To find the cost of a draft, the face and rate per cent of exchange being given.
Rule.—Find the percentage of the given rate per cent of exchange and add it to, or subtract it from the amount of draft.
Example: What is the cost, in Chicago, of a sight draft on Denver for $400, if exchange is3⁄4% premium; and how much if1⁄2% discount?
$400 × .003⁄4= $3; $400 + $3 = $403, at3⁄4% premium.$400 × .001⁄2= $2; $400 - $2 = $398, at1⁄2% discount.
To find the face of a draft, cost and rate per cent of exchange given.
Rule.—Divide by the cost of a draft for $1, at given rate per cent of exchange.
Example: Find face of draft that can be bought for $1000 at 1% premium; at 1% discount.
$1000 ÷ 1.01 = $990.10, at 1% premium.$1000 ÷ .99 = $1010.10, at 1% discount.
Time Drafts, when negotiated before maturity, are subject to discount which is computed on the face of the draft, the same as interest.
Example: What is the proceeds of a 60-day draft for $800, at5⁄8% premium, and discounted at 7%?
Foreign Drafts are usually made payable in the money of the country on which they are drawn.
To find the equivalent of foreign money in United States money and vice versa.
Rule.—Multiply, or divide (as the case may require) the given sum, by the equivalent of a unit in United States money.
Example: What is the cost of a draft on London for £125, reckoning exchange at $4.8665?
125 × 4.8665 = 608.31.Ans.$608.31.
Wishing to remit $182.50 to Ireland, for what amount must I buy a draft on London?
182.50 ÷ 4.8665 = 37.5.Ans.£371⁄2.
How many francs in $100?
100.000 ÷ .193 = 518.13.Ans.518.13 francs.
How many dollars in 7500 German marks?
7500 × .238 = $1785,Ans.
How many Swedish crowns in $750?
750 ÷ .268 = 27981⁄2crowns,Ans.
How many dollars in 4635 rubles?
4635 × .772 = $3578.32,Ans.
A simple method to reduce pounds sterling to United States money, and vice versa; exchange being at $4.8665.
Rule.—Multiply pounds sterling by 73, and divide the product by 15. Or multiply dollars by 15 and divide the product by 73.
Examples: How many dollars in £85?
85 ×73⁄15= 413.67.Ans.$413.67.
How many £’s in $748.25?
748.25 ×15⁄73= 1533⁄4.Ans.£1533⁄4.
Another method to change pounds sterling, shillings and pence, to dollars and cents.
Rule.—Reduce pounds sterling to shillings, add the shillings, and multiply the sum by .241⁄3—the product will be cents. Add 2 cents for each pence, if any.
Example: Change £46, 13s. 9d. to United States money.
Tourists of today patronize express companies forForeign Money Orders. These are made out similar to regular express money orders and may be cashed in any of the larger cities of all foreign countries. They take the place, to a large extent, ofLetters of Credit, which are letters from banking houses in one country to those in another, allowing sums to be drawn not to exceed a total named in the letter.
Stocksis a general name given to the capital of incorporated companies. They are divided into equal parts, usually of $100 each, calledShares, the owners of which are calledStockholders. ADividendis a part of the net income of the company, divided among the stockholders.
Acertificate of stockis a written paper signed by the proper officers of the corporation, naming the number of shares to which the person named therein is entitled, and the original value of the same.
Preferred stockis stock which is given a preference over the common stock. Ordinarily, a dividend is paid on the preferred stock before any is paid on the common shares.
Common stockis the ordinary stock of a corporation, which has no preference, in the payment of dividends, over any other.
Thepar valueof a share of stock is the value named in the certificate of stock.
When a corporation is prosperous, its shares of stock often sell for more than the value named in the certificate of stock. They are then said to beabove par, orat a premium. In times of business depression, often these shares of stock sell below their face value. They are then said to bebelow par, orat a discount.
Themarket valueof a share of stock is the value for which it sells in the open market.
Astock brokeris one who makes a business of buying and selling stocks and bonds. He charges a commission for this which is calledbrokerage.
