============================================================================== SOLUBILITY EQUILIBRIA: THE COMMON ION EFFECT, DONE EXACTLY ============================================================================== Seed: 20250306 (numpy default_rng, PCG64) numpy version: 2.4.2 Python version: 3.12.3 ============================================================================== PART 1. VALIDATION ============================================================================== --- V1. Mass balance, equilibrium expressions and Ksp: residuals at every grid point --- Grid checked: 192 (C, pH) points per salt, 576 total solves. worst relative residual, baio3 : 7.903e-16 (3.6 eps) worst relative residual, caf2 : 6.645e-16 (3.0 eps) worst relative residual, agcl_ksp : 1.460e-16 (0.7 eps) worst relative residual, agcl_mass_ag : 4.033e-16 (1.8 eps) worst relative residual, agcl_mass_cl : 3.968e-15 (17.9 eps) worst relative residual, agcl_beta : 2.654e-16 (1.2 eps) --- V1b. Charge balance closure: two independent derivations of the same titrant, compared --- worst |Ca_A - Ca_B| / |Ca_B|, baio3 : 9.529e-09 (42915354.2 eps) worst |Ca_A - Ca_B| / |Ca_B|, caf2 : 1.137e-10 (512160.7 eps) worst |Ca_A - Ca_B| / |Ca_B|, agcl : 4.604e-09 (20735895.5 eps) --- V2. Closed-form cubic (np.roots) vs bisection solver, Ba(IO3)2 and CaF2 --- salt C (M) bisection x cubic root x rel. diff Ba(IO3)2 0.00e+00 7.3217246238e-04 7.3217246238e-04 1.481e-16 Ba(IO3)2 1.00e-04 6.9922427186e-04 6.9922427186e-04 1.551e-16 Ba(IO3)2 1.00e-02 1.5602491445e-05 1.5602491445e-05 2.172e-16 Ba(IO3)2 1.00e+00 1.5700018372e-09 1.5700018372e-09 9.220e-16 CaF2 0.00e+00 2.1347174563e-04 2.1347174563e-04 1.270e-16 CaF2 1.00e-04 1.8150693024e-04 1.8150693024e-04 8.960e-16 CaF2 1.00e-02 3.8905733912e-07 3.8905733912e-07 1.361e-16 CaF2 1.00e+00 3.8911788766e-11 3.8911788766e-11 1.661e-16 --- V3. AgCl pure-water solubility: solver vs closed form vs literature --- Solver (full coupled system, C=0): 1.349860e-05 mol/L Closed form sqrt(Ksp) (no complexes): 1.330413e-05 mol/L (rel. diff from solver: 1.462e-02) Literature value (e.g. common general-chemistry tables): 1.330e-05 mol/L (rel. diff: 1.493e-02) Ba(IO3)2 pure-water solubility, solver: 7.321725e-04 mol/L Closed form (Ksp/4)^(1/3): 7.321722e-04 mol/L (rel. diff: 3.922e-07) Commonly quoted value: 7.320e-04 mol/L (rel. diff: 2.356e-04) --- V4. AgCl solubility minimum: internal check, then against the literature --- Free [Cl-] at minimum, ternary search on solver's own x(c): 3.010826e-03 M Free [Cl-] at minimum, exact quartic root (np.roots): 3.010826e-03 M Relative difference (internal consistency of two independent numerical routes): 4.671e-09 Corresponding added common-ion concentration at the minimum: C = 3.0108e-03 M NaCl Solubility at the minimum: x = 3.1147e-07 M Range widely reported in analytical-chemistry teaching for