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weight. (For further development of this matter, vid. Density of Compounds.)

Atomic weight of Compounds. The two laws above laid down (page 41) apply to compounds as well as to simple substances. If one compound substance A is capable of com. bining with another compound substance B in different proportions, the smallest quantity of B with which A can combine, multiplied by 1, 2, 3, 4 .... gives the other quantities of B which can enter into combination with A. Thus, 47.2 parts of potash are united in carbonate of potash with 22, and in bicarbonate with 44 parts of carbonic acid:111.8 oxide (of lead can combine with 9, 18, 27 and 54 parts of nitric acid. The second law is also applicable : from the proportions in which one compound substance combines with two others may likewise be determined the proportion according to which these two combine with one another. Hydrate of magnesia contains 20-7 magnesia and 9 water; sulphate of magnesia, 20-7 magnesia and 40 sulphuric acid: and accordingly 9 water and 40 sulphuric acid are exactly the proportions of these two bodies contained in oil of vitriol. In this manner the atomic weights or equivalents of compound bodies may be determined quite independently of those of simple substances. For example, we might assume the atom of sulphuric acid 1000, and then determine that of water = 225, of magnesia 517.5, and oxide of lead 2795, these being the quantities of these several substances, which combine with 1000 parts of sulphuric acid: moreover, since these quantities of the several bases saturate 1350 nitric acid, this number 1350 would, on the same hypothesis, express the atomic weight of nitric acid. Numbers so determined would not, however, be in accordance with those of the simple substances obtained on the supposition of hydrogen = 1 or oxygen = 100.

The atomic weight of any compound is equal to the sum of the atomic weights of the simple substances which compose it. This is in exact accordance with the atomic theory; for the atom of a compound must weigh as much as the individual atoms of the simple substances composing it taken together. 1 At. hydrogen = 1 and 1 At. oxygen = 8 form 1 At. water = 1 + 8 = 9; 1 At. lead = 103.8 and 1 At. oxygen = 8 form 1 At. oxide of lead = 111:8; 1 At. sulphur = 16 and 3 At. oxygen = 24 form 1 At. sulphuric acid = 16 + 24 = 40. Hence 111.8 parts of oxide of lead combine with exactly 40 parts of sulphuric acid, because this is the proportion in which 1 At. oxide of lead combines with 1 At. sulphuric acid. If 111.8 parts of oxide of lead be heated to redness with an excess of aqueous sulphuric acid, that part of the acid not taken up by the oxide of lead evaporates together with the water, and there remain exactly 151.8 parts of sulphate of lead, containing 111.8 oxide of lead and 40 sulphuric acid. When galena, a compound of 1 At. lead with 1 At. sulphur is digested with nitric acid, which gives to the lead and the sulphur the quantities of oxygen required for converting them respectively into oxide of lead and sulphuric acid, and the liquid is evaporated to dryness, there remains the same compound of 111.8 oxide of lead and 40 sulphuric acid, so that no excess of sulphuric acid can be removed by water or of oxide of lead by acetic acid, because 1 At. lead by combining with oxygen forms exactly 1 At. oxide of lead, and 1 At. sulphur by combining with oxygen forms exactly 1 At. sulphuric acid, and moreover oxide of lead and sulphuric acid combine precisely in the proportion of 1 atom to 1 atom. It is a necessary concomitant of this law,

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that when the proximate elements of such compounds of the second order, sulphate of lead for example, contain a common ultimate element, as oxygen in this case, the quantities of this ultimate element contained in the two proximate elements must bear a simple relation to each other: e.g., the quantity of oxygen in sulphuric acid is exactly 3 times as great as that in the oxide of lead combined with it.