Asurplusis a part of the earnings of a corporation.
Thegross earningsof a corporation are its total receipts from all sources.
Thenet earningsare the profits remaining when all expenses, losses, interest and debts due are paid.
Anassessmentis a sum levied proportionate to stock held by stockholders, to help out the business when it is not prospering, or when more money is needed to carry it on. It is levied as so many dollars on each share at its par value.
Thedirectorsare those shareholders elected by all to manage the affairs of the corporation.
Abondis, in form, a carefully drawn interest-bearing promissory note. Ordinarily, it runs for a period of years with interest often payable semi-annually. It is more formal than the ordinary promissory note. Bonds are usually[877]issued by national, state, county, or local governments, or by corporations, when they wish to raise large sums of money for immediate use.
A bond runs for a specified time. It bears a specified interest, and is an absolute promise to pay the face of it at maturity. It matures at a definite time, and at that time the holder is paid itsface valueand no more, by the organization that issued it, unless such organization is insolvent, or has repudiated its debts.
Stocks.—A certificate of stock is no promise to pay. It simply shows that the holder owns as much stock in the corporation as is shown by the face of the certificate. It bears no interest and has no date of maturity.
The interest returns of the bondholder are certain and definite. The returns of the stockholder, dividends, are uncertain and depend on the profits of the business.
Consequently, no table can be arranged to show at what rate stocks can be bought to yield a definite return; but with bonds, tables may be made which show at a glance what the return will be from a purchase made at any rate.
1. To find the value of stocks, when above or below par.
Rule.—Multiply the price per share, by the number of shares.
Example: Find cost of 65 shares of bank stock, at $107 per share, or 7% premium. Also of 48 shares of railroad stock, at $871⁄2per share, or 121⁄2% discount.
(1) 65 × 107 = 6955.Ans.$6955.(2) 48 × 871⁄2= 4200.Ans.$4200.
2. To find what rate per cent is realized by investing in stocks or bonds when above or below par.
Rule.—Annex two ciphers to the fixed rate per cent, and divide by the cost per share.Or by proportion:As the cost per share is to the fixed rate, so is 100 to the required rate.
Example: Mr. Warren bought ten shares of Illinois Central Railroad stock at 96. What does he get when a dividend of 6% is declared? What per cent is that on his investment?
Work and Explanation:
(1) 1 share at 6% yields $6(1)10 shares yield 10 × $6 = $60.(2) Each share at 96 costs $96.(2)Each share yields $6.Query?$6 is what per cent of $96?Query?$6 is6⁄96of 100%, or 61⁄4%.Query?∴ the investment yields 61⁄4%.
3. To find which is the more profitable investment.
Rule.—Find the rate per cent that each investment yields, by rule, under item 2; then compare rates.
Example: Which is the better investment; 6% mortgages at 10% premium, or 5% bonds at 10% discount?
(1) 110)600(55⁄11%.
(2) 90)500(55⁄9%.5⁄9-5⁄11=10⁄99, practically1⁄10.
Ans.The latter, by1⁄10of 1%, nearly.
Ataxis a contribution levied on persons, property, incomes, or business, for public purposes.
Some Uses for Taxes.—TheNational Governmentrequires money to support the army and navy, to pay the salaries of government employes, to pay pensions, and to finance other activities carried on by the nation.
TheState Governmentsrequire money for the expense of their officers, and to support their various institutions, schools, universities, asylums, and penitentiaries.
Thecountiesrequire money for the building of bridges, the trial of criminal cases, the salaries of officers, the relief of the poor, etc.
Citiesmust pay for police and fire protection, care of streets, etc.
School districtscontribute to the support of the public schools.
The money required for all these expenses is raised by taxes, licenses, fees, assessments, and fines.
State and Local Taxes.—The amount of tax paid by any individual to state and local governments depends upon the value of the property which he owns and the tax rate. In many places the adult male citizen pays a poll tax.
The tax levied on property is called aproperty tax.