where this minimum falls: 1.0e-03 to 1.0e-02 M Cl- (order-of-magnitude description, e.g. [1][2]) Club's computed minimum falls inside that range (log10 distance from nearer edge: 0.00 decades). HONEST NOTE: this is a comparison to a range quoted to one significant figure in secondary sources, not to a single re-verified primary number; see the article SS10 and V5 below. --- V5. Monte Carlo: how much does the reversal depend on the uncertain formation constants? --- N = 100000 draws, log10(beta_n) ~ Normal(reported, 0.05) independently for n=1..4 log10(C_min / M): mean = -2.5212, SE = 0.0001 => C_min = 3.012e-03 M (a factor-of-1.00 1-SE band) Enhancement ratio x(5 M)/x(minimum): mean = 16164.8, SE = 6.50 Fraction of draws where 5 M chloride dissolves MORE AgCl than the minimum does: 100.0000% (A value near 100%% means the reversal's existence is essentially certain under this assumed uncertainty, even though its exact location and size are not.) Convergence trace (n draws, running mean log10 C_min, running SE): n= 10 mean=-2.5321 SE=0.0036 n= 25 mean=-2.5254 SE=0.0041 n= 66 mean=-2.5249 SE=0.0028 n= 170 mean=-2.5233 SE=0.0019 n= 437 mean=-2.5214 SE=0.0012 n= 1125 mean=-2.5212 SE=0.0008 n= 2894 mean=-2.5210 SE=0.0005 n= 7443 mean=-2.5212 SE=0.0003 n= 19144 mean=-2.5210 SE=0.0002 n= 49238 mean=-2.5212 SE=0.0001 ============================================================================== PART 2. THE THREE SALTS ACROSS THE GRID ============================================================================== --- Table data: summary per salt --- salt Ksp n(anion) pure-water x C at min (M) max enhancement* Ba(IO3)2 1.570e-09 2 7.3217e-04 none (monotone) 1.00 (never reverses) CaF2 3.890e-11 2 2.1347e-04 none (monotone) 1.00 (never reverses) AgCl 1.770e-10 1 1.3499e-05 3.0108e-03 16164.8 * solubility at 5 M common ion divided by solubility at the minimum (AgCl only; the other two salts have no minimum because they have no complexation channel modelled). --- Figure 1 data: AgCl solubility vs added [Cl-], exact solver and naive rule, pH=7 --- i C_added (M) x_exact (M) x_naive (M) 0 1.000000e-07 1.344869e-05 1.770000e-03 3 2.704703e-07 1.336405e-05 6.544158e-04 6 7.315416e-07 1.313786e-05 2.419548e-04 9 1.978602e-06 1.254605e-05 8.945708e-05 12 5.351531e-06 1.108930e-05 3.307465e-05 15 1.447430e-05 8.102650e-06 1.222857e-05 18 3.914868e-05 4.288238e-06 4.521226e-06 21 1.058855e-04 1.842224e-06 1.671617e-06 24 2.863889e-04 8.163730e-07 6.180408e-07 27 7.745967e-04 4.375686e-07 2.285060e-07 30 2.095054e-03 3.193060e-07 8.448471e-08 33 5.666497e-03 3.359148e-07 3.123623e-08 36 1.532619e-02 5.077512e-07 1.154886e-08 39 4.145278e-02 1.038694e-06 4.269918e-09 42 1.121174e-01 2.665256e-06 1.578702e-09 45 3.032443e-01 8.848898e-06 5.836877e-10 48 8.201858e-01 4.864093e-05 2.158048e-10 51 2.218359e+00 5.234240e-04 7.978873e-11 54 6.000000e+00 