Equations are derived for the relationship between temperature change and volume of titrant added in thermometric titrations. The effects of the heat capacity of the apparatus, the change in volume during titration, and nonadiabatic conditions are derived and discussed. It is shown how heats of reaction, solution, and dilution may be estimated accurately from automatically recorded thermometric titration curves by interpretation of slopes; results obtained are compared with literature values.H E automatic recording of thermometric titration curves T was described several years ago by Linde, Rogers, and Hume (4). Extension of this work to titrations in nonaqueous media and various refinements in measuring techniques have made it of interest to compare theoretical and observed titration curves and to determine the best method for obtaining fundamental thermochemical data from titration curves measured under ordinary experimental conditions. The usual technique of automatic thermometric titration (4) involves addition of titrant, isothermal with the solution to be titrated, a t a constant rate and measurement of any temperature change in the mixture by means of a rapid-response element such as a thermistor. A Dewar flask and appropriate thermal shielding are employed to make I 1 I I I 0 60 120 180 240 3 Time in Sec.Figure 1. Comparison of curves of temperature us. time Heat generated electrically at constant rate 1. Recorded 1. A . Calculated 1the system as nearly adiabatic as possible. The speeds of reaction and mixing are such that thermal equilibrium is established immediately in the solution, but because a titration requires only a few minutes for performance, true thermal equilibrium is not reached between the solution and its container. This and the fact that the heat capacity of the system is undergoing constant change due to the addition of titrant makes the temperature t's. volume plot nonlinear.It is useful, first, to consider the effect of nonequilibrium with cell and surroundings by examining n hat happens when a small electric heating coil is used to deliver knobvn amounts of heat to a solution in the titration cell. Because no titrant is being added, the heat capacity of the system is constant. The heat added, dt, during an infinitesimal interval is given by the relationwhere i is current in amperes; R, resistance in ohms; t, time in seconds; H , heat in calories; T , centigrade temperature; and C,, the heat capacity, in calories, of the titration cell and its contents. Accordingly, the relationship between temperature change and time is given byTemperature rise is linear with time i f no heat is lost to the environment. Comparison v-ith a typical curve of T us. t obtained this way under ordinary good experimental conditions reveals that the empirical plots are invariably curved because of heat loss (Figure 1). This might a t fiist seem to be a serious deterrent to use of titration curves for measuring heats of reaction, but, as will be seen, it is an effect which can be eliminated readily by taking th...
A rapid and precise method was desired for determination of the sulfate impurity in reagent grade calcium carbonate, sodium carbonate, and potassium chloride. A nephelometric procedure involving the addition of solid barium chloride to hydrochloric acid solutions of the sample containing 20% ethyl alcohol proved to be applicable. The salt being analj zed, its concentration, and the method of adding the reagent w-ere investigated in detail. Prior filtration of the test solutions was shown to be essential when the sulfate concentration was below 2 p.p.m. Agreement within a range of 1.0 to 1.5 "nephelos" units was obtained at all levels of sulfate concentration (from 0.2 to approximately 10.0 p.p.m.) up to 100 nephelos units. The method of atandard addition and entrapolation provided a determination of the sulfate ip a particular salt sample and a calibration curve of permanent value. The procedure is general and should be easily applicable to many salts.MALL amounts of sulfate present as an impurity in inorganic S analytical reagents are still determined in most control laboratories by the precipitation and weighing of barium sulfate. The low level of the impurity places considerable strain on the gravimetric procedure because, even when large samples are employed, the amount of barium sulfate produced is of the order of 1 mg. (3, 30). A t best, the determination is semiquantitative, despite the fact that much time is consumed in digesting and filtering the precipitate.A variety of volumetric methods have been proposed for the determination of sulfate. The most promising ones involve the use of tetrahydroxyquinone (16, , E?+?) or rhodizonates ( 8 ) as indicators for barium ions. The standard chromate procedure has also been adapted to the micro scale (9). I n addition, photometric precipitation titrations have been developed (19,26,31 ). Potentiometric determinations have employed the lead-amalgam electrode ( 7 ) , bimetallic electrodes (25), and the ferrocyanideferricyanide couple (1, 13). A study using an amperometric titration in 30% ethyl alcohol with lead ions has been rpported (1 6).Two indirect polarographic procedures have been suggested. One of these involved the measurement of the concentration of mcess lcad i m s after equilibrium has been reached with lead sulfate ( 1 7 ) ; the other (10) introduced preliminary reduction of the sulfate to sulfide, followed by distillation, precipitation Kith cadmium ion, and subsequent measurement of the cadmium ion. The sulfide has also been determined colorimetrically (11) by formation of methylene blue. A spectrophotometric modification of the benzidine method ( 4 ) has also been reported. Kephelometric, or the closely related turbidimetric, determination of harium sulfate has been frequently used for the estimation of sulfate (5, 6, 15, SO, 21, 23, $4, 88).Of these methods only the measurement of the methylene blue color for sulfide or the light-scattering power of suspensions of barium sulfate seemed applicable to the levels of sulfate that n-ere anticipated. The d...
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