The tax levied on persons is called apoll tax. This is sometimes called acapitation(by the head)tax.
Sometimes a man’s income is taxed. This is anincome tax.
After the amount of money to be raised by tax is decided upon, a man, called theassessor, examines each piece of taxable personal property and real estate, and places a value upon it. This is taken as a basis for proportioning the tax among the property owners.
Atax collectoris one who collects the taxes. He is sometimes paid a salary. Sometimes he gets only a percentage of the money he collects.
Thetreasurerreceives and takes care of the money collected by the tax collector. He is paid a salary.
The Tax Rate.—Sometimes the rate is fixed by law or by vote of the citizens. More often the lump sum to be raised is named, and the assessor determines the rate.
When the assessor is to determine the rate, he proceeds in this way: First, he assesses each piece of property, usually not at its full market value. Then he determines the total value of all the property in his district. Next, he divides the total tax to be raised by the total value of the property in his district. The result is therate of taxon the dollar.
Use of the Mill in Taxes.—When a tax is apportioned, it is usually found that if a few mills are paid on each dollar’s worth of property in the district, the aggregate amount is equal to the whole sum of tax needed. Consequently, we often hear of tax levies of so manymillson thedollar, as, 2 mills on the dollar, 5 mills on the dollar, etc.
The denomination of our money system called themillhas practically its only use in the levy of taxes.
Assessors make use of atablelike the one given on thefollowing page. This table is based on a tax levy of 9 mills on the dollar.
The following tax rates are equivalent:
16 mills (on the dollar);
1.6%;
$1.60 (on each hundred dollars).
Explanation of Table.The second column shows the tax at nine mills on the dollar, for values of $1 to $30.[878]The fourth column shows the tax for values of $40 and multiples of ten, to $600. The sixth column shows the tax for values of $700 and multiples of one hundred, to $10,000.
Tax Table
The Amount of Tax.—To find the amount of tax to be paid by any property owner.
Rule.—Multiply the assessed value of the property by the tax rate.
Example: Taylor’s property is assessed at $3800. The rate is 24 mills.
Example: The town of Grant is to raise $4725 in tax. The property in the town has an assessed valuation of $395,140. What is the rate?
If on $395,140 a tax of $4725 is to be raised, on $1 as much tax must be raised as $395,140 is contained times in $4725, which is .0119+, or about $.0119. This would be called $0.012, or 12 mills on the dollar.
Example: Finch’s property is assessed at $5470. The tax rate is $1.95.
Solution:
Indirect Taxesare taxes placed upon goods by the national government, and collected before the goods are sold to the consumer.
The national government needs this money to pay:—
1. Interest on the public debt.
2. To support an army and navy, to build vessels, and keep up arsenals and forts.
3. To pay pensions.
4. To improve the rivers and harbors.
5. To pay the salaries of its officers; as, the president, cabinet officers, judges, ministers to foreign countries, congressmen, etc.
Indirect taxes are of two kinds,customs or duties, andexcisesorinternal revenue.
Excisesorinternal revenueare taxes levied on certain domestic goods, as, manufactured tobacco, liquors, and the like.
Indirect taxes levied by the government on imported goods or merchandise are calleddutiesorcustoms.
Acustom houseis a government office where duties are collected and where vessels are entered and cleared. Nearly every seaport of consequence has a custom house. So also have important towns near the Canadian and Mexican boundaries.
Duties are of two kinds,specificandad valorem.
Aspecificduty is one levied at a specified sum per yard, gallon, ton, etc.
Anad valoremduty is one levied at a certain percentage of the value of the goods, at the port of export.
Tareis an allowance made for the weight of bags, barrels, or cases, in which merchandise is shipped.
Leakageis an allowance made for loss of liquids from casks, barrels, etc., in shipping.
Breakageis an allowance made for the loss of liquids from bottles in shipping.
Example: Find the duty on 4 dozen bottles of cologne, allowing 4% for leakage and 3% for tare. The invoice value is 90 cents a bottle and the duty is 25% ad valorem and 20 cents specific. Find the total cost per bottle.