8.345932e-03 2.950000e-11 --- Figure 2 data: CaF2 solubility vs pH at fixed C = 1e-3 M NaF --- i pH CaF2 x (M) CaF2 naive AgCl x (M), C=1e-3 0 0.00 2.783797e-02 3.890000e-05 3.904791e-07 2 0.36 1.579777e-02 3.890000e-05 3.904790e-07 4 0.73 8.911796e-03 3.890000e-05 3.904790e-07 6 1.09 4.976875e-03 3.890000e-05 3.904789e-07 8 1.45 2.733082e-03 3.890000e-05 3.904789e-07 10 1.82 1.460668e-03 3.890000e-05 3.904789e-07 12 2.18 7.494644e-04 3.890000e-05 3.904789e-07 14 2.55 3.661886e-04 3.890000e-05 3.904789e-07 16 2.91 1.753684e-04 3.890000e-05 3.904789e-07 18 3.27 9.105671e-05 3.890000e-05 3.904789e-07 20 3.64 5.710735e-05 3.890000e-05 3.904789e-07 22 4.00 4.363319e-05 3.890000e-05 3.904789e-07 24 4.36 3.813203e-05 3.890000e-05 3.904789e-07 26 4.73 3.582312e-05 3.890000e-05 3.904789e-07 28 5.09 3.483812e-05 3.890000e-05 3.904789e-07 30 5.45 3.441452e-05 3.890000e-05 3.904789e-07 32 5.82 3.423169e-05 3.890000e-05 3.904789e-07 34 6.18 3.415264e-05 3.890000e-05 3.904789e-07 36 6.55 3.411844e-05 3.890000e-05 3.904789e-07 38 6.91 3.410364e-05 3.890000e-05 3.904789e-07 40 7.27 3.409724e-05 3.890000e-05 3.904789e-07 42 7.64 3.409446e-05 3.890000e-05 3.904789e-07 44 8.00 3.409326e-05 3.890000e-05 3.904789e-07 AgCl range over this pH sweep: max/min = 1.000000 (i.e. 0.0000% variation) --- Figure 3 data: relative error of the naive textbook rule for AgCl, vs [Cl-] --- i C_added (M) rel. error (naive-exact)/exact 0 1.000000e-07 1.306113e+02 3 2.704703e-07 4.796836e+01 6 7.315416e-07 1.741660e+01 9 1.978602e-06 6.130299e+00 12 5.351531e-06 1.982573e+00 15 1.447430e-05 5.092063e-01 18 3.914868e-05 5.433176e-02 21 1.058855e-04 -9.260934e-02 24 2.863889e-04 -2.429431e-01 27 7.745967e-04 -4.777825e-01 30 2.095054e-03 -7.354115e-01 33 5.666497e-03 -9.070114e-01 36 1.532619e-02 -9.772549e-01 39 4.145278e-02 -9.958891e-01 42 1.121174e-01 -9.994077e-01 45 3.032443e-01 -9.999340e-01 48 8.201858e-01 -9.999956e-01 51 2.218359e+00 -9.999998e-01 54 6.000000e+00 -1.000000e+00 Naive rule crosses +100% relative error at C >= 1.0000e-07 M At C = 5 M (near-saturated NaCl), naive predicts x = 3.540e-11 M; exact solver gives x = 4.956e-03 M naive is wrong by a factor of 140012147.7, and wrong in DIRECTION below C=3.011e-03 M --- Figure 4 data: two-ligand regime map, Ag+/Cl-/NH3, sign of d(ln x)/d(ln[Cl-]) --- Grid: 26 x 26 points, [Cl-] in [1e-6, 5] M, [NH3] in [1e-6, 2] M, pH=7. Points where d(ln x)/d(ln[Cl-]) > 0 (rule reverses): 222 of 676 (32.8%) Sample rows (NH3 index, [NH3] M, then sign pattern across the Cl- axis, - = holds, + = reverses): i= 0 [NH3]=1.000e-06 -------------+++++++++++++ i= 5 [NH3]=1.821e-05 --------------++++++++++++ i=10 [NH3]=3.314e-04 --------------++++++++++++ i=15 [NH3]=6.034e-03 ------------------++++++++ i=20 [NH3]=1.099e-01 ----------------------++++ i=25 [NH3]=2.000e+00 -------------------------+ Default interactive-model