1 JOURNAL OF RESEARCH of the National Bureau of Standard-A. Phyic and Chemitry Vol. 81 A, No. 1, January-February 1977 Humidity Fixed Point of Binary Saturated Aqueou Solution Lewi Greenpan Intitute for Baic Standard, National Bureau of Standard, Wahington, D. C (October, 19) An evaluated compilation of equilibrium relative humiditie in air veru temperature from pure phae to approximately 10 5 pacal (1 atm) in preure i preented for 28 binary aturated aqueou olution. The relative humiditie of the olution range from about to 98 percent. Uing a data bae from 21 eparate invetigation compriing 1106 individual meaurement, fit were made by the method of leat quare to regular polynomial equation with two through four coefficient. Equation and table are preented along with the etimated uncertaintie in the correlated reult. Key word: aqueou olution; equilibrium; humidity; relative humidity; alt; aturated alt olution; vapor preure; water vapor. 1. Introduction Reearch, hygrometer calibration, teting and material conditioning often require the accurate control of humidity in a working pace. The common method of controlling the humidity accurately ue either a humidity generator [1A] 1 or the equilibration of a cloed pace with a chemical ytem [IB] which produce the deired equilibrium vapor preure. Humidity generator tend to be expenive and complex wherea equilibration with chemical ytem that provide fixed point i a relatively inexpenive and imple method of humidity control. Among the chemical ytem ued for thi purpoe are aqueou ulphuric acid olution, glycerine and water olution and ingle and binary alt olution. Each uch olution offer a degree of humidity adjutment that can be achieved by changing it concentration. On the other hand, pecial problem are aociated with the ue of olution becaue their concentration mut be meaured and controlled. Not only mut the concentration of the olution be determined initially but the preence of any humidity ource or ink in the controlled pace and even the initial equilibration proce of the pace can alter the olution concentration. An epecially ueful method of humidity control by chemical ytem involve the ue of binary aturated aqueou olution (primarily of ingle alt) in which the olute i highly non-volatile. At any temperature, the concentration of a aturated olution i fixed and doe not have to be determined. By providing exce olute, the olution will remain aturated even in the preence of modet ource or ink. Where the olute i a olid in the pure phae, it i eay to determine that there i indeed aturation. Due to the eae of it ue, thi i a popular method of humidity control. Since a given aturated alt olution provide only one relative humidity (RH) at any deired temperature, a different relative humidity mut be achieved by electing another appropriate alt. Though much data on aturated alt olu- 1 Figure in bracket indicate the literature reference at the end of thi paper. tion have been produced and many compilation of the equilibrium relative humiditie of elected aturated alt olution exit, there are no compilation for which the data have been critically analyzed and etimate of the uncertaintie involved given, a tep which i abolutely eential to the implimentation of the concept of fixed point. We have moved to fill thi gap by compiling, from the literature, data on a ufficient variety of aturated alt olution to cover the entire range of relative humidity at reaonably cloe interval. We have adjuted thee data [1-21] to be conitent with temperature on IPTS-68 and the mot recent equation for the vapor preure of water . We have alo analyzed the experimental technique ued in obtaining the original data and have made etimate of the uncertaintie in the original data. We have then ued thee data to calculate "bet" value of relative humidity in air a a function of temperature from pure phae to approximately 10 5 pacal (1 atm) in preure for thee aturated olution. 2. Background The method ued by invetigator to determine the water vapor in equilibrium with aturated alt olution are divere. A hort decription of the variou method ued in the referenced paper i of interet. (1) The direct meaurement of the vapor preure. A chamber containing a aturated alt olution at a controlled temperature i firt evacuated to remove all gae. Evaporation from the olution i then allowed to proceed until the ambient vapor, eentially all water, ha come to equilibrium with the olution and a direct determination of the total preure within the chamber i made by conventional preure meaurement technique. (2) Dew point meaurement. The dew point of the ga within a chamber containing a aturated alt olution at controlled temperature i meaured by mean of a cooled mirror within the chamber. Uing vapor preure table or equation, thi dew point i converted to the vapor preure of water. () Iopietic vapor preure meaurement. The vapor pre- 89