Chemical Formulæ. A chemical formula is an expression by symbols and numbers of the composition of a definite chemical compound according to its elements and their relative quantities. The symbols are the initial letters of the names of the elementary substances given in the table, page 50, column B. Certain compounds, particularly of the organic class, have likewise particular symbols appropriated to them: e. 9., Water = Aq; Cyanogen = Cy; Tartaric acid = T; Citric acid = C; Acetic acid = Ā; Quinine

Ch; Morphia M, &c. The numbers annexed to the symbols denote the numbers of atoms of the several constituents existing in the compound; a symbol with no number annexed to it implies that one atom only of the corresponding substance exists in the compound. Electropositive substances, such as metals and salifiable bases, precede electronegative substances, such as oxygen and acids in the forinulæ. This order is the reverse of that adopted in the nomenclature, but it would perhaps be better in this as well as in the formulæ to give precedence to the electro-positive element. When a compound contains proximate and ultimate elements, the mode of combination is expressed by means of points, commas, + signs, and brackets. Oxygen, which occurs so frequently in compounds, is often expressed by points placed over the symbol of the body with which it is in combination, the number of these points being equal to the number of atoms of oxygen present. In a similar manner, strokes leaning from right to left are used to denote atoms of sulphur, and points under the symbol of the other body, atoms of hydrogen.

Oxide of lead is PbO = Pb; potash (1 At. potassium and 1 At. oxygen) is KO = K; water is HO H; alumina (2 At. aluminum and 3 At. oxygen) is Al? Oʻ = Al; carbonic acid is CO2 = C; silica is Si 0 = Ši; sulphuric acid is 90=S; nitric acid is NOS = N; ammonia is NH' = N; sulphate of lead is PbO + S0 = PbO, SO = Pb S; bicarbonate of potash (1 At. potash, 2 At. carbonic acid, and 1 At. water) is KO + 2CO2 + HO = KO, CO’, HO = KC H; crystallized sulphate of amnionia (1 At. ammonia, 1 At. sulphuric acid, and 2 At. water) is NH? + SO3 + 2H0 = NH, SO, 2H0, = NS Hʼ; crystallized potash alum (1 At. potash, 1 At. alumina, 4 At. sulphuric acid, and 24 At. water) is (KO + S0%) + (AlO3 + 380) + (24 HO) = KO, SO3 + Al 03, 350 + 24 HO = KS, ALS', H"; sulphuret of potassium (1 At. potassium and 1 At. sulphur) is KS = K; tersulphuret of molybdenum is MOS = Mo; the combination of these two metallic sulphurets in cqual numlar

of atoms is KS + MoS = KS, MOS? = KMo. A number placed on the right and at the upper part of a symbol denotes merely the number of atoms of the substance denoted by the symbol: e.g., SO' must be understood to denote 3 atonis of oxygen and only 1 of sulphur; when oxygen is expressed by points, the number placed on the right refers to the whole compound containing the oxygen; thus in bicarbonate of potash KCH we must understand 2 At. CO’, not merely 2 At. C. On the other hand, a number placed before several symbols multiplies them all as far as the next + sign or comma, or if the number stands before a bracket, it multiplies all the symbols and numbers included within the brackets: thus 6PbO + NOS or 6PbO, NOS means a combination of 6 At. oxide of lead with 1 At. nitric acid; and KCl + 4 HgCl + 4H0, or KCI, 4HgCl + 4HO, the combination of 1 At. chloride of potassium with 4 At. chloride of mercury and 4 At. water. Many chemists write the number or index on the right below, instead of the right above the symbols (thus, SO, for sulphuric acid), because, in algebraical formulæ, a number on the right above expresses a power: but there is no risk of confusion between algebraical and chemical formulæ, and the number when written above is more easily read than when placed below.

Stoichiometrical Calculation. The greater the number of atoms of any substance in a given compound, and the greater the weight of those atoms, the greater will be the quantity of that substance in the compound. Hence the quantity (M) of the constituents in a given quantity of the compound (in 100 parts for example) is determined by multiplying the number of atoms (Ž) of each constituent by the atomic weight (G). Hence we have the three following formula:

M

M
;
z

G The first formula comes into use in determining the quantities of the several constituents contained in a given quantity of any compound. The process consists in multiplying the atomic weight of each constituent by the number of its atoms contained in the compound atom, and adding the quantities so obtained: the sum is the atomic weight of the compound, and since the quantity of each element coutained in it has also been determined, the quantities of those several elements in any other quantity of the compound may be found by the Rule of Three.

