The Leuchter Report, Revisited

It has been some ten years since my critical analysis of Kenneth Stern's Critique of the Leuchter Report. This article takes a new look at that report, providing additional information and analysis.[*]

I identified ten of Mr. Leuchter's 32 samples as deriving from sheltered locations: samples 4-6 from Krema II and samples 25-31 from Krema I. In assessing average ferric ferrocyanide residue, I assigned a value of 0.99 mg/kg to those samples Alpha Analytic labeled “Non-Detectable” (ND). I do this because a) we know some trace residue ought to be present, even if undetectable, and b) the highest amount that could be present, yet still undetectable, is theoretically 0.99 mg/kg. Obviously, it could be less, but I chose to err on the side of the maximum undetectable value. Given this, my estimate of the average residue value over the ten samples identified from sheltered locations proceeds from the following:

As to the average ferric ferrocyanide residue relative the 20 samples from unsheltered locations:

We readily see the ferric ferrocyandie residue is somewhat less on average for samples deriving from unsheltered versus sheltered locations. This result should not be surprising, however, for although ferric ferrocyanide is insoluble in water, a forty-year period of erosion due to the shearing action of wind and rain would have reduced that part of the original residue exposed at the surface.

As to comparing average ferric ferrocyanide residues between locations that were allegedly homicidal gas chambers versus those that were something else (e.g., undressing rooms, etc.), I must begin by identifying the 19 samples extracted from locations alleged to be gas chambers. These are:

Note: sample #12 was gasket material taken from the Sauna at Birkenau and is not included in my analysis.

Given the residue values already identified above, the average ferric ferrocyanide concentration for alleged execution gas chambers is 1.91 mg/kg. As for samples coming from non-gas chamber locations, we have the following:

The rooms indicated as “unidentified” are ones shown as part of the on-site Krema schematic, but have no name and are not otherwise labeled as “gas chambers.” The room numbers correspond to Fred Leuchter's identification in his 1988 report. Given the sample values identified above, the average ferric ferrocyanide concentration for non-gas chamber locations is 1.67 mg/kg. We note this value is slightly less than for the alleged gas chambers. Yet the difference is small, and it is small to the same degree we found the average difference between sheltered and unsheltered locations. And here is the probable explanation for the difference. For a preponderant number of samples taken from the alleged “gas chambers” are from sheltered locations, whereas a preponderant number of samples taken from other than gas chambers are from unsheltered locations. Fully 9 out of 19 alleged “gas chamber” samples (10 out of 20 sample analyses) are from protected locations, whereas only one out of nine samples representing non-gas chambers are. The higher average ferric ferrocyanide residue in the alleged gas chamber samples is likely due to the fact five times as many of these samples came from locations protected from 40-years' exposure to wind and rain.

The foregoing aside, it is also my estimation there are anomalies in how Fred Leuchter collected his samples, if not also how they were handled and analyzed by Alpha Analytic afterward. For it is my observation Fred Leuchter's samples varied to a large degree in their proportion of surface area to overall mass, and there is no indication Alpha Analytic shaped the samples afterward to achieve a consistent proportionality. Since the residue would essentially be at, and just beneath, the original exposure surface, a sample that is deep rather than broad will have a residue to overall sample mass that is relatively small, and by contrast, a sample that is broad in surface area but not bulky in terms of depth will have a residue to overall sample mass that is relatively large. This, of course, assumes we are talking about samples taken from the same Krema, where periods of gas exposure are hypothetically equivalent. It is, in fact, detection differences for samples from a given Krema which suggest something wrong. Take Krema I for instance: why should we find samples #29 and #30 so different from one another: 7.9 vs. 1.1 mg/kg? Both are taken from the same wall, #29 roughly equidistant from three roof ports, while #30 is equidistant from two roof ports. Those who maintain the exterminationist thesis might say it is the proximity to an additional Zyklon point of entry that is the reason, but I think this would be hasty – there are too many contradictions, e.g., sample 28, taken from Krema I's “washing room,” has roughly the same residue concentration as sample #30 (1.3 vs. 1.1 mg/kg), while sample #27, like sample #29, is also equidistant between three roof ports but has a residue that is “ND.” Furthermore, regarding Krema IV, sample #15 taken from the “chimney room” has that Krema's highest detection level (2.3 mg/kg), whereas sample #14, from the same room, is “ND.” We find even more problems when we compare the different Kremas with their varying usage periods and estimated gas exposures. Krema II was in operation three months longer than Krema III (with an estimated 88 theoretical gassings vs. 74 – see usage rationale in Kenneth Stern's Critique of the Leuchter Report – A Critical Analysis, cited above) and yet, even though three of Krema II's sample locations are sheltered relative to Krema III's samples (all taken from exposed locations), higher detections are found in Krema III than in Krema II. The highest detection, sample #29 (7.9 mg/kg), was taken from Krema I with the least period of use (10 months) while the next highest detection (sample #9: 6.7 mg/kg) came from Krema III with a higher period of use (16 months). Both samples are from protected locations. All in all, it is my belief the anomalies are to be explained by inconsistencies in sample collection. However, this criticism does not undermine Fred Leuchter's basic thrust, for there is one thing his data nevertheless reveal to the detriment of the establishment thesis: the comparable detection levels for samples taken from alleged gas chambers versus rooms within the same facility identified as washing rooms, undressing rooms, Sonderkommando quarters, etc.[1] In other words, Fred Leuchter's broad sample gathering, despite flaws, establishes a reasonable basis for inferring that the presence of cyanide residue is due to benign rather than homicidal purposes.