2 ure of a aturated alt olution in one cell or chamber i allowed to come to equilibrium with a cell or chamber containing a reference olution at a fixed temperature. The reference olution mut be well characterized a to vapor preure a a function of concentration at the reference temperature. Under the equilibrium condition, the equilibrium vapor preure of the aturated alt olution i identical to the equilibrium vapor preure of the reference olution. After the two cell have reached equilibrium, the concentration of the reference olution i determined (uually by weighing) and the vapor preure i calculated. (4) Relative vapor preure meaurement. A chamber containing a aturated alt olution and a chamber containing pure water or other well characterized olution are each evacuated to remove all non-water vapor gae. The two chamber are maintained at the ame temperature and the abolute preure of the aturated alt olution i meaured a in the firt method. In addition the preure difference between the two chamber and/or the preure of the reference olution i determined. The ratio of the vapor preure of the aturated alt olution to the vapor preure of the water i the activity (or relative humidity) of the aturated alt olution. (5) Meaurement with a calibrated humidity enor. A chamber containing a aturated alt olution and a humidity enor are brought to equilibrium at a controlled temperature. Calibration of the enor before or/and after the meaurement provide the mean of determining the equilibrium vapor preure. (6) Gravimetric determination. Dry ga i paed through the binary aturated olution at a fixed temperature. The water vapor in the effluent ga i aborbed by a deiccant and meaured by weighing. The volume of the ga i alo determined. From thee the vapor preure or the mixing ratio can be determined. A one would imagine, the error aociated with thee method differ a to ource and magnitude. The error in any of the method are alo function of the level of vapor preure being meaured a well a the temperature of the aturated alt olution. There i, therefore, probably no one method that give a bet meaurement under all condition.. Method We have accumulated experimental data from variou reearcher [1-21] and calculated "bet" value of relative humidity and the aociated uncertaintie of thoe value. Typical method of calculating or recalculating the relative humidity and aociated uncertaintie for the variou invetigation are given in the Appendix. Our data bae conit of 21 invetigation and include ome of the mot cited work in the field. In total, 1106 individual calculation of relative humiditie and aociated uncertaintie were made which involved 89 aturated olution. Not all data nor all aturated olution in thi tudy were found atifactory for ue. The original data were corrected to be conitent with temperature on IPTS-68, with the mot recent formulation for the vapor preure of water  and with the mot recent equation for the enhancement of water vapor in air . The computed relative humidity data were then collated and fitted by the method of leat quare to regular polynomial a a function of temperature in degree Celiu (IPTS-68). In the fitting proce, each datum wa weighted inverely proportional to the etimated uncertainty of the datum. The order of the polynomial ued in the fit wa determined by an F-tet or by analyi of the reult of fit to variou order. An arbitrary deciion wa made not to ue any order higher than. Alo, no data at temperature below 0 C or above 104 C were ued in the fit. In the fitting proce, the tandard deviation of the predicted value wa computed for each datum. Thee tandard deviation were themelve fitted to a quadratic equation, a a function of temperature, by the method of leat quare. At any deired temperature for a given aturated alt olution, the tandard deviation of the predicted value wa calculated uing the appropriate quadratic equation. Three time thi value wa then aigned a the etimated uncertainty for the correponding value of relative humidity, with certain exception dicued below. Thi i the value which appear in table 2. Where a number of invetigation of the ame olution exited and the relative humidity v temperature reult of one invetigation were completely inconitent with the reult of the other invetigation, the data of the deviant invetigation were eliminated and a new fit made. The data ued in thi paper met one of the following criteria: (1) a large number of invetigation were included and exhibited a mall reidual tandard deviation of the relative humidity v temperature fit; (2) although few invetigation were included, the method of meaurement wa judged to be uperior and etimate of the uncertaintie of the original meaurement themelve were mall; and () the data were in a relative humidity range which wa not approximated by any of the other binary aturated olution. 