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A diagram is shown. At the center of the diagram is a T-shaped structure labeled, “Anode ( positive sign ),” that is on a mesh-like background labeled, “Iron screen.” The anode is connected to a box labeled, “Voltage source,” by a line, and the voltage source is connected to one of two L-shaped structures that surround the anode. They are labeled, “Cathode ( negative sign ).” Above the cathode on the right side of the diagram is a tube connected to a collection chamber labeled, “N a metal,” that has a lower outlet labeled, “N a outlet.” Surrounding all of these components is a blue background labeled, “Molten N a C l,” and a series of tubes that form a square outside the diagram. They have an opening in the upper right corner labeled, “Inlet for N a C l.” At the top of the diagram is a large tube with an upward-facing arrow drawn on it. The tube turns right, has a right-facing arrow on it, and is labeled, “C l subscript 2 outlet.”
Pure sodium metal is isolated by electrolysis of molten sodium chloride using a Downs cell. It is not possible to isolate sodium by electrolysis of aqueous solutions of sodium salts because hydrogen ions are more easily reduced than are sodium ions; as a result, hydrogen gas forms at the cathode instead of the desired sodium metal. The high temperature required to melt NaCl means that liquid sodium metal forms.

The preparation of aluminum

The preparation of aluminum utilizes a process invented in 1886 by Charles M. Hall , who began to work on the problem while a student at Oberlin College in Ohio. Paul L. T. Héroult discovered the process independently a month or two later in France. In honor to the two inventors, this electrolysis cell is known as the Hall–Héroult cell    . The Hall–Héroult cell is an electrolysis cell for the production of aluminum. [link] illustrates the Hall–Héroult cell.

The production of aluminum begins with the purification of bauxite, the most common source of aluminum. The reaction of bauxite, AlO(OH), with hot sodium hydroxide forms soluble sodium aluminate, while clay and other impurities remain undissolved:

AlO ( OH ) ( s ) + NaOH ( a q ) + H 2 O ( l ) Na [ Al ( OH ) 4 ] ( a q )

After the removal of the impurities by filtration, the addition of acid to the aluminate leads to the reprecipitation of aluminum hydroxide:

Na [ Al ( OH ) 4 ] ( a q ) + H 3 O + ( a q ) Al ( OH ) 3 ( s ) + Na + ( a q ) + 2H 2 O ( l )

The next step is to remove the precipitated aluminum hydroxide by filtration. Heating the hydroxide produces aluminum oxide, Al 2 O 3 , which dissolves in a molten mixture of cryolite, Na 3 AlF 6 , and calcium fluoride, CaF 2 . Electrolysis of this solution takes place in a cell like that shown in [link] . Reduction of aluminum ions to the metal occurs at the cathode, while oxygen, carbon monoxide, and carbon dioxide form at the anode.

A diagram is shown. At the center of the diagram are two black squares, each labeled, “Carbon anode ( positive sign ),” and connected by forked tubes to a horizontal tube labeled with a positive sign. The carbon anodes are submerged in a green liquid labeled, “A l subscript 2 O subscript 3 dissolved in molten N a subscript 3 A l F subscript 6.” It is held in place by a three-sided, double layered container which is labeled, “Steel sheet,” on the outer layer and, “Ceramic,” on the inner layer. The carbon anodes are surrounded by bubbles labeled, “Bubbles of O subscript 2, C O, and C O subscript 2.” Below the green liquids lies a silver layer labeled, “Molten aluminum,” and a black layer labeled, “Carbon cathode ( negative sign ).” Above the diagram is an outlet tube labeled with an upward-facing arrow and the words, “H F and particulates exhaust to filter plant.”
An electrolytic cell is used for the production of aluminum. The electrolysis of a solution of cryolite and calcium fluoride results in aluminum metal at the cathode, and oxygen, carbon monoxide, and carbon dioxide at the anode.

The preparation of magnesium

Magnesium is the other metal that is isolated in large quantities by electrolysis. Seawater, which contains approximately 0.5% magnesium chloride, serves as the major source of magnesium. Addition of calcium hydroxide to seawater precipitates magnesium hydroxide. The addition of hydrochloric acid to magnesium hydroxide, followed by evaporation of the resultant aqueous solution, leaves pure magnesium chloride. The electrolysis of molten magnesium chloride forms liquid magnesium and chlorine gas:

MgCl 2 ( a q ) + Ca ( OH ) 2 ( a q ) Mg ( OH ) 2 ( s ) + CaCl 2 ( a q )
Mg ( OH ) 2 ( s ) + 2HCl ( a q ) MgCl 2 ( a q ) + 2H 2 O ( l )
MgCl 2 ( l ) Mg ( l ) + Cl 2 ( g )

Some production facilities have moved away from electrolysis completely. In the next section, we will see how the Pidgeon process leads to the chemical reduction of magnesium.

Chemical reduction

It is possible to isolate many of the representative metals by chemical reduction    using other elements as reducing agents. In general, chemical reduction is much less expensive than electrolysis, and for this reason, chemical reduction is the method of choice for the isolation of these elements. For example, it is possible to produce potassium, rubidium, and cesium by chemical reduction, as it is possible to reduce the molten chlorides of these metals with sodium metal. This may be surprising given that these metals are more reactive than sodium; however, the metals formed are more volatile than sodium and can be distilled for collection. The removal of the metal vapor leads to a shift in the equilibrium to produce more metal (see how reactions can be driven in the discussions of Le Châtelier’s principle in the chapter on fundamental equilibrium concepts).

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When MP₁ becomes negative, TP start to decline. Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
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In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
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In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
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Suppose a consumer consuming two commodities X and Y has The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50. A,Calculate quantities of x and y which maximize utility. B,Calculate value of Lagrange multiplier. C,Calculate quantities of X and Y consumed with a given price. D,alculate optimum level of output .
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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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