The question arises as to what degree of ferric ferrocyanide residue one should find given a) exposure for purposes of delousing, and b) exposure for purposes of homicidal extermination? Although I cannot propose to answer this question precisely, there are things we do know which allow us to give an approximate answer. We know, for example, Fred Leuchter's sample #32, the “control sample,” was taken from one of two delousing chambers at Birkenau and revealed a 1,050 mg/kg ferric ferrocyanide residue concentration. In reviewing the sample collection procedure, I believe it is valid.[2] I say this because it appears the breadth to depth ratio maximized the total available residue: the scrapings go only about 0.25 in. deep, a depth at which we can just see white (unreacted) mortar underneath and white (unreacted) mortar at the base of the sample. The reacted mortar starting at the surface is deep blue. This would indicate the presence of the residue of interest, ferric ferrocyanide, or “Prussian Blue,” and to whatever depth some degree of this color is present, we know we have cyanide residue. If we are quantifying this residue as a ratio of the sample mass, we ideally want a sample mass whose depth includes all trace of CN^–, but nothing more (and nothing less). In this way, we can know total CN^– ion that reacted with available iron during the operational life of the delousing chamber . It is important to recognize ferric ferrocyanide would not have a uniform concentration, but would decrease as a function of depth. Cross-sections of our sample would go from dark blue at the surface to unreacted white at the point of termination, indicating progressively less ferric ferrocyanide presence per unit depth. Reaching white is our indication there is little or no further presence of residue. This is the apparent point at which Leuchter's sample ends, and the analytic determination of 1,050 mg/kg ferric ferrocyanide per mass of mortar therefore appears to be a reasonably accurate quantification.

I propose we can use the above determination for comparison with the alleged execution gas chambers. I make this proposal assuming the character of reaction materials, i.e., the constituency of the surface mortar employed in the delousing chambers and alleged execution gas chambers, is roughly the same. As a first approximation, we might assume the reaction rate for 36 HCN + 7 Fe₂O₃ → 2 Fe₄[Fe(CN)₆]₃ + 18 H₂O + 1.5 O₂ to be linear, even though it is not. It is not because as ferro ferriccyanide forms at and beneath the mortar surface, it takes appreciably longer for HCN to reach and react with available iron sesquioxide (Fe₂O₃) further beneath the mortar surface. But as a starting point, we shall assume the reaction rate is constant. Doing so allows us to look at the relatively long exposure experienced by the delousing chambers and compare with the relatively short periods of exposure experienced by the alleged execution gas chambers.

It is Dr. Francisek Piper's view (see interview of 30 May 1996 in My Visit to Auschwitz-Birkenau) the delousing chambers at Auschwitz-Birkenau were “in near continuous use,” with the period of use lasting 24 hours at a time. On the other hand, French pharmacist Jean-Claude Pressac provides an alternate and even more detailed description:[3]

In the delousing chambers, a minimum concentration of 5 g/m³ was used over the course of several daily cycles… This cyanide saturation for 12 to 18 hours a day was strengthened by the heat of the stoves… providing a temperature of 30° Celsius.