4. Reult Table 1 contain coefficient for the data of the elected alt fitted to an equation of the form: RH = 2 4/ 1=0 where RH i in percent and t i in C (IPTS-68). The alt are lited in acending order of RH at 25 C. Alo included in table 1 i the reidual tandard deviation of the fit, the range of temperature over which the fit wa performed and reference for the fundamental data that were involved in that particular fit. Table 2 give the calculated relative humiditie for each of the binary aturated olution at 5-degree interval along with the etimated uncertaintie in relative humidity at each of the temperature. The aturated alt olution are preented in the ame order a in table Dicuion Although the method ued for fitting the data gave no problem, the aignment of weight to each datum required ome judgment. Three method of weighting were conidered: (1) weight were aigned inverely proportional to the variance of the individual datum where the variance wa taken a the quare of the total uncertainty; (2) weight were aigned inverely proportional to the etimated total uncertainty of the individual datum; and () weight of unity were aigned to all data. All of the data were fitted three time, once for each type of weighting. The reult were aembled into three table of 90
3 ^max Data Source (a) 2, 17 2, 14 2, , 16 1,, 10, 11, 17, 18, 20 11, 14 2, 14 11, 14, 17 6, 14 1, 7, 11, 14, 17, 19, 21 1, 6, 11, 14 8, 14, 17 1, 8, 17, 19, 21 2, 6, 11, , 6 1, 17 1, 6, 9, 17 1, 6, 8, 11,, 1, 15, 17, 19, 21 9, 11 1, 6, 17 9, 18, 20 1, 6, 8, 9,, , 17, 19, 21, 19, 21, 17 TABLE 1. Summary of Leat Square Fit to RH = 2 Ait 1 for Selected Saturated Salt Solution i = 0 Salt A Q Ay A 2 A cr No. of Point ^min Ceium Fluoride Lithium Bromide Zinc Bromide Potaium Hydroxide Sodium Hydroxide Lithium Chloride Calcium Bromide Lithium Iodide Potaium Acetate Potaium Fluoride Magneium Chloride Sodium Iodide Potaium Carbonate Magneium Nitrate Sodium Bromide Cobalt Chloride Potaium Iodide Strontium Chloride Sodium Nitrate Sodium Chloride Ammonium Chloride Potaium Bromide Ammonium Sulfate Potaium Chloride Strontium Nitrate Potaium Nitrate Potaium Sulfate Potaium Chromate : x 10-* X 10~ x 10~ X 10~ 2 ' X 10" x 10~ x 10~ X 10~ 2 56 x 10" X X 10~ X lo x 10" X X 10" x 10~ X 10~ X 10~ x 10~ x lo' x x 10~ x 10~ x 10~ X X X 10" X 10~ x 10" (a) Number correpond to reference.
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5 2 '«II 2 J $ B (NO\oin ^ oo io eg - O to io io c^ c^ o^ c?^ io ^ OCOCOONOO LO CO CNJ (N CO CO i < CO CO relative humidity at 5-degree interval. Each calculated value of relative humidity wa aigned an uncertainty equal to three time the tandard deviation of the predicted value. A might be expected, the calculated relative humiditie and the correponding uncertaintie differed for each of the three weighting. For the aturated olution choen for preentation in thi paper, it wa noted with ome atifaction that all relative humiditie calculated from the three differently weighted fit agreed with each other to within the aigned uncertainty for each. A weighting inverely proportional to the quare of the etimated total uncertainty for each datum wa judged to be inappropriate. Although it i common to aign weight proportional to the invere of igma quared uch an approach i uually baed on a igma which i tatitically determined. Thi i not the cae here. The method ued to obtain the etimated total uncertainty i given in the Appendix. It wa felt that the ue of the quare of the etimated uncertainty would have placed an unacceptably high value on the author' etimate of the error contributing to the total uncertainty. Some invetigator did not provide ufficient information in their publication to make poible completely objective etimate of their error. In thoe cae, the etimated total uncertainty included component baed on the author' ubjective judgment. A weighting of unity wa likewie unatifactory ince it would in no way take into account the innate difference in uncertainty due to method, temperature and relative humidity range, nor would it place any reliance on the author' judgment of the quality of the reearch. A weighting proportional to the invere of the etimated uncertainty appeared to be a reaonable compromie between the other extreme and all data preented in thi publication were proceed uing that weighting method. Where the