condition ([Cl-]=1e-3 M added, [NH3]=0): x=3.9048e-07 M, matches the plain-AgCl solver at the same C to within 0.000e+00 (relative). ============================================================================== PART 3. SVG COORDINATE DATA FOR THE ARTICLE'S FIGURES ============================================================================== --- Fig 1 SVG points: log10(C) -> x-pixel [80,580], log10(x) -> y-pixel [280,34] --- EX 80.00, 192.72 EX 107.78, 192.84 EX 135.56, 193.14 EX 163.33, 193.96 EX 191.11, 196.16 EX 218.89, 201.75 EX 246.67, 213.08 EX 274.44, 228.12 EX 302.22, 242.61 EX 330.00, 253.72 EX 357.78, 259.33 EX 385.56, 258.42 EX 413.33, 251.07 EX 441.11, 238.32 EX 468.89, 221.54 EX 496.67, 200.18 EX 524.44, 169.83 EX 552.22, 127.53 EX 580.00, 78.22 NV 80.00, 105.83 NV 107.78, 123.55 NV 135.56, 141.27 NV 163.33, 158.98 NV 191.11, 176.70 NV 218.89, 194.42 NV 246.67, 212.13 NV 274.44, 229.85 NV 302.22, 247.57 NV 330.00, 265.29 NV 357.78, 280.00 NV 385.56, 280.00 NV 413.33, 280.00 NV 441.11, 280.00 NV 468.89, 280.00 NV 496.67, 280.00 NV 524.44, 280.00 NV 552.22, 280.00 NV 580.00, 280.00 MIN 367.90, 259.77 --- Fig 2 SVG points: pH -> x-pixel [80,580], log10(x, M) -> y-pixel [280,34] --- CF 80.00, 36.30 CF 91.36, 44.98 CF 102.73, 53.71 CF 114.09, 62.47 CF 125.45, 71.30 CF 136.82, 80.20 CF 148.18, 89.20 CF 159.55, 98.32 CF 170.91, 107.61 CF 182.27, 117.11 CF 193.64, 126.86 CF 205.00, 136.93 CF 216.36, 147.36 CF 227.73, 158.19 CF 239.09, 169.37 CF 250.45, 180.75 CF 261.82, 191.99 CF 273.18, 202.63 CF 284.55, 212.13 CF 295.91, 220.12 CF 307.27, 226.47 CF 318.64, 231.26 CF 330.00, 234.73 CF 341.36, 237.18 CF 352.73, 238.87 CF 364.09, 240.02 CF 375.45, 240.79 CF 386.82, 241.31 CF 398.18, 241.65 CF 409.55, 241.88 CF 420.91, 242.03 CF 432.27, 242.13 CF 443.64, 242.19 CF 455.00, 242.23 CF 466.36, 242.26 CF 477.73, 242.28 CF 489.09, 242.29 CF 500.45, 242.30 CF 511.82, 242.31 CF 523.18, 242.31 CF 534.55, 242.31 CF 545.91, 242.31 CF 557.27, 242.31 CF 568.64, 242.31 CF 580.00, 242.31 NV 80.00, 238.26 NV 91.36, 238.26 NV 102.73, 238.26 NV 114.09, 238.26 NV 125.45, 238.26 NV 136.82, 238.26 NV 148.18, 238.26 NV 159.55, 238.26 NV 170.91, 238.26 NV 182.27, 238.26 NV 193.64, 238.26 NV 205.00, 238.26 NV 216.36, 238.26 NV 227.73, 238.26 NV 239.09, 238.26 NV 250.45, 238.26 NV 261.82, 238.26 NV 273.18, 238.26 NV 284.55, 238.26 NV 295.91, 238.26 NV 307.27, 238.26 NV 318.64, 238.26 NV 330.00, 238.26 NV 341.36, 238.26 NV 352.73, 238.26 NV 364.09, 238.26 NV 375.45, 238.26 NV 386.82, 238.26 NV 398.18, 238.26 NV 409.55, 238.26 NV 420.91, 238.26 NV 432.27, 238.26 NV 443.64, 238.26 NV 455.00, 238.26 NV 466.36, 238.26 NV 477.73, 238.26 NV 489.09, 238.26 NV 500.45, 238.26 NV 511.82, 238.26 NV 523.18, 238.26 NV 534.55, 238.26 NV 545.91, 238.26 NV 557.27, 238.26 NV 568.64, 238.26 NV 580.00, 238.26 (AgCl over this same pH sweep is flat to 0.0000% and