Work and Explanation:
The total cost per bottle is1⁄48of $62.84, or $1.31-.
Powers and Roots.—When a product consists of the same factor repeated any number of times it is called apowerof that factor.
7 × 7 is thesecond power, or thesquareof 7.
7 × 7 × 7 is thethird power, or thecubeof 7.
A power of a number is generally expressed by writing the number only once, and placing after it, above the line, a small figure to show how many factors are to be taken. The small figure is called anindex.
Thus, 72= 49; 73= 343; 74= 2401.
A number is called thesquare rootof its square.
Since 72= 49, the square root of 49 is 7.
The “square root of 49” is written √49.
Again, a number is called thecube rootof its cube. 73= 343. Therefore, the cube root of 343 is 7.
The “cube root of 343” is written ∛343.
Aperfect squareis a number whose square root is a whole number. Aperfect cubeis a number whose cube root is a whole number.
Square Root.—If a number can be put into prime factors, its square root can be written down by inspection.
Example: Find the square root of 27225.
Rule for Digits.—We know that √1 = 1, and √100 = 10. Therefore, the square root of any number which lies between 1 and 100 lies between 1 and 10;i.e., if a number contains one or two digits, its square root consists of one digit.
Similarly, since √100 = 10 and √10000 = 100, the square root of a number between 100 and 10000 lies between 10 and 100. That is, if a number contains three or four digits, its square root consists of two digits.
Proceeding in this way, we obtain a general result—viz., the square of a number has either twice as many digits as the number, or one less than twice as many.
Hence, to ascertain the number of digits in the square root of a perfect square, mark off the[879]digits in pairs, beginning from the right. Each pair marked off gives a digit in the square root; and, if there is an odd digit remaining, that digit also gives a digit in the square root.
Examples: There are three digits in the square root of 546121, and four in the square root of 5774409.
For, marking off the digits from the right, we get in the first case 54,61,21, giving three digits in the square root, and in the second case 5,77,44,09, the odd digit giving the fourth in the square root.
The method of finding the square root of a given number depends on theformof the square of the sum of two numbers.
Explanation: The square root of 144 is 12. Let us see how we found it.
12 = 1 ten + 2 units.
122is the same as (10 + 2)2.
Let us square (10 + 2), that is, multiply 10 + 2 by 10 + 2.
Rule.—The square of any number made up of tens and units is equal to the square of the tens, plus twice the product of the tens by the units, plus the square of the units.
Another Explanation: Find the square root of 45369.
Solution:4·53·69)213441534142312691269(1) Point off the number into periods of two figures each, as before.(2) The square root of the first period is 2. 2 × 2 = 4. Write the 2 in the root and subtract the 4 from 4. Bring down the next period, 53.(3) 2 × 2 = 4. (Remember the 4 is to be used as a trial divisor, being 2 × thetens.)4 is contained in 5 about 1 time. Place 1 in the root, also on the right of the 4 in the divisor. Multiply 41 by 1. Subtract and bring down the next period.(4) 2 × 21 = 42. 42 is thetrial divisor. 126 ÷ 42 =about3 times. Place the 3 in the root also at the right of the 42 in the divisor. Multiply out.Square root = 213.
Solution:4·53·69)213441534142312691269
Solution:
(1) Point off the number into periods of two figures each, as before.
(2) The square root of the first period is 2. 2 × 2 = 4. Write the 2 in the root and subtract the 4 from 4. Bring down the next period, 53.
(3) 2 × 2 = 4. (Remember the 4 is to be used as a trial divisor, being 2 × thetens.)
4 is contained in 5 about 1 time. Place 1 in the root, also on the right of the 4 in the divisor. Multiply 41 by 1. Subtract and bring down the next period.
(4) 2 × 21 = 42. 42 is thetrial divisor. 126 ÷ 42 =about3 times. Place the 3 in the root also at the right of the 42 in the divisor. Multiply out.
Square root = 213.
