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65 NACE INTERNATIONAL: VOL. 54, NO. 5 MATERIALS PERFORMANCE MAY 2015 Data Sensitivity Dunlop stated that the ratio value of 500 wa s vali d , " i g n orin g t emp erature effects and solution imperfections." There is also a tacit assumption in the quality of the thermodynamic data that was used. Since Latimer's data was so old, a new set of thermodynamic data was used to evaluate the effect that more modern data would have upon the calculation. Since it is preferable to use data from a single source whenever possible to maintain consistency, all data used for the comparison were from Naumov 7 except that Berner's 8 value for mackinawite was used. When Latimer's values were replaced with the values from Naumov that appear in Table 1, a ratio of 2070 is calculated instead of 490. Compar- ing the values in the table, there are minor changes in the free energy values, but noth- ing that explained a four-fold increase in the ratio. At this point, a sensitivity analysis was undertaken to better understand the sen- sitivity of the calculation to what seemed to b e minor changes in th e th ermody- namic input values. Dunlop's calculations were repeated using Latimer's data, ex- cept that the free energy value for FeCO 3 was varied by up to 1%, a value that is still larger than the value provided by Naumov. No other input values were altered. As seen in Figure 1, this minor reduc- tion in one variable increased the calcu- lated ratio from 490 to 7,462. The calcula- tion is therefore extremely sensitive to minor chan ge s in th e th ermo dynamic input data. If these small f luctuations did not occur equally in both the numerator and denominator of the CO 2 and H 2 S ratio terms, then fluctuations of over several or- ders of magnitude in ratio could easily re- sult. In most cases, the random nature of variations between the eight thermody- namic values involved in the calculation tends to diminish the magnitude of the change in the ratio. However, any changes that occur will still be magnified, so that even small overall variations can create significant deviations from 500. Temperature Effects The ef fect of temperature upon the ratio was investigated since one of Dunlop's assumptions was that the temperature was 25 °C and that temperature effects would be ignored. Naumov's approach to modify- ing the thermodynamic values for reac- tions as a function of temperature was used. The results of these calculations are shown in Figure 2. Since the calculations for Figure 2 used Naumov's data, the minor variations in val- ues introduced by the temperature adjust- ment calculation combined with the sensi- tivity to th e th ermodynamic data has reduced the starting point ratio at 25 °C from 500 to 15. This is because the temper- ature compensation calculation required additional thermodynamic inputs and the i n c re a s e d n u m b e r of i n p u t v a r i a b l e s increased the sensitivity to variations in quality. The resulting changes in the ratio as a function of temperature when compared to the variations that occur between thermo- dynamic data sets are minor within the temperature range of 25 to 100 °C. The cal- culation was not extended beyond 120 °C because Naumov 's extrapolation process becomes progressively less reliable and there are phase changes that start to occur at the higher temperatures in some of the TABLE 1. THERMODYNAMIC FREE ENERGY VALUES USED IN EVALUATION Species ∆G° Latimer ∆G° Naumov CO 2vapor –94,450 –94,255 H 2 CO 3 –149,170 –148,940 HCO 3 – –140,490 –140,260 CO 3 2– –126,390 –126,170 H 2 S vapor –7,870 –7,955 H 2 S aqueous –6,520 –6,660 HS – 2,950 2,880 S 2– 23,420 20,500 Fe 2+ –20,310 –22,050 FeCO 3 –161,260 –159,350 FeS –22,900 –22,300 H 2 O –56,690 –56,687 FIGURE 1 Plot of calculated ratio as function of % reduction in ∆G FeCO 3 .

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