We will ignore the temperature and concentration data for the moment and instead focus on the period of use. Here I shall combine the statements of Piper and Pressac by assuming the delousing chambers were in daily use per Piper, applying what Pressac suggests, i.e., an average period of 15 hours per day. As to total time, here another assumption must be made. My assumption is that the Birkenau delousing chambers were at least operating from the time of start up of the first Birkenau gas chamber, Krema II, on 22 March 1943, till shut down of the remaining Birkenau gas chambers, Kremas II, III and V, on 30 October 1944. Likely, the delousing chambers began operating before 22 March 1943 and ran till near the final evacuation of the camp on 18 January 1945, but again, this will serve as a first approximation. Employing this assumption gives us a total delousing chamber time of 587 days @ 15 hours/day, or a total of 528,300 minutes. I now refer the reader to the HCN exposure times for Kremas I – V rationalized in “Kenneth Stern's Critique of The Leuchter Report: A Critical Analysis” (p. 8) to arrive at the following table:

The results are rather startling, for the predicted values are within the ballpark of the average measured values. Recall that the predicted values tell us what we should expect had the alleged gas chambers been used for homicidal purposes. On the other hand, had the facilities merely been fumigated for lice, one fumigation at 900 minutes (the 15-hour mean time based on Pressac), would establish a predicted residue of 1.789 mg/kg, while two fumigations at 1800 minutes (30 hours), would establish a predicted residue of 3.578 mg/kg, etc. Note that for Kremas I, III and V we have measured values, on average, between one and two fumigations, and for Kremas II and IV, something less than one.

As already stated, the foregoing is a first approximation. There are several deficiencies with our predicted values. Following are some of the factors needing further consideration:

1. the true period of operation of the delousing chambers
2. the non-linearity of the reaction rate of HCN with Fe₂O₃ over time
3. the concentration of HCN used in the delousing chambers vs. the alleged execution gas chambers
4. the percentage of iron impurity in the delousing chamber mortar vs. that in the alleged execution gas chambers
5. the operational temperature difference between the delousing chambers and the alleged execution gas chambers
6. the validity of Fred Leuchter's sample collections and the accuracy of their analysis

Rate of reaction is a product of three factors: total number of collisions per unit volume per second, the fraction of collisions having sufficient energy, and the fraction of collisions having proper orientation. The collision frequency depends on how closely the reactants are brought together, i.e., the concentration of Zyklon B (HCN) gas and the density of Fe₂O₃, how large the reactant molecules are and how fast they are moving, which is determined by their weight and temperature. Changing the concentration of HCN and the temperature of reaction will most certainly affect the rate. In the quotation cited above, Pressac states the heat of the stoves provided a delousing chamber temperature of 30°C, but he also says 30°C was the operating temperature of the alleged gas chambers, so there is no difference here. On the other hand, he says the killing of lice requires a concentration of 5 g/m³, and if we assume this is what was used at Birkenau rather than what has been calculated for the alleged gas chambers, we find the HCN concentration for the alleged gas chambers anywhere from four to seven times the concentration used in the delousing chambers.[4] If we hold to the assumptions of our first approximation and vary just this factor, we can now adjust the above table as follows:

Now the predicted residue values are much higher. And whereas the predicted vs. measured value for Krema I now becomes quite proximate, the other predicted values for Kremas II-V become much larger than the measured values. Note that in achieving the revised predicted values, we used an average HCN gas concentration for the various kremas, then divided by the concentration given by Pressac for delousing chambers. This gave us a ratio we could then apply to the original predicted residue. This is reasonable since reaction rate is directly proportional to collision frequency, which, in turn, is linearly dependent on concentration. As the reaction between HCN and Fe₂O₃ progresses, intermediate molecules form which have heavier weight. A heavier weight particle tends to be a slower moving particle at a given temperature, which, of itself, would tend to decrease the collision frequency. The heavier particle, however, is also a larger particle, and the larger size tends to increase collision frequency. These two factors then, weight and size, tend to cancel out, leaving concentration as the key element of collision frequency. Collision frequency, as has been stated, is linearly proportional to reaction rate, i.e., the rate at which ferric ferrocyanide residue is formed.

We do, however, realize that as HCN impregnates the mortar and reacts with Fe₂O₃,virgin Fe₂O₃ becomes less available except at greater and greater depths beneath the mortar surface. This would mean it takes longer for a migrating HCN molecule to find unreacted iron in order to begin the process of forming a ferric ferrocyanide molecule. Dr. James Roth, of Alpha Analytic, has stated he believes all ferric ferrocyanide would reside at a depth no greater than 10 microns. In other words, total penetration of HCN would terminate at about 2.54 × 10^-7 meters. But I believe this is wrong. I believe it is wrong based on the apparent depth of blue stain seen in the control sample Fred Leuchter took from the Birkenau delousing chamber. I also believe it is wrong if Dr. Roth means to imply there is a characteristic about the reaction which makes it depth-limiting. If, on the other hand, Dr. Roth is commenting on the depth of sample necessary to capture the totality of cyanide residues found in the alleged gas chambers, these being relatively marginal, then possibly he is correct, although the theory would assume HCN concentration and total exposure time was uniform for each of the various crematoria and that there are no differences between exposure to mortar vs. brick. Both, in my opinion, are bad assumptions.[5]