Cube Root.—Thecube rootof a number is one of the three equal factors of that number.
Thus, 5 is the cube root of 125, because 5 × 5 × 5 = 125.
Theradical signwith a figure 3 over it (∛) means that the cube root of the number following it is to be taken.
∛125reads, “The cube root of 125.”
If we can find the prime factors of any perfect cube, we can write down its cube root by inspection.
Example: Find the cube root of 74088.
874088992613102973437497∴74088=8 × 9 × 3 × 7 × 7 × 7=23× 33× 73∴∛74088=2 × 3 × 7=42Ans.
874088992613102973437497
Rule for Digits.—Since 13= 1 and 103= 1000, therefore the cube of a number which lies between 1 and 10 lies between 1 and 1000,i. e., the cube of a number of one digit contains either one, two or three digits.
Again, since 103= 1000 and 1003= 1000000, the cube of a number of two digits contains either four, five, or six digits.
Proceeding in this way, we see that the cube of a number contains three times, or one less or two less than three times, as many digits as the number.
Hence, to find the number of digits in the cube root of a given number, we mark off the digits in sets of three, beginning at the decimal point, and marking both to the right and to the left.
FIGURES REPRESENTING THE PROCESSES OF FINDING CUBE ROOT
FIGURES REPRESENTING THE PROCESSES OF FINDING CUBE ROOT
Thus, 289383 will be pointed off into two periods—289·383—and we readily see there will be only 2 figures in the root.
The simplest method of finding the cube root of numbers whose prime factors are not known is analogous to the method of finding square root, being based upon the form of the cube of the sum of two numbers.
Explanation: The cube root of 1728 is 12. Let us see how we found it.
12 = 1 ten + 2 units
123= (10 + 2)3
(10 + 2)3means 10 + 2 × 10 + 2 × 10 + 2
That is, the cube of any number made up of tens and units equals—
The cube of the tens + three times the product of the square of the tens by the units + three times the product of the tens by the square of the units + the cube of the units,
or
tens3+ 3(tens2× units) + 3(tens × units2) + units3.
For graphic illustration the geometrical representation of the cube of units and tens in thedrawingsis helpful.
After the process is understood, this short method of writing the work may be used by the pupil:
Example: Find the cube root of .0163956, carrying the root to 3 decimal places.
Work:
Its Use and Importance—What it is—How it Differs from Physics—Its Divisions—Distinction between Theoretical and Practical Chemistry—Outline of Theoretical Chemistry—Laws of Chemistry—Atomic Theory—Chemical Notation—Molecular Weights—Reactions—Chemical Arithmetic—Bases—Quantivalence—Tests—Table of Chemical Elements—-Chemistry of Familiar Things—Common Names of Chemicals—Radio-Activity and Radio-Active Substances—Radium and its Uses—The Spinthariscope
A certain amount of knowledge of chemistry is eminently useful in almost every walk of life. An intelligent knowledge of the chemistry involved in the processes of the kitchen, the dairy, the dye-house, the farm, or the manufactory, places the possessor engaged in any of these processes on a different level from the rule-of-thumb worker, who is as ignorant of the reason for adopting a particular method as he is of the properties of the materials he employs.
Technicalchemistry deals especially with the application of the principles and processes of chemistry to the arts and manufactures, and it is to those who are engaged in manufactures of almost every kind that a knowledge of chemistry is a particular advantage.
It is not a question of expediency alone, but one of absolute necessity that a technical education, including chemistry as one of its principal subjects, should form not the least important part of the equipment for his work of any artisan who is to excel in his employment in intelligence and skill.
What is chemistry?
Chemistry is that branch of science which treats of theintimate composition of matter, and the changes produced in it when subjected to particular conditions—such astemperature,pressure,mass,light,catalysis, etc.
How does chemistry differ from physics?
The two branches, physics and chemistry, overlap a great deal, it being very difficult to draw the line of demarcation between them, particularly in the higher stages of thephysicalandchemicalchanges of matter.
