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IN DEFENSE OF TITRES A survey of the textbooks of quantitative analysis in common use will reveal the fact that the titre system of computation is little used in this country. Many of the books do not even mention the word, a few of them give a brief summary of the system, but only one that the writer knows of1 places any special emphasis on the method. This is not as it should be, however, for those chemists who have been taught the normality system of computation and have later become familiar with the titre system are often inclined to discard the older method. There are certain fundamental reasons why this should be true and it is the purpose of this paper to demonstrate those reasons. Titre is defined as the number of grams of a substance equivalent to one cubic centimeter of a reagent. It represents therefore the-simplest possible way of designating the concentration of a standardized solution. Suppose for instance: A 1.1000 g. sample of NaeCOais used for the standardization of an HC1 solution and, after making corrections for the necessaty excess, i t is found that 31.65 cc. of that solution was just sufficient to neutralize the sample. It is then said that the sodium carbonate titre of the hydrochloric acid is 1.1000/31.65 or 0.03474 g. per cc. This may be written, Na&Oa T HCl = 0.03474.2 Suppose further that the hydrochloric acid is used to analyze the same weight of an unknown soda ash and that the volume required in the titration is 26.51 cc. The percentage of N%COs is then simply (26.51/ 31.65) 100 = 83.76%. + If different sample weights are used the computation is quite as simple. Suppose the sample weight of the unknown to be 1.2000. The formula then becomes: (Na2C03 T HCI) (V/S) = % Na&Oa or 0.3474 (26.51/ 1.2000) 100 = 76.76%. This may be reasoned out as follows: the titre is the weight of Na?COa equivalent to 1 cc. of the acid. The product of that number times the total volume of reagent used will give the total weight of Na2COain the unknown sample. This latter weight divided by the sample weight andmultiplied by 100 will give the percentage of NazC03. Wben this explanation is used it is much easier to make the elementary student understand the relation between standardization and analysis. He can master this one relationship without at the same time having to learn the use of equivalent weights and normalities. That will seem like a trifling point to some, but any one who has taught analytical chemistry will testify that many students do not find it easy to learn the use of equivalents. To apply the titre system of computation to the more general case of Popom, "QuantitativeAnalysis." P. Blakiston's Son and Co., Philadelphia, 1927, pp. 226-47. a
J. CHEM.EDUC., 8, 1396 (July, 1931).
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volumetric analysis in which a reagent is standardized against one substance and then used to analyze for another it is necessary to make use of chemical factors. This point is one that is also too often neglected. One book in common use states that if duplicate problems are to be worked out a chemical factor is always used since it saves duplication of arithmetical work, but that no particular advantage is found in using the chemical factor in single problems. This is hardly the correct view of the matter. Every ordinary problem in chemical proportion is rearranged (solved algebraically for x) before doing the final arithmetical work. The student who has a knowledge of chemical factors will set the problem down in this order and not have to rearrange it. He therefore saves a step in every problem he solves. Furthermore, tables of chemical factors are so common that he will usually be able to find the value of the factor directly iustead of having to look up two molecular weights, thereby saving another step. To ask students to work all their problems by the old proportion method is a lesser crime of the same nature as asking them to calculate all the molecular weights they use instead of looking them up. The weight of any pure substance multiplied by a chemical factor will give the weight of another pure substance equivalent to it. Therefore after a titre of a reagent has been found by standardizing it against any convenient standard the titre (concentration) of that reagent may be expressed in terms of any substance to be sought in an analysis, using that reagent. Suppose for instance the MaCOa T HCI has been found and it is expected to use that reagent to find the per cent. NH3 in a sample of NHaOH. Two simple equations : NHa HC1 = NHPCI, and N a C 0 3 2HC1 = 2NaCI 2Hz0,will show that two molecular weights of NH3 are equivalent to one molecular weight of Na2C03. (The student will soon learn to visualize such facts without the equations.) Using this information we can now see that: NH3 T HCI = N a C 0 3 T HC1 times (2NH3/Na2CO8),and we have found the weight of NHBthat will be indicated every time a cubic centimeter of the HCI is used in titrating the unknown. Once the titre is expressed in terms of the substance sought the rest of the computation is directly analogous to the one explained for percentage of NazCO8in a soda ash. In other words: (NH8 T HCl) (V/S) 100 = O/, NHI, or, employing the original titre: (Na2C03T HCI) (2NH3/NaC03) (V/S) 100 = yo NH3, or, employing the data as it is recorded in the laboratory: (S1/V1) (2NH3/NaC03) (Vz/SJ 100 = YoNHz. (Vl and SI apply to the standardization and VZand & apply to the analysis.) Experience has shown the writer that students find this system of computation much simpler than the older method for:
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1 . The simpler cases show the student that percentage as determined in a chemical analysis does not differ from the percentage he has been accustomed to work with since grammar-school days. 2. The use of chemical factors makes the computations for volumetric analysis directly analogous to those for gravimetric analysis. 3. They are not burdened with the necessity of learning the additional concept of equivalent weights and normality, for this has been shown to be totally unnecessary. W. P. CORTELYOU NEWYORKSTATE COLLEGE OF CERAMICS ALFREDU N I V B R S I ALFRED, ~. N. Y.
BALANCING CHEMICAL EQUATIONS DEARDR. KENDALL: * Protracted convalescence after a rather sharp attack of "flu" has given me the opportunity of reading more closely than might otherwise have EDUCATION. been possible the February issue of the JOURNAL OR CHEMICAL May I first of all take this opportunity of thanking you on behalf of myself and my colleagues of the chemistry department of Geo. Heriot's School for recommending the addition of the JOURNAL to school magazine lists. We adopted your suggestion and have had many pleasant and profitable hours in consequence. I had not noticed Mr. Endslow's letter to thereditor in the December issue, re "Balancing Chemical Equations," but reading the February number closely I came on the replies, including your own. It may be of interest to you to know that in Geo. Heriot's School-at least since the early days of the War-I have generally spent one lesson teaching to my Leaving Certificate Class this "Algebraical Method" of balancing. The objects in view have been mainly: 1 . To satisfy the more "mathematically minded" pupils that i t is generally possible to find the coefficients without resorting to what otherwise might seem to them a species of "juggling." 2. To point out that whereas the writing of a balanced equation may suggest a possible chemical reaction, this is a reversal of the proper order that a chemical equation should express quantitatively a change which has actually taken place. 3. To warn them that in many cases a textbook equation is only one of an infinite number which also seem possible. 'This letter was addressed to Dr. James Kendall. The University, Edinburgh, Scotland, and forwarded by him to the editorial office.