This last point brings up yet another way in which our first approximation needs to be refined when comparing the residues found in the delousing chambers vs. those found in the alleged execution gas chambers. Fred Leuchter's samples from the latter were sometimes mortar, sometimes brick, and sometimes both, whereas his sample from the delousing chamber was specifically mortar. To improve on our first approximation, we will need to look at only those gas chamber samples that are materially similar to those from the delousing facility, i.e., those that are uniquely mortar. Again, we are assuming the mortar used in all facilities was roughly the same in terms of percent Fe₂O₃, if not other constituents (silicon oxide, aluminum oxide, calcium oxide, etc.) which characterize the quality of mortar, including its density.

Let us now refine the above table to present measured residue values based solely on collection samples known to be mortar only:

Note that for Krema I, the numbers have not changed: all samples were mortar. For Krema II, sample #4 (roof), #6 (pillar) and # 7 (floor) were retained but all else dismissed and yet the result is the same because all samples were originally “ND.” Krema III now comprises only sample #9 (pillar), whereas Kremas IV and V are N/A, because no samples collected from these sites were specifically mortar (there is no evidence of mortar used as an overlay to the brick for these sites, only intersticial mortar, which Mr. Leuchter removed in conjunction with brick). The net result of our refinement is to make Krema III's measured residue come closer to the predicted residue. On the other hand, the increase represents approximately four 15-hour periods of delousing.

The foregoing is perhaps the only way in which we can address imperfections in Fred Leuchter's sampling or Alpha Analytic's analysis. For by looking at mortar only, we are necessarily focussing on samples with a more limited thickness, where the ratio of residue mass to sample mass would be more uniform.

The only further refinement we can exact is to look at a more probable period of operation for the Birkenau delousing chambers. For initially we took this to be from start up of Krema IV, on 22 March 1943, till shut down of Kremas II, III and V, on 30 October 1944. But indeed, the purpose of the delousing chambers was not necessarily tied to the crematoria, but to the existence of the prison population, and so a more probable end point for the delousing chambers is when Birkenau was evacuated on 18 January 1945. Too, the start up of the delousing facilities may certainly have been earlier than 22 March 1943. But for the sake of examining an expanded period of operation, I think we are going in the right direction, and so let us look at what happens to our predicted ferric ferrocyanide residues for Kremas I, II and III given the above refinement. We are now taking the delousing chamber exposure to be an additional 80 days, for a total of 667 days, or 600,300 minutes (recall Pressac's 15-hour day):

We now find the measured residues for Kremas I and III some 2.5 to 5.5 times higher than the predicted residues. By contrast, the measured residue for Krema II is some three times less than the predicted value. At least four of Krema II's samples are from protected locations (three of which are the basis for the measured residue, above), while all of those from Krema I are. Perhaps the most striking result is that predicted residues are quite small and within the same order of magnitude of what has actually been measured. Furthermore, for Kremas I and III, the measured values are in fact larger than the predicted values. One must be mindful, however, that the measured residues are also in the ballpark of what would prevail had the facilities been subjected to one or several delousing treatments.

It is important to remember we are still assuming a linear rate of reaction and applying this assumption to both the delousing chamber and the alleged gas chambers. The rate, in fact, would be non-linear, relatively high at first, then decreasing over time. This would make our gas chamber predictions higher than what we have so far predicted, but how much so is difficult to estimate. I again go back to the observation made in my article Kenneth Stern Versus “The Leuchter Report”: A Critical Analysis (p. 8), that we must have a better understanding of the rate of reaction between HCN and the mortar and/or brick of the crematoria and delousing chamber walls. Mortar is the primary reaction arena for the delousing chamber and Kremas I, II and III, whereas it is brick (or apparently so) for Kremas IV and V. Because the phenomenon is non-linear, it can only be known in a precise way through development of a rate equation, something that will need to be done through experimental analysis. There is one last consideration. The given predictions for the alleged gas chambers depend on the assumption the mortar used in the delousing chamber is roughly the same as the mortar used in the alleged execution gas chambers. If it can be shown this is not the case, then the above approximations are erroneous. This, of course, applies to differences in temperature, as well.