For example, a steel needle rubbed on a magnet in a definite way undergoesphysicalchange by means of which it acquires the power of the magnet. On the other hand, a match rubbed on a match-box undergoes achemicalchange by means of which flame is produced. Thus it is possible to make a distinction between the sciences of physics and chemistry. A chemical change involves some alteration in the essential nature of the substance. The match having been ignited has undergone a permanent change, whereby it is no longer combustible. The physical change quoted above involves no alteration in the substance itself, and the acquired property is further only temporary and can be continually lost and reacquired.
The difficulty occurs in this fact, however, that every chemical change is accompanied by physical change, and the physical change may often be the only sign that chemical change has taken place.
What are the chief divisions of chemistry?
Organic and Inorganic Chemistry.—There are two great divisions in the science of chemistry, organic and inorganic. The branch which is best known is that of inorganic chemistry, which covers the chemistry of all the purely mineral substances. Organic chemistry has to do primarily with that of substances obtained from animal or vegetable sources. Now, however, it has resolved itself into the study of the compounds of carbon, always bearing in mind the fact that many carbon compounds have no organic origin, and therefore really fall outside the scope of organic chemistry.
The fundamentals of both branches are the same, and the real reason for the division is the number of the carbon compounds and their[881]highly complex character. It is in this realm that the graphic formula is of most service, and in its organic branch chemistry most nearly approaches biology.
The branch of inorganic chemistry which treats of the composition, etc., of naturally occurring minerals, receives the title ofmineralogical chemistry.
Physical Chemistryexplains processes, formulates laws for these processes, and is divided within itself again into electro-chemistry and thermo-chemistry, etc. One branch of physical chemistry in which great strides have been made, is the study of the general properties of gases. But it is really as much in the realm of physics as it is in the realm of chemistry.
The study of the chemical nature of substances entering into the constitution of the animal organism, and the chemical changes taking place during the life processes of animals, forms the domain ofphysiological chemistry.
The investigation of the influence of soils, and manures, etc., of different compositions, upon vegetable life, and the chemical principles underlying the art of agriculture, are included in the province ofagricultural chemistry.
Pharmaceutical chemistrydeals with the nature and mode of preparation of the various drugs, ointments, etc., employed for medicinal purposes.
The science in its relations to the arts, manufactures, and industrial processes is embraced in the wide titles oftechnicalandapplied chemistry.
What is the difference between theoretical and practical chemistry?
There are in every science two great divisions. These are known as the “theory” and the “practice” (or, as they are sometimes called, the science and the art). The theory of any science is that part of it which forms the answer in any case to the question “Why?” The practice in the same way answers to the question “How?”
If we find, for example, that by putting a fire under a vessel of water, the water gradually begins to boil, as we say, “boils away,” we have learned something that relates topractice. We have learned how to change water into vapor. It is not necessary that we should know why the result is brought about, so long as we are satisfied with the result alone.
But as soon as we begin to wish to bring about any result in the best possible way, we must inquire why a certain course of action causes the result; and in the case of the water, we ask why heat should make water boil and then disappear. The answer to the question “How?” is usually a simple one. It can be found out by experiment. Once having found out, we may usually repeat the work as often as we choose.
But the question “Why?” lies deeper, and sometimes cannot be answered at all. The answer to it is in all cases merely a guess—an attempt to explain more or less fully and satisfactorily. If we find that our explanation or theory makes it possible to foretell what will happen in new cases, then we may safely trust it and believe in it.
Give a clear, succinct outline of the essentials of theoretical chemistry.
The whole matter of molecules and atoms is one oftheory. None of our senses can enable us to know directly either molecules or atoms. We can only imagine that they exist, and then give reasons why their existence makes clear to us the action of elements or of compounds one upon the other.
But in a course of descriptive chemistry, a good knowledge of theoretical chemistry is necessary in order to fully understand all that will be taken up.
(1)Definitions.—An element is a substance thatcannotbe decomposed.
A compound is a substance thatcanbe decomposed into other different substances; and if the decomposition goes far enough, these substances will be elements.