What are the quantities of the several elements of sulphate of lead (PbO, SO3) contained in 100 parts? PbO is 103:8 + 8 = 111:8; SOP is 16 + 24 = 40; therefore PbO + SO3 is 111.8 + 40 = 151.8. Wc know then that the proximate elements of 151.8 parts of sulphate of lead are 111.8 oxide of lead and 40 sulphuric acid; the ultimate elements are 103.8 lead, 16 sulphur and 32 oxygen. If now 151.8 parts of sulphate of lead contain 111.8 oxide of lead, 100 parts must contain (151.8 : 111:8 = 100 : 73•65) 73.65 parts; similarly the proportiou 151.8 : 40 = 100 : x gives 26.35 per cent. of sulphuric acid; 151.8 : 103:8 = 100 : x gives 68:38 per cent. lead; 151.8 : 16 = 100 : & gives 10:54 per cent. sulphur, and 151.8 : 32 = 100 : x gives 21:08 per cent. oxygen.- What are thic constituents of 85 parts of morphia (C35 NH” (*)? 35 At. carbon weighi 35.6 = 210: 1 At. nitrogen 14; 20 At. hydrogen 20.1= 20; and 6 At. oxygen 6.8 = 48; and 210 + 14 + 20 + 48 = 292; now 292 : 210 = 85 : x gives 61.13 carbon in 85 parts of morphia; 292 : 14 = 85 : x that when the proximate elements of such compounds of the second order, sulphate of lead for example, contain a common ultimate element, as oxygen in this case, the quantities of this ultimate element contained in the two proximate elements must bear a simple relation to each other: e.g., the quantity of oxygen in sulphuric acid is exactly 3 times as great as that in the oxide of lead combined with it.

Chemical Formulæ. A chemical formula is an expression by symbols and numbers of the composition of a definite chemical compound according to its elements and their relative quantities. The symbols are the initial letters of the names of the elementary substances given in the table, page 50, column B. Certain compounds, particularly of the organic class, have likewise particular symbols appropriated to them: e.g., Water = Aq; Cyanogen =Cy; Tartaric acid = T; Citric acid = C; Acetic acid = A; Quinine = Ch; Morphia = M, &c. The numbers annexed to the symbols denote the numbers of atoms of the several constituents existing in the compound; a symbol with no number annexed to it implies that one atom only of the corresponding substance exists in the compound. Electropositive substances, such as metals and salifiable bases, precede electronegative substances, such as oxygen and acids in the forinulæ. This order is the reverse of that adopted in the nomenclature, but it would perhaps be better in this as well as in the formulæ to give precedence to the electro-positive element. When a compound contains proximate and ultimate elements

, the mode of combination is expressed by means of points, commas, + signs, and brackets. Oxygen, which occurs so frequently in compounds, is often expressed by points placed over the symbol of the body with which it is in combination, the number of these points being equal to the number of atoms of oxygen present. In a simisar manner, strokes leaning from right to left are used to denote atoms of sulphur, and points under the symbol of the other body, atoms of hydrogen.