© 1 October 2007

Notes

[*]

The given re-analysis stems from inquiries made by Nick Kollerstrom, dating from 26 June and 7 July 2007.

[1]

I have reviewed the VHS tape “Leuchter in Poland” (copyright 1988, Samisdat Publishers) documenting Fred Leuchter's sample taking at Auschwitz and Birkenau. In my estimation, there is no doubt the samples taken from Krema I at Auschwitz or the delousing chamber at Birkenau are valid in terms of capturing original exposure surface with minimal (≤ 0.5 in.) depth. The delousing chamber sample, in fact, is a revelation in itself in terms of revealing maximum depth of reaction (≤ 0.25 in.) for mortar surfaces in superabundant contact with HCN. Kremas II – V, however, are less certain in terms of sample consistency. Notes follow:

Krema	Sample #	Notes
II	1	used screw chisel to capture overlay mortar dust to a depth of approx. 0.5 in.; used flat chisel to capture overlay mortar chips; also took some degree of red brick behind overlay mortar chips
	2	used flat chisel to take red brick only, to approx. 1″ depth; breaks brick into pieces
	3	used flat chisel to take red brick only (from rear wall, 4'6″ below grade) to depth between 1 – 2 in.; also takes smaller chips from brick surface; no mortar
	4	flat chisel used to take mortar from ceiling of collapsed roof, approx. 4″ long, 1″ deep
	5	out of camera view; took two chunks from wall underneath collapsed roof, approx. 1″ thickness. Red brick only?
	6	used flat chisel to extract concrete from support Pillar (approx. 1″ deep); location was protected from exterior by collapsed roof
	7	gathered loose sediment from floor, under water; location protected under collapsed roof
III	8	not documented
	9	used flat chisel to extract concrete from support pillar, approx. 0.5″ deep
	10	N. wall: used flat chisel to extract brick and inter-sticial mortar (≥ 1″ depth)
	11	W. wall: used flat chisel to extract brick to depth ≥ 1″
IV	13	removes brick wedge with deep end ≥ 1″, breaks in Half. Not sure which half was retained if not both
	14	used flat chisel to extract brick surface (≤ 0.5″ deep) plus some intersticial mortar
	15	used flat chisel to remove brick surface (depth?); breaks sample into smaller pieces
	16	used flat chisel to remove brick surface, starting at edge, plus some intersticial mortar. Brick is broken into approx. 1″ thick pieces, although deeper sections appear to be retained
	17	used flat chisel to extract brick chips from brick surface (≤ 0.5″ depth) plus interstice mortar
	18	as per sample #17
	19	as per samples 17 and 18
	20	not documented
V	21	used flat chisel to extract brick surface, to include some interstice mortar
	22	as per sample #21. Camera did not reveal how sample was partitioned (and what was retained)
	23	used flat chisel to remove ≤ 0.5″ brick surface plus possibly some interstice mortar (but can't clearly see). Fred breaks up sample, some pieces fall on ground, which he retrieves – which pieces?
	24	not documented

[2]

“Leuchter in Poland,” VHS video recording, copyright 1988, Samisdat Publishers.

[3]

See “Kenneth Stern's Critique of The Leuchter Report: A Critical Analysis” by D.D.Desjardins, 23 March 1997, p. 4.

[4]

See interview with Dr. Piper, My Visit to Auschwitz-Birkenau, May 30-31, 1996, p. 4. Dr. Piper did not know the quantity of Zyklon B gas used in the delousing facilities. Also see Kenneth Stern's Critique of “The Leuchter Report”: A Critical Analysis, p. 6. The analysis lays the basis for estimating the following HCN concentrations for Kremas I – V:

Krema I:	19.5-28.9 g/m3
Krema II:	23.7-35.6 g/m3
Krema III:	23.7-35.6 g/m3
Krema IV:	19.1-28.5 g/m3
Krema V:	19.1-28.5 g/m3

[5]

