Specific Heats of Volatile Liquids G. C . WILLIAMS Cniversity of Louisville, Louisville, K y .
The fundamental equation for calorimetry is expressed as = TPC,AT, where the heat input is equated to the product of the weight of the substance, the specific heat, and the temperature change. However, a portion of the heat must almays be absorbed by the calorimeter vessel, thermometer, stirrer, etc. The heat requirements of the system, other than those of the substancr under study, are usually grouped and called “the heat equivalent of the calorimeter” (C.E.). The equation should therefore read
Q
Q
=
[WC,
+ (C.E.)]17‘
Because of the differences in temperature between the liquid and its container, and the system from the surrounding atmosphere, a small portion of heat is either gained or lost by radiation; in addition, any vaporization of the material under study will also absorb a quantity of heat. These conditions would produce a true heat balance for a unit time such that
Q I
Figure 1.
=
[WC,
+ (C.E.)]AT + H , + H,
where H , = radiation heat loss and H , = vaporization heat loss. This equation may be expressed differentially as a function of time as
I
Diagrammatic Sketch of Specific Neat Apparatus
d0
T
HERE are many instances in the laboiatory determination of physical properties of liquids when it is necessary to de-
It is significant that although a slight loss in material may produce an appreciable effect on the term dH./de, W is normally large, and the difference in it may be considered negligible. During the periods prior to and subsequent to the heat addition to the calorimeter, no heat is being added, and dQ/da = 0; therefore
termine the specific heat of a liquid of relatively high volatility. This situation arose when the author attempted to determine the enthalpies of mixtures of benzene and methanol. Both components were highly volatile; and when specific heats were necessary a t temperatures close to the boiling points, the normal procedures were inaccurate. The following procedure was devised for this specific investigation, but is general in nature and will fit many similar problems. In this case specific heats were necessary in a range where the vapor pressures of the two components, and of the mixture, were relatively high. The standard calorinietric method for obtaining specific heats of liquids is to apply a measured quantity of heat to a measured amount of the liquid and note the resulting temperature rise. The heating procedure is normally by electrical means, utilizing a known resistance, and measuring the time-amperage quantities. This method necessitates an extremely constant current control, and even then it requires an estimation of the proper timing for the measuring of the temperature rise. I n a case where the normal volatility of the substance is high, considerable error may be introduced by the vaporization of small amounts of the substance. The error sometimes may be eliminated to a degree by proper extrapolation of the time-temperature curve, but the procedure is not highly accurate. The heat of vaporization, moreover, is of substantial proportions for methyl alcohol and an uncorrected vaporization loss of one part in a thousand in specific heat measurements mould raise a true specific heat of 0.60 to an apparent one of 0.86 (cal.) (gram) -1(”C.) -1. Thus, although the vaporization loss is negligible from a material standpoint, it is highly significant from a heat standpoint. TKOpoints of improvement are possible: (I) Limit the available vapor space by the shape of the vessel, and confine it by allowing the liquid to fill the vessel as much as practicable. (2) Adjust the method of calculation to minimize the effect of volatilization or to include it in the correcting factors.
where the subscript o represents the condition during the no-heat part of the cycle. If experimental conditions are further arranged so that dTo/d8 and d T / & are measured a t the same temperature, a proper combination of equations results in the following: ,
dT
dT,
de
According to this equation, it is possible to relate specific heats to the weight of substance employed, the heat equivalent of the
41.0
ci 0
i Id
L
=w.O
i? E W
B
z I-
49.0 I
Figure 2.
340
ELAPSED TIME
- MINUTES
Graphical Determination of Rates Values for Specific Heat Calculation
INDUSTRIAL AND ENGINEERING CHEMISTRY
February 1948
C+ulations.
calorimeter, and three rate expressions: heat input, measured temperature rise, and temperature change at no-heat period. A diagrammatic sketch of the apparatus used for the system benzene-methanol is presented in p g u r e 1, and a sample calculation using data obtained with the device is given below.
