO₃, HCO₃⁻ and CO₃²⁻) as well as the equilibrium between H₂CO₃ and the dissolved CO₂ and the equilibrium between the dissolved CO₂ and the gaseous CO₂ above the solution. The reactions involved are the following (see carbonic acid):

• CO₂(gas) ↔ CO₂(dissolved) with where k'_c=29.76 atm/(mol/L) at 25°C (Henry constant), being the CO₂ partial pressure.

• CO₂(dissolved) + H₂O ↔ H₂CO₃ with at 25°C

• H₂CO₃ ↔ H⁺ + HCO₃⁻ with at 25°C

• HCO₃⁻ ↔ H⁺ + CO₃²⁻ with at 25°C

The above relations (together with the relation and the neutrality condition , i.e. 7 equations for 7 unknowns) allow the numerical calculation of the pH and of the Ca²⁺ concentration as a function of . The result is given in the table below:

(atm)	pH	[Ca2+] (mol/L)
10−12	12.0	5.19 x 10−3
10−10	11.3	1.12 x 10−3
10−8	10.7	2.55 x 10−4
10−6	9.83	1.20 x 10−4
10−4	8.62	3.16 x 10−4
3.5 x 10−4	8.27	4.70 x 10−4
10−3	7.96	6.62 x 10−4
10−2	7.30	1.42 x 10−3
10−1	6.63	3.05 x 10−3
1	5.96	6.58 x 10−3
10	5.30	1.42 x 10−2

We see that for normal atmospheric conditions ( atm), we get a slightly basic solution (pH = 8.3) with a low Ca²⁺ concentration (4.7 x 10⁻⁴ mol/L i.e. 0.019 g/L of Ca). Increasing the CO₂ pressure makes the solution slightly acid with a better Ca solubility (0.57 g/L of Ca at 10 atm). For decreasing CO₂ pressure values, the solubility goes to a minimum for atm and then increases again as the solution gets strongly basic.

Remark: For > 10⁻⁴ atm, CO₃²⁻, H⁺ and OH⁻ concentrations can be neglected in the neutrality condition. This means physically that we have essentially a calcium bicarbonate solution. In this case, the system can be solved analytically, giving (with a very good precision)

[edit] Current state of rewritten version

Calcium carbonate is poorly soluble in water. The equilibrium of its solution is given by the equation (with dissolved calcium carbonate on the right):

CaCO3 ⇋ Ca2+ + CO32–

Ksp = 3.7×10–9 to 8.7×10–9 at 25 °C

where the solubility product for [Ca²⁺][CO₃^2–] is given as anywhere from K_sp = 3.7×10^–9 to K_sp = 8.7×10^–9 at 25 °C, depending upon the data source.^[4][5] What the equation means is that the product of number of moles of dissolved Ca²⁺ with the number of moles of dissolved CO₃^2– cannot exceed the value of K_sp. This seemingly simple solubility equation, however, must be taken along with the more complicated equilibrium of carbon dioxide with water. Some of the CO₃^2– combines with H⁺ in the solution according to:

HCO3– ⇋ H+ + CO32–

Ka2 = 5.61×10–11 at 25 °C

HCO₃^– is known as the bicarbonate ion. Calcium bicarbonate is many times more soluble in water than calcium carbonate -- indeed it exists only in solution.

Some of the HCO₃^– combines with H⁺ in solution according to:

H2CO3 ⇋ H+ + HCO3–

Ka1 = 2.5×10–4 at 25 °C

Some of the H₂CO₃ breaks up into water and dissolved carbon dioxide according to:

H2O + CO2(dissolved) ⇋ H2CO3

Kh = 1.70×10–3 at 25 °C

And dissolved carbon dioxide is in equilibrium with atmospheric carbon dioxide according to:

where k'c = 29.76 atm/(mol/L) at 25°C (Henry constant), being the CO2 partial pressure.

Calcium Ion Solubility as a function of CO2 partial pressure
(atm)	pH	[Ca2+] (mol/L)
10−12	12.0	5.19 × 10−3
10−10	11.3	1.12 × 10−3
10−8	10.7	2.55 × 10−4
10−6	9.83	1.20 × 10−4
10−4	8.62	3.16 × 10−4
3.5 × 10−4	8.27	4.70 × 10−4
10−3	7.96	6.62 × 10−4
10−2	7.30	1.42 × 10−3
10−1	6.63	3.05 × 10−3
1	5.96	6.58 × 10−3
10	5.30	1.42 × 10−2

For ambient air, is around 3.5×10^–4 atmospheres (or equivalently 35 Pa). The last equation above fixes the concentration of dissolved CO₂ as a function of , independent of the concentration of dissolved CaCO₃. At atmospheric partial pressure of CO₂, dissolved CO₂ concentration is 1.2×10^–5 moles/liter. The equation before that fixes the concentration of H₂CO₃ as a function of [CO₂]. For [CO₂]=1.2×10^–5, it results in [H₂CO₃]=2.0×10^–8 moles per liter. When [H₂CO₃] is known, the remaining three equations together with

H2O ⇋ H+ + OH–

K = 10–14 at 25 °C

(which is true for all aqueous solutions), and the fact that the solution must be electrically neutral,

2[Ca²⁺] + [H⁺] = [HCO₃^–] + 2[CO₃^2–] + [OH^–]

make it possible to solve simultaneously for the remaining five unknown concentrations. The table on the right shows the solution for [Ca²⁺] and [H⁺] (in the form of pH) as a function of ambient partial pressure of CO₂. At atmopheric levels of ambient CO₂ the table indicates the solution will be slightly alkaline. The trends the table shows are

1) As ambient CO₂ partial pressure is reduced below atmospheric levels, the solution becomes more and more alkaline. At extremly low , dissolved CO₂, bicarbonate ion, and carbonate ion largely evaporate from the solution, leaving a highly alkaline solution of calcium hydroxide, which is more soluble than CaCO₃.

2) As ambient CO₂ partial pressure increases to levels above atmospheric, pH drops, and much of the carbonate ion is converted to bicarbonate ion, which results in higher solubility of Ca²⁺.

The effect of the latter is especially evident in day to day life of people who have hard water. Water in aquifers underground can be exposed to levels of CO₂ much higher than atmospheric. As such water perculates through calcium carbonate rock, the CaCO₃ dissolves according to the second trend. When that same water then water emerges from the tap, in time it comes into equilibrium with CO₂ levels in the air by outgassing its excess CO₂. The calcium carbonate becomes less soluble as a result and the excess precipitates as lime scale. This same process is responsible for the formation of stalactites and stalagmites in limestone caves.

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[edit] Future Project: Tide Prediction

Plan to explain the method of harmonic constituents as detailed in U.S. Govt. Special Publication 92.

[edit] Notes

1. ^ ^{a b c} Pauling, Linus General Chemistry, W.H. Freeman 1947 ed.
2. ^ ^{a b} Brady, James E. and Holum, John R. Descriptive Chemistry of the Elements John Wiley and Sons
3. ^ CSUDH
4. ^ CSUDH
5. ^ CRC Handbook of Chemistry and Physics, 44th ed.