At least two arguments HCN would be prevented from travelling appreciable depths are, first, that the formation of the relatively large Fe₄[Fe(CN)₆]₃ molecule would form a barrier blocking its path, and, second, the decreasing probability HCN would achieve a successful collision with an available Fe₂O₃ molecule. Regarding the first point, reference to the CRC Handbook of Chemistry and Physics, 71^st Edition, one finds both the crystal ionic radii for Fe⁺², Fe⁺³, C^-4, N^-3, and bond lengths for Fe-C and C-N, and can thereby estimate a worst-case molecular length for ferric ferrocyanide of 116 Angstroms (1.16 x 10^-7 meters). This assumes a straight chain, for which the widest width would be that of C^-4 measuring 2.60A. This gives us an approximate molecular surface area. Next, we must estimate the number of ferric ferrocyanide molecules resident within a given surface plane perpendicular to the HCN trajectory. For this, we might assume the delousing chamber, with its superabundant exposure to HCN gas, presents a case where density of ferric ferrocyanide molecules is maximumized. But we still need chamber measurements and mortar density. And while I do not have this information for the delousing chamber, I do have it for Krema II, where mortar was used for the exposure surface. Here, however, I must assume Krema II's mortar constituency is similar to that of the delousing chamber, e.g., same concentration of impurities, esp. Fe₂O_3. Krema II's floor and ceiling area measures 210 m² with a wall height of 2.4 m, hence giving an overall interior surface area of 559.12 m². From mortar samples removed from Krema II in 1996, laboratory analysis has allowed me to determine an approximate mortar density of 2.35 g/cm³. Calculations now allow us to determine that a 10 micron depth of surface represents 0.334 kg of total mortar, for which, worst case (according to delousing chamber determinations) we would have 0.351 grams ferric ferrocyanide residue. At a molecular weight of 859.253 g/mole, this residue represents 4.08 x 10^-4 moles, or 2.46 x 10²⁰ molecules. If we now assume, worst case, that all ferric ferrocyanide molecules are oriented within a given plane such as to present their maximum surface area toward the HCN trajectory, we might calculate the intersticial free space in order to determine whether an HCN molecule can pass. Since we have chosen the particular worst case orientation, however, we must also account for the fact that a 10 micron depth of surface actually allows for stacking of ferric ferrocyanide, i.e., they are not all within the same plane. Taking the width of the molecule to also be its depth (1.71 Angstroms), we can calculate the number of molecules in any given plane to be 4.21 x 10¹⁵. This represents a total surface area of 0.00835 m² relative a total chamber surface area of 559.12 m² , allowing us to see there is a 66,960:1 ratio of intersticial free space to space occupied by ferric ferrocyanide molecules in a given plane. This means the spacing between any given ferric ferrocyanide molecule is roughly 3630 Angstroms. If we take the HCN molecule to have a length x width of 6.5 x 1.71 Angstroms (again, by reference to bond lengths and ionic radii found in CRC), we see HCN has a wide berth and can readily pass. The effect of accumulating ferric ferrocyanide would therefore not be to halt the reaction at a given depth (e.g., 10 microns) but at worst to slow the reaction by impeding HCN's mean free path. This would be in addition to the fact that over time, available Fe₂O₃ per unit depth is diminished and therefore there is an increasing distance and time in transit of HCN from point of entry to first (successful) collision with an available Fe₂O₃ molecule. The foregoing estimate must be somewhat altered, however, with reference to the Wikipedia. For this source proposes (based on IR and Moessbauer spectroscopy) a cubic molecular configuration for “Prussian Blue.” It is further suggested the overall molecule comprises, in addition to seven Fe atoms and 18 CN molecules, between 14 and 16 water molecules depending on degree of hydration. This obviously changes the molecular weight and therefore the number of moles and number of molecules to be hypothetically found within our 10 microns of Krema II mortar depth, and consequently, the number of molecules resident within a given surface plane. Given as many as 16 water molecules associated with each ferric ferrocyanide molecule, the overall molecular weight is now 1,147.493 g/mole, hence there would be 3.059 x 10^-4 moles, or 1.84 x 10^-20 molecules per 10 micron mortar depth. How many molecules within a given plane and total surface area per molecule, however, would need to be calculated based on a more exact knowledge of how the atoms are configured within the cube. Regardless, I would predict the situation is not appreciably altered, i.e., the resultant spacing between ferric ferrocyanide molecules, cubic rather than planar, would still be amply generous to allow passage of HCN.
The second point, above, regarding the decreasing probability HCN would achieve a successful collision with an available Fe₂O₃ molecule at successive mortar depths likely has validity, but is difficult to assess. As successful collision is based on the probability of proper orientation (which cannot be controlled) but also, and most importantly, the energy factor, i.e., the fraction of collisions that have sufficient energy to break bonds in order to form new ones. This factor depends upon temperature and the energy of activation particular to each reaction. The case can perhaps be made there is a temperature gradient, decreasing with increasing depth into the reaction surface, but as I have no data on this matter, I cannot pursue it.