data for a particular aturated alt olution included a number of invetigation, three time the tandard deviation of the computed value were accepted a the etimated uncertainty. Where the data were baed only on one or two invetigation it i evident that elf conitent data, though quite inaccurate, could give mall etimated tandard deviation of the computed value. It i alo evident that uch tandard deviation are not a valid etimate of uncertainty. Under thoe circumtance where the reult from fitting the polynomial equation to the original data for any aturated alt olution gave value for three time the tandard deviation of the predicted value that were le than the etimated total uncertainty of the original data, it wa the etimated total uncertainty of the original data which wa ued a the final etimate of uncertainty for the calculated "bet" value of relative humidity. The data preented in table 2 are given at 5 C interval over the temperature range of the original data with extrapolation beyond thee range never exceeding 2.5 C. All calculated value of relative humidity are given to 1 percent relative humidity. Thi doe not in any way imply an accuracy of 1 percent. The deignated etimated uncertaintie till give the bet prediction of accuracy. It wa felt that to fail to give the relative humiditie to.01 percent would be dicarding information, imprecie a it might be. Since the etimated uncertaintie are given, we ee no problem with preenting the value of relative humidity with figure far beyond their etimated uncertaintie. The uncertaintie preented do not include uncertaintie in the vapor preure equation  or enhancement equation 9
6 b C c d e TABLE. Comparion of Relative Humidity Value of Selected Saturated Salt Solution for Variou Compilation Relative Humidity, % Saturated Salt 10 C 20 C 0 a b c d a b c d e f a b c d e i f a Potaium Hydroxide Lithium Chloride Potaium Acetate Magneium Chloride Sodium Iodide Potaium Carbonate Magneium Nitrate Sodium Bromide Cobalt Chloride Potaium Iodide Sodium Chloride Ammonium Chloride Potaium Bromide Ammonium Sulfate Potaium Chloride Potaium Nitrate Potaium Sulfate a Value from thi work. b Value from reference 24 and 25 which are identical. c Value from reference 26. d Value from reference 27. e Value from reference 28. f Value from reference 29.
7  ued. The reult preented are therefore for the exact value of reference  and . The enhancement factor for a aturated alt olution in air i not known preciely. Analyi of the factor involved indicate that at one atmophere preure or le, the difference between the enhancement factor over a aturated alt olution and over pure water i negligible. That i not the cae at high preure. The data preented are therefore conidered valid near or below one atmophere total preure. If aturation vapor preure value other than thoe given by Wexler  are ued, the relative humiditie hould be multiplied by the ratio of thee aturation vapor preure to thoe of Wexler. Many compilation of non-critically evaluated data on the equilibrium humidity of aturated alt olution exit [24-8]. Table i a comparion of value from thi work and correponding value taken from five of thee other compilation at four temperature. Of the lited compilation, only thi work (column a) and Hickman' work (column d) give the ource of the data. Hickman' value (in column d) were directly copied from hi cited reference without modification. None of the compilation other than our (column a) give etimate of uncertainty. Therefore, one would logically conclude that the author of thoe compilation conider their value to be uncertain only in the lat figure preented. It i alo likely that ome of the value in one compilation came from the ame ource a the value in other compilation uch a relationhip appear to exit between column b and column d. If we aume an uncertainty of 1/2 of the lat digit in the value given in thee other compilation, and if we add that uncertainty to the etimated uncertainty for the correponding value in column a, we find that the value in column a (the reult of thi work) agree with the value in at leat one of the other compilation to within thi compoite uncertainty at all point, except for: Potaium carbonate at 10 C Sodium bromide at 20 C Ammonium chloride at 0 C Potaium bromide at 10 C, 20 C, and 0 C Potaium chloride at 10 C, and 20 C It hould be noted that thi comparion of compilation i over a limited temperature range and for only 17 of the 28 alt olution evaluated and collated in thi paper. 