![]() R = d / (2 2) <- one of two alternate formulationsģ) Determine the volume of the unit cell: Use the Pythagorean Theorem (see problem #1 for a discussion): Assuming that calcium has an atomic radius of 197 pm, calculate the density of solid calcium.ġ97 pm x (1 cm/10 10 pm) = 1.97 x 10¯ 8 cmĢ) Determine the edge length of the unit cell: Problem #4: Calcium has a cubic closest packed structure as a solid. (See problem 5a below for an example set of calculations.)ģ) Calculate the average mass of one atom of NiĤ) Calculate the mass of the 4 nickel atoms in the face-centered cubic unit cellĥ) Calculate the density (value from step 4 divided by value from step 2) This problem is the exact reverse of problem #2. Problem #3: Nickel has a face-centered cubic structure with an edge length of 352.4 picometers. This problem is like the one above, it just stops short of determining the atomic radius.ġ) Calculate the average mass of one atom of Ni:ĥ8.6934 g mol¯ 1 / 6.022 x 10 23 atoms mol¯ 1 = 9.746496 x 10¯ 23 g/atomĢ) Calculate the mass of the 4 nickel atoms in the face-centered cubic unit cell: If the density of the metal is 8.908 g/cm 3, what is the unit cell edge length in pm? Problem #2: Nickel crystallizes in a face-centered cubic lattice. ![]() You may be asked to do the opposite, that is, to determine d in terms of r for a fcc cell. The above discusses how to determine r in terms of d in a face-centered unit cell. ![]() Try it before looking at the solution to the next problem. You may wish to convert the cm value to picometers, the most common measurement used in reporting atomic radii. R = d / (2 2) <- an alternate formulation Here is the same view, with 'd' representing the side of the cube and '4r' representing the 4 atomic radii across the face diagonal. The square represents one face of a face-centered cube: Remember that a face-centered unit cell has an atom in the middle of each face of the cube. Calculate the atomic radius of palladium.ġ) Calculate the average mass of one atom of Pd:ġ06.42 g mol¯ 1 / 6.022 x 10 23 atoms mol¯ 1 = 1.767187 x 10¯ 22 g/atomĢ) Calculate the mass of the 4 palladium atoms in the face-centered cubic unit cell: Problem #1: Palladium crystallizes in a face-centered cubic unit cell. Other important compounds are the carbide, chloride, cyanamide, hypochlorite, nitrate, and sulfide.Face-centered cubic problems Face-centered cubic problems Solubility of the carbonate in water containing carbon dioxide is high, which causes the formation of caves with stalactites and stalagmites and is responsible for hardness in water. Calcium from limestone is an important element in Portland cement. When mixed with sand, it hardens mortar and plaster by taking up carbon dioxide from the air. Quicklime (CaO), which is made by heating limestone that is changed into slaked lime by carefully adding water, is the great base of chemical refinery with countless uses. Its natural and prepared compounds are widely used. It is also used as an alloying agent for aluminum, beryllium, copper, lead, and magnesium alloys, and serves as a "getter" for residual gases in vacuum tubes, etc. The metal is used as a reducing agent in preparing other metals such as thorium, uranium, zirconium, etc., and is used as a deoxidizer, desulfurizer, or decarburizer for various ferrous and nonferrous alloys. The metal has a silvery color, is rather hard, and is prepared by electrolysis of fused chloride and calcium fluoride (to lower the melting point).Ĭhemically it is one of the alkaline earth elements it readily forms a white coating of nitride in air, reacts with water, burns with a yellow-red flame. Apatite is the fluorophosphate or chlorophosphate of calcium. Never found in nature uncombined, it occurs abundantly as limestone, gypsum, and fluorite. It is an essential constituent of leaves, bones, teeth, and shells. SourcesĬalcium, a metallic element, is fifth in abundance in the earth's crust, of which it forms more than 3%. After learning that Berzelius and Pontin prepared calcium amalgam by electrolyzing lime in mercury, Davy was able to isolate the impure metal. Though lime was prepared by the Romans in the first century under the name calx, the metal was not discovered until 1808. The shell of the chicken egg is primarily calcium carbonate.įrom the Latin word calx, lime.
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