Oxide of lead is PbO = Pb; potash (1 At. potassium and 1 At. oxygen) is KO = K; water is H0 = H; alumina (2 At. aluminum and 3 At. oxygen) is Al 02 = Al; carbonic acid is CO2 = C; silica is Si 0? = ši; sulphuric acid is SO' = S; nitric acid is NOS = N; ammonia is NH = N; sulphate of lead is PbO + S0 = PbO, SO' = Pb S; bicarbonate of potash (1 At. potash, 2 At. carbonic acid, and 1 At. water) is KO + 2C0+ HO = KO, CO’, HO = KC'll crystallized sulphate of ammonia (1 At. ammonia, 1 At. sulphuric acid, am 2 At. water) is NH' + SO3 + 2H0 = NH®, SO', 2HO, = NSII'; cryntallized potash alum (1 At. potash, 1 At. alumina, 4 At. sulphuric aciil, aml 24 At. water) is (KO + SO") + (Al 0' + 350") + (24 110) = KO, SO' + AT 0, 350% + 24 HO = KS, ALS', H"; sulphuret of potassium (1 At. potassium and 1 At. sulphur) is KS = K; tersulphuret of molybdenum is MOS! = Mo; the combination of these two metallic sulphurets in cqual numlbers of atoms is KS + MOS = KS, MOS} = KMo. A number placed on the right and at the upper part of a synıbol denotes merely the number of atoms of the substance denoted by the symbol: 1.9., SO: must be understood to denote 3 atoms of oxygen and only 1 of sulphur; when oxygen is expressed by points, the number placed on the right refers to the whole compound containing the oxygen; thus in bicarbonate of potash KCH we must understand 2 At. COʻ, not merely 2 At. C. On the other hand, a number placed before several symbols multiplies them all as far as the next + sign or comma, or if the number stands before a bracket, it multiplies all the symbols and numbers included within the brackets: thus .6PbO + NO or 6PbO, NOS means a combination of 6 At. oxide of lead with 1 At. nitric acid; and KCl + 4 HgCl + 4H0, or KC1, 4HgCl + 4H0, the combination of 1 At. chloride of potassium with 4 At. chloride of mercury and 4 At. water. Many chemists write the number or index on the right below, instead of the right above the symbols (thus, SO, for sulphuric acid), because, in algebraical formulæ, à number on the right above expresses a power: but there is no risk of confusion between algebraical and chemical formulæ, and the number when written above is more easily read than when placed below.

Stoichiometrical Calculation. The greater the number of atoms of any substance in a given compound, and the greater the weight of those atoms, the greater will be the quantity of that substance in the compound. Hence the quantity (M) of the constituents in a given quantity of the compound (in 100 parts for example) is determined by multiplying the number of atoms (Ž) of each constituent by the atomic weight (G). Hence we have the three following formulae:

M

M
M=; G

3Z =
z

G The first formula comes into use in determining the quantities of the several constituents contained in a given quantity of any compound. The process consists in multiplying the atomic weight of each constituent by the number of its atoms contained in the compound atom, and adding the quantities so obtained: the sum is the atomic weight of the compound, and since the quantity of each element coutained in it has also been determined, the quantities of those several elements in any other quantity of the compound may be found by the Rule of Three.

What are the quantities of the several elements of sulphate of lead (PbO, SO3) contained in 100 parts? PbO is 103:8 + 8 = 111:8; SO3 is 16 + 24 = 40; therefore PbO + SO3 is 111:8 + 40 = 151.8. know then that the proximate elements of 151.8 parts of sulphate of lead are 111.8 oxide of lead and 40 sulphuric acid; the ultimate elements are 103-8 lead, 16 sulphur and 32 oxygen. If now 151.8 parts of sulphate of lead contain 111.8 oxide of lead, 100 parts must contain (151.8 : 111.8 = 100 : 73•65) 73.65 parts; similarly the proportion 151.8 : 40 = 100 : 3 gives 26:35 per cent. of sulphuric acid; 151.8 : 103:8 = 100 : x gives 68-38 per cent. lead; 151.8 : 16 = 100 : x gives 10:54 per cent. sulphur, and 151.8 : 32 = 100 : & gives 21:08 per cent. oxygen.- What are the constituents of 85 parts of morphia (C NHOo)? 35 At. carbon weighi 35.6 = 210: 1 At. nitrogen 14; 20 At. hydrogen 20.1= 20; and 6 At. oxygen 6.8 = 48; and 210 + 14 + 20 + 48 = 292; now 292 : 210 = 85 : x gives 61•13 carbon in 85 parts of morphia; 292 : 14 = 85 : x

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