is drawn as a plain reference line, not plotted point by point.) --- Fig 3 SVG points: log10(C) -> x-pixel [80,580], rel. error (%) -> y-pixel [280,34], clipped +-300% --- ER 80.00, 34.00 ER 107.78, 34.00 ER 135.56, 34.00 ER 163.33, 34.00 ER 191.11, 96.57 ER 218.89, 187.18 ER 246.67, 215.16 ER 274.44, 224.20 ER 302.22, 233.44 ER 330.00, 247.88 ER 357.78, 263.73 ER 385.56, 274.28 ER 413.33, 278.60 ER 441.11, 279.75 ER 468.89, 279.96 ER 496.67, 280.00 ER 524.44, 280.00 ER 552.22, 280.00 ER 580.00, 280.00 ZERO_Y 218.50 --- Fig 4 SVG cells: regime map grid, [Cl-] -> x [80,580], [NH3] -> y [280,34], flag +/- --- CELL H 70.38 275.27 19.23 9.46 CELL H 90.38 275.27 19.23 9.46 CELL H 110.38 275.27 19.23 9.46 CELL H 130.38 275.27 19.23 9.46 CELL H 150.38 275.27 19.23 9.46 CELL H 170.38 275.27 19.23 9.46 CELL H 190.38 275.27 19.23 9.46 CELL H 210.38 275.27 19.23 9.46 CELL H 230.38 275.27 19.23 9.46 CELL H 250.38 275.27 19.23 9.46 CELL H 270.38 275.27 19.23 9.46 CELL H 290.38 275.27 19.23 9.46 CELL H 310.38 275.27 19.23 9.46 CELL R 330.38 275.27 19.23 9.46 CELL R 350.38 275.27 19.23 9.46 CELL R 370.38 275.27 19.23 9.46 CELL R 390.38 275.27 19.23 9.46 CELL R 410.38 275.27 19.23 9.46 CELL R 430.38 275.27 19.23 9.46 CELL R 450.38 275.27 19.23 9.46 CELL R 470.38 275.27 19.23 9.46 CELL R 490.38 275.27 19.23 9.46 CELL R 510.38 275.27 19.23 9.46 CELL R 530.38 275.27 19.23 9.46 CELL R 550.38 275.27 19.23 9.46 CELL R 570.38 275.27 19.23 9.46 CELL H 70.38 265.43 19.23 9.46 CELL H 90.38 265.43 19.23 9.46 CELL H 110.38 265.43 19.23 9.46 CELL H 130.38 265.43 19.23 9.46 CELL H 150.38 265.43 19.23 9.46 CELL H 170.38 265.43 19.23 9.46 CELL H 190.38 265.43 19.23 9.46 CELL H 210.38 265.43 19.23 9.46 CELL H 230.38 265.43 19.23 9.46 CELL H 250.38 265.43 19.23 9.46 CELL H 270.38 265.43 19.23 9.46 CELL H 290.38 265.43 19.23 9.46 CELL H 310.38 265.43 19.23 9.46 CELL R 330.38 265.43 19.23 9.46 CELL R 350.38 265.43 19.23 9.46 CELL R 370.38 265.43 19.23 9.46 CELL R 390.38 265.43 19.23 9.46 CELL R 410.38 265.43 19.23 9.46 CELL R 430.38 265.43 19.23 9.46 CELL R 450.38 265.43 19.23 9.46 CELL R 470.38 265.43 19.23 9.46 CELL R 490.38 265.43 19.23 9.46 CELL R 510.38 265.43 19.23 9.46 CELL R 530.38 265.43 19.23 9.46 CELL R 550.38 265.43 19.23 9.46 CELL R 570.38 265.43 19.23 9.46 CELL H 70.38 255.59 19.23 9.46 CELL H 90.38 255.59 19.23 9.46 CELL H 110.38 255.59 19.23 9.46 CELL H 130.38 255.59 19.23 9.46 CELL H 150.38 255.59 19.23 9.46 CELL H 170.38 255.59 19.23 9.46 CELL H 190.38 255.59 19.23 9.46 CELL H 210.38 255.59 19.23 9.46 CELL H 230.38 255.59 19.23 9.46 CELL H 250.38 255.59 19.23 9.46 CELL H 270.38 255.59 19.23 9.46 CELL H 290.38 255.59 19.23 9.46 CELL H 310.38 255.59 19.23 9.46 CELL R 330.38 255.59 19.23 9.46 CELL R 350.38 255.59 19.23 9.46 CELL R 370.38 255.59 19.23 9.46 CELL R 390.38 255.59 19.23 9.46 CELL R 410.38 255.59 19.23 9.46 CELL R 430.38 255.59 