6. Appendix In all cae, the mot fundamental meaurement preented were ued to calculate the actual relative humidity obtained by each invetigator for each datum. No attempt wa made to evaluate purity of water or olute or it effect in any invetigation. A a firt tep, all temperature were converted from the temperature cale in which the data were preented into IPTS-68 temperature equivalent. Where the temperature cale were not given, a judgment wa made a to the mot likely temperature cale ued, baed on the date of the reearch. Likewie, where vapor preure baed on vapor preure equation or table were given, thee were converted to new vapor preure baed on the Wexler formulation. In the cae of reported relative humiditie baed on dew-point meaurement, the dew-point temperature wa recontructed from a knowledge of the vapor preure equation ued. From the reported control temperature and the recontructed dew-point temperature a new relative humidity wa calculated uing the Wexler and Greenpan equation for vapor preure and enhancement factor, repectively. Where the iopietic method wa ued with ulfuric acid a the iopietic olution, the value of Shankman  for ulfuric acid activity were ued to determine the relative humidity of the aturated alt olution. Thi wa done (1) for conitency, becaue many of the reearcher had done likewie; (2) becaue Shankman decribed hi experimerftal work in ufficient detail to enable u'to judge it quality and to etimate the uncertainty in hi work; and () hi value appeared to be the mot accurate available. In determining etimate of total uncertainty for each datum, the uncertainty wa taken a the quare root of the um of individual uncertaintie (in term of relative humidity) quared a decribed by Ku . Individual uncertaintie involved in the individual meaurement were obtained from the invetigator' own etimate where thee eemed reaonable. Where the invetigator did not preent a reaonable etimate of uncertainty for a particular parameter, thi author made hi own etimate of the uncertainty of that parameter baed on hi judgment of the invetigator' work and hi etimate of the tate of the art at the time of the invetigation. The relative humidity uncertainty aociated with each of the parameter uncertaintie wa obtained by calculating the relative humidity with and without the uncertainty added to the related parameter, the difference being the relative humidity uncertainty for that particular parameter. In ome cae the individual parameter uncertaintie are not independent in their effect on the relative humidity uncertainty. A cae in point i the relative vapor preure meaurement method. In thi technique, the individual temperature and preure meaurement uncertaintie are of no great conequence, it i the etimate of the temperature difference and the preure difference in the two preure meaurement that are ignificant. In addition, an etimate of the degree of equilibrium achieved i of ignificance. In thee type of ituation, etimate of the difference were ued in lieu of etimate of the individual meaurement. In the cae of the relative humidity enor calibration technique, an etimate of the calibration uncertainty a well a temperature uncertainty were ued. In the iopietic technqiue, the relevant uncertaintie are the temperature difference, the concentration determination, the uncertainty in equilibrium and the uncertainty in the reference olution data. Compoite uncertaintie for each datum baed on the quare root of the um of the individual parameter uncertaintie quared were thu obtained. A tated earlier, thee etimate of uncertaintie are the reult of ubjective judgment a well a objective etimate. For the great preponderance of data preented in thi paper, thee judgment have a minor effect on the relative humidity value a well a the total uncertainty, a wa hown by the mall difference obtained for the three different method of weighting. 95
8 7. Reference [1A] Wexler, A., Calibration of humidity meauring intrument at the National Bureau of Standard, ISA Tranaction, 7, No. 4, 56 (18). [IB] Wexler, A., and Brombacher, W. G., Method of meauring and teting hygrometer, Nat. Bur. Stand. (U.S.), Circ. 5, 1 (1951).  Acheon, D. T., Vapor preure of aturated aqueou alt olution, Humidity and Moiture, Vol. (Reinhold Publihing Corporation, New York, 15) p  Acheon, D. T., Vapor Preure of Saturated Aqueou Solution of Selected Inorganic Salt, Mater of Science Thei, Department of Phyic Univerity of Maryland (15).  Applebey, M. P., Crawford, F. H., and Gordon, K., Vapor preure of aturated olution. Lithium Chloride and lithium ulphate, J. Chem. Soc, 11, 1665(194).  Baxter, G. P., and Laning, J. E., The aqueou preure of ome hydrated crytal. Oxalic acid, trontium chloride and odium ulfate, J. Am. Chem. Soc, 42, 419 (1920).  Baxter, G. P., and Cooper, W. C, Jr., The aqueou preure of hydrated crytal. II. 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