A mixture is made up of two or more components (elements and compounds or both),physicallyput together. It differs from a compound whose compounds arechemicallyunited.
(2)Laws.—Law of Definite Proportions: All specimens of a compound contain the same elements in the same proportions.
Law of Multiple Proportions: When two compounds consist of the same elements, the proportion of one is a simple multiple of the proportion of the other.
Law of Combining Proportions: Each element enters into all its compounds by a fixed proportional weight.
The fundamental laws of chemistry are proved by experiment.
(3)The Atomic Theory.—The atomic theory teaches that matter is composed of minute particles which themselves cannot be divided, but which unite to form molecules which can be divided.
Amolecule, then, is the smallest amount of a substance that can exist in a free state.
The diameters of molecules have been ascertained by Jeans to be—
These figures express number of billionths of a meter.
Anatomis an indivisible particle of an element, and goes to make up the molecule.
(4)Chemical Notation.—The symbols used to represent the different elements (e.g.H for hydrogen, O for oxygen, etc.), when used in chemical compounds, refer to the number of atoms which go to make up the molecule of that particular compound. For example, the expression H2SO4means that in one molecule of that acid there are 2 atoms of hydrogen, 1 of sulphur, and 4 of oxygen.
(5)Molecular Weights.—To determine the molecular weight of a compound it is necessary to knowAvogadro’s Law: Equal volumes of all gases under the same conditions contain the same number of molecules; and Molecular Weight = Vapor Density × 2.
(6)Reactions.—A reaction or chemical equation is a method of representing a chemical change.
In chemistry we have three kinds of reactions, namely:
(1)Analyticalreaction, which is the breaking up of compound bodies into simple,e.g., H2CO3can be broken up into its components, H2O and CO2,e.g., H2CO3= H2O + CO2.
(2)Syntheticalreaction is the building up of a compound body by the union of two or more simple bodies,e.g., H2+ O = H2O and H + Cl = HCl.
(3)Metatheticalreaction consists in the interchange of two radicals in two substances,e.g.,
2HCl + Zn = ZnCl2+ H2. Here the H of the acid is replaced by the Zn.
KCl + AgNO3= AgCl + KNO3. Here the Ag and the K change places.
(7)The Chemical Arithmeticby which from the molecular weights of two substances, and the weight of one substance we are enabled to get the weight of the required substance is called Stoichiometry.
Example: Required the amount of zinc necessary to generate 10 grams of hydrogen.
Atomic weights of H, Cl, and Zn are respectively 1, 35.5, and 65.3.
The reaction is as follows:—
Zn + 2HCl = ZnCl2+ H2, and shows that 2 atoms of H are used for every 1 of Zn.
65.3 × 102= x = 326.5 grams of Zn.
(8)Berthollet’s Law.—Berthollet established the following law, which is of great importance. When two substances can form a substance insoluble or volatile, under the condition of the reaction, that substance will be formed till one of the factors is exhausted.
(9)Radicals.—A radical is an atom or group of atoms which changes places in a reaction. A compound radical is made up of different sorts of radicals, as NH4.
A basic radical is a metal, or a compound radical which behaves like a metal,e.g., Zn and NH4.
(10)Hydrates.—A hydrate is a substance formed from water by replacing half of its hydrogen by a radical,e.g., H2O + 2Na = 2NaOH + H2, where the sodium has taken the place of one atom of hydrogen.
(11)Base.—If a hydrate is formed by a basic radical, the hydrate is called a base,e.g., ZnO2H2.
(12)Alkali.—An alkali is a soluble base,e.g., NaOH, KOH, NH4OH, LiOH.
(13)Acid.—An acid is a substance containing hydrogen which may be replaced by a basic radical,e.g., 2HCl + Zn = ZnCl2+ H2.
(14)Salts.—A salt is a substance formed from an acid replacing its hydrogen by a basic radical,e.g.2HCl + Zn = ZnCl2+ H2.
An acid salt is a compound derived from an acid which has not all of its hydrogen replaced,e.g., 2NaCl + H2SO4= NaHSO4+ HCl + NaCl.