19.23 9.46 CELL R 450.38 255.59 19.23 9.46 CELL R 470.38 255.59 19.23 9.46 CELL R 490.38 255.59 19.23 9.46 CELL R 510.38 255.59 19.23 9.46 CELL R 530.38 255.59 19.23 9.46 CELL R 550.38 255.59 19.23 9.46 CELL R 570.38 255.59 19.23 9.46 CELL H 70.38 245.75 19.23 9.46 CELL H 90.38 245.75 19.23 9.46 CELL H 110.38 245.75 19.23 9.46 CELL H 130.38 245.75 19.23 9.46 CELL H 150.38 245.75 19.23 9.46 CELL H 170.38 245.75 19.23 9.46 CELL H 190.38 245.75 19.23 9.46 CELL H 210.38 245.75 19.23 9.46 CELL H 230.38 245.75 19.23 9.46 CELL H 250.38 245.75 19.23 9.46 CELL H 270.38 245.75 19.23 9.46 CELL H 290.38 245.75 19.23 9.46 CELL H 310.38 245.75 19.23 9.46 CELL R 330.38 245.75 19.23 9.46 CELL R 350.38 245.75 19.23 9.46 CELL R 370.38 245.75 19.23 9.46 CELL R 390.38 245.75 19.23 9.46 CELL R 410.38 245.75 19.23 9.46 CELL R 430.38 245.75 19.23 9.46 CELL R 450.38 245.75 19.23 9.46 CELL R 470.38 245.75 19.23 9.46 CELL R 490.38 245.75 19.23 9.46 CELL R 510.38 245.75 19.23 9.46 CELL R 530.38 245.75 19.23 9.46 CELL R 550.38 245.75 19.23 9.46 CELL R 570.38 245.75 19.23 9.46 CELL H 70.38 235.91 19.23 9.46 CELL H 90.38 235.91 19.23 9.46 CELL H 110.38 235.91 19.23 9.46 CELL H 130.38 235.91 19.23 9.46 CELL H 150.38 235.91 19.23 9.46 CELL H 170.38 235.91 19.23 9.46 CELL H 190.38 235.91 19.23 9.46 CELL H 210.38 235.91 19.23 9.46 CELL H 230.38 235.91 19.23 9.46 CELL H 250.38 235.91 19.23 9.46 CELL H 270.38 235.91 19.23 9.46 CELL H 290.38 235.91 19.23 9.46 CELL H 310.38 235.91 19.23 9.46 CELL R 330.38 235.91 19.23 9.46 CELL R 350.38 235.91 19.23 9.46 CELL R 370.38 235.91 19.23 9.46 CELL R 390.38 235.91 19.23 9.46 CELL R 410.38 235.91 19.23 9.46 CELL R 430.38 235.91 19.23 9.46 CELL R 450.38 235.91 19.23 9.46 CELL R 470.38 235.91 19.23 9.46 CELL R 490.38 235.91 19.23 9.46 CELL R 510.38 235.91 19.23 9.46 CELL R 530.38 235.91 19.23 9.46 CELL R 550.38 235.91 19.23 9.46 CELL R 570.38 235.91 19.23 9.46 CELL H 70.38 226.07 19.23 9.46 CELL H 90.38 226.07 19.23 9.46 CELL H 110.38 226.07 19.23 9.46 CELL H 130.38 226.07 19.23 9.46 CELL H 150.38 226.07 19.23 9.46 CELL H 170.38 226.07 19.23 9.46 CELL H 190.38 226.07 19.23 9.46 CELL H 210.38 226.07 19.23 9.46 CELL H 230.38 226.07 19.23 9.46 CELL H 250.38 226.07 19.23 9.46 CELL H 270.38 226.07 19.23 9.46 CELL H 290.38 226.07 19.23 9.46 CELL H 310.38 226.07 19.23 9.46 CELL H 330.38 226.07 19.23 9.46 CELL R 350.38 226.07 19.23 9.46 CELL R 370.38 226.07 19.23 9.46 CELL R 390.38 226.07 19.23 9.46 CELL R 410.38 226.07 19.23 9.46 CELL R 430.38 226.07 19.23 9.46 CELL R 450.38 226.07 19.23 9.46 CELL R 470.38 226.07 19.23 9.46 CELL R 490.38 226.07 19.23 9.46 CELL R 510.38 226.07 19.23 9.46 CELL R 530.38 226.07 19.23 9.46 CELL R 550.38 226.07 19.23 9.46 CELL R 570.38 226.07 19.23 9.46 CELL H 70.38 216.23 19.23 9.46 CELL H 90.38 216.23 19.23 9.46 CELL H 110.38 216.23 19.23 9.46 CELL H 130.38 216.23 19.23 9.46 CELL H 150.38 216.23 19