| The propagation of random errors in the process of calculating the activity coefficients of all other components from the activity coefficient of one component in a multicomponent system is analyzed on the basis of isopiestic experiments. The analysis gives several views about the control of the errors and the array of the experimental molalities during the experiments. The isopiestic method is systematically studied, and the study includes theoretical analysis and experimental investigation. The theoretical analysis includes the analyses of the temperature factor and the various individual equilibration processes in isopiestic experiments. And the analysis gives several conclusions about the temperature control, the order of the rates of various equilibration processes, etc. On the basis of our theoretical analysis and the improvements introduced by the other researchers, a new apparatus was designed and manufactured. Using this apparatus and the experimental procedure suggested by us, we have done a lot of experiments on NaOH solutions. On the basis of the experimental results, we discussed the evacuation process, the consistence among the molalities of the solutions in small cups in equilibrium, the whole equilibration process, and the determined osmotic coefficients of NaOH solutions. And the results show that our apparatus possesses the following characteristics: 1) The inside of the apparatus can reach a very uniform experimental temperature within a short time, and the consistent equilibrium temperature among the samples can satisfy the requirement of the experiments on the samples of much less than 0.05 mol/kgH2O. 2) The equilibration process is essentially determined by the changes of the reference standard solutions in the small cups, therefore the apparatus hasfavorable reliability and stability in the equilibration process, and it is suitable for the experiments on solutions, which are sluggish, very complex, unstable, and of other disadvantageous properties. 3) The equilibration is fairly fast, which is practical for the samples of the molality less than 0.05 mol/kgH2O. 4) It is easy and effective to decide the end point of the equilibration. 5) The equilibration process can be described approximately by the equation,Our study on the selection of basic species or components for a system gives several criteria. According to these criteria and the other researchers' studies, NaAl(OH)4, NaOH and H2O are selected as the basic components in the sodium aluminate solution system. The isopiestic method is seleted in our study on the sodium aluminate solution. By using our specially designed and manufactured isopiestic apparatus, the osmotic coefficients at 313.2 K were measured for the NaOH-NaAl(OH)4-H2O system with the total alkli molality, mNaOHT (mNaOH+mNaAl(OH)4), from 0.05 mol/kgH2O to 12 mol/kgHbO and aK (mNaOHT/ mNaAl(OH)4) from 1.64 to 5.53. The mean standard deviation of the measurements is 0.0038. The Pitzer model was used to regress the measured osmotic coefficients with two sets of reference Pitzer model parameters for NaOH(aq). Several sets of the Pitzer model parameters for NaOH-NaAl(OH)4-H2O system were then obtained. One set of the results is as follows: B(O)naOH: 0.08669, B(1)NaOH: 0.31446, B(2) -0.00007367, CNaOH: 0.003180, B(0)NaAl(OH)4: 0.03507, B(1)NaAl(OH)4: 0.02401, CNaAl(OH)4: -0.001066, oh-al(OH)4: 0.08177, Na+OH-Al(OH)4-: -0.01162. The mean standard difference between the calculated and the measured osmotic coefficients is 0.0088. With the obtained Pitzer model parameters, we also calculated the values of K'=(rNaAl(OH)4,cal2mAl(OH)4-,exp)/(rNaOH.cal2 mOH-,exp) for the reference gibbsitesolubility data. The results show that the obtained Pitzer model parameters are reliable, and the relative error of the calculated activity coefficients with our Pitzer parameters should be less than 2.1%. We also estimated the NaAl(OH)4(aq) Pitzer model parameters at other temperatures, and compared the calculated gi...
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