The basic equation is
% ! d9
=
[WC,
-&I
dT + (C.E.)] [-& - dT,
3 - 60EZ - (60)(3.52)(1.16) = 58.58 tal* per nfin, 4.182
d9
Data. 80% benzene by volume. Desired temperature, 50' C. Weight of flask, stirrer, thermometer, etc., empty C* 9.5042 g r a m Initial weight of flask, etc., plus liquid C 99.7764 grams C 99.6352 grams Final weight of flask, etc., plus liquid 90.2016 grams Average weight of liquid Voltage across coil, 3.52 Amperage, 1.16
++ +
*C=
341
C.E.
4.182
= 11.42 from calibration with pure CeHsand pure
CHsOH.
Rates, taken from data plotted in Figure 2. A. Initial radiation, etc., rate at 50" C. = -0.348 1 B. Final radiation, etc., rate at 50" C. = -0.336 J or average = 0.342 C. per min.
counterbalance.
O
0
Temperatures at 15-Second Intervals, C. 50.40 11 21 49.57 50.68 31 50.31 22 49.50 50.83b 32 12 60.23 23 49.44' 50.79 33 13 50.14 24 50.72 34 14 49.58 50.06 25 49.74 50.62 35 15 26 50.52 49.96 36 49.90 16 49.87 27 50.06 50.43 37 17 49.79 28 50.21 50.35 38 18 50.26 49.72 29 50.38 39 19 50.18 40 49.64 30 50.53 20 Current on. b Current off.
C. Average heating rate at 50' C. = 0.630 C. per min.
50.10 50.02 49.93 49.85 49.76 49.68 49.60 49.53 49.44 49.36
O
Therefore 58.58 = [90.2016 C , '
c,
+ 11.421[0.630 + 0.3421
= 48'85 = 0.642 cal. per
90.2016
O
C. at 50" C.
RRICEIVED February 25, 1947.
Thermodynamics of Nonelectrolyte Solutions d
~ 7 -RELATIONS t IN A BINARY SYSTEM OTTO REDLICH AND A. T. KISTER Shell Development Company, Emeryville, Calif. T h e development of specialized processes of distillation and extraction creates a demand for efficient methods of describing the thermodynamic properties of nonelectrolyte solutions. The present paper discusses the examination of experimental data for the composition of a binary solution and its vapor, as functions of the temperature at constant pressure.
T
HE papers of this series attempt to present various conclusions from the thermodynamics of solutions in a form which is most convenient for practical applications. VAPOR-LIQUID EQUILIBRIUM
The design of a distillation column is based, in general, on laboratory data which represent the mole fractions x of the liquid and y of the vapor in equilibrium as functions of the temperature t at a constant pressure P. The functions x and y determine only a single independent function. The known relation between x, y, and t can be used, therefore, for minimizing the influence of experimental errors, which are bound' to be considerable for low concentrations of either component. This problem is usually solved by means of introducing the activity coefficients
van Laar, or Scatchard. This procedure, however, introduces some uncertainty as to whether the deviations of the original values from the smoothed ones are due to experimental errors or t o the insufficientvalidity of the approximation formula. Furthermore, the use of derived function like the activity COefficient instead of the immediate experimental data for the process of smoothing is always disadvantageous, especially if the limits of the experimental error, as in the present case, vary considerably within one set. Any adjustment requires the comparison of the likelihood of different sets of deviations. I t is difficult to exert proper judgment with functions which are somewhat remote from the immediate experimental data. In addition, the problem is complicated by another condition-namely,
yp/xp;; YZ = (1 Y)P/(l X M where p;T and p i are the vapor pressures of the pure components, and by using Duhem's equation
Any set of y1 and yz is inconsistent if it does not satisfy this condition. In general, any reasonable representation of experimental data will satisfy the stability conditions
The considerable labor which would be required in this calculation is reduced t o a fairly satisfactory amount by the use of suitable approximation formulas like the equations of Margyles,
However, in the case of an interpolation or extrapolation over a wide range these conditions may reveal an inconsistency and thus prove useful by restricting the arbitrariness of the representation.
Y1 =
-
-
cli
4