(15)Chemical Nomenclature.—Termination“—UM” is now applied to allMetals, though the older-known metals retain the former names,e.g.—Aluminium, Tellurium, etc.
Termination“—IDE” denotes aBinary Compound, that is, a substance composed of only two elements,e.g., Sodium Chloride (NaCl).
Termination“—OUS” is applied to the first of two elements when it exists in a greater proportion than in another combination with the same element,e.g., one atom of phosphorus and three atoms of chlorine formPhosphorous Chloride.
Termination“—IC,” when the first exists in a lesser proportion,e.g., one atom of phosphorus with five atoms of chlorine formPhosphoric Chloride.
Prefixes“MONO—,” “BI—,” “TRI—,” etc., indicate the proportion of the latter of two elements, and are sometimes used instead of the above termination. Thus phosphorous chloride may also be calledPhosphorous Tri-Chloride; so one atom of carbon with one atom of oxygen isCarbon Monoxide.
Prefix“HYPO—” (under) and “PER—” (over), specify compounds formed by the same two elements containing less (or more) of an element than is in the usual compound.
Nomenclature of Salts.—From the common acids we get the following salts:—
A rough rule for the nomenclature of acids may be made from the above. Acids with the prefixhydroand the suffixicform salts inide; with suffixate, salts inate; with suffixous, salts inite.
(16)Basicity.—The basicity of a substance is measured by the amount of hydrogen which it contains that can be replaced by a basic radical,e.g., H2SO4is di-basic,i.e., the two atoms of hydrogen can be replaced by a basic radical. H2SO4+ CaCl2= CaSO4+ 2HCl.
(17)Quantivalence.—The quantivalence of an element is measured by the number of atoms of hydrogen it combines with or replaces.E.g., Na is univalent, for when added to HCl it replaces one atom of hydrogen; Ca is bivalent, for, as seen in the above reaction, it replaces two atoms of hydrogen.
(18)Test for a Chloride.—To test for HCl or any chloride, add to the solution to be tested a little AgNO3, and if a chloride is present, a milky-white precipitate will be formed. The reaction is as follows: HCl + AgNO3= AgCl (white precipitate) + HNO3. A metal almost invariably changes places with hydrogen.
Caution.—In diluting H2SO4add the acid to the water; for the evolution of heat from the process will cause the water to boil, and reversing this process will cause the liquid to boil over and possibly result disastrously.
(19)Impurity inH2SO4.—Commercial sulphuric acid contains PbSO4as an impurity. This gives it the colored appearance, plumbic sulphate being soluble in strong sulphuric acid.
(20) H2S.—Sulphuretted hydrogen is somewhat soluble in water, slightly poisonous, and is a reducing agent.
(21)Carbonic Acid.—H2CO3does not exist as an acid. We infer its existence from the presence of its salts. Na2CO3+ 2HCl = 2NaCl + H2CO3, but the H2CO3is so unstable that it breaks up at once into H2O and CO2.
(22)Test for a Carbonate.—To test for a carbonate, treat the substance with an acid; CO2is formed; pour the gas into a solution of lime-water, and a white insoluble precipitate is formed, CaCO3.
TheChemical Elementsare the simplest known constituents of all compound substances. Chemists regard them as elements or elementary substances only when they have been proved to benotcompound. The elements are somewhat arbitrarily divided into metals and non-metals, the former constituting by far the larger class. Several elements occupy positions on the border line. Below is a list of the elements at present known with certainty, and of their atomic weights as fixed by the various kinds of evidence obtained by very numerous, and in many cases varied, experiments. The values are all referred to oxygen as standard with atomic weight 16, and are those adopted, for 1910, by the International Commission on Atomic Weights. The standard O = 16 has been pretty generally adopted by chemists as, upon the whole, more satisfactory than H = 1.
Abbreviations.—At. wt., atomic weight; S. G., specific gravity; M. P., melting point; B. P., boiling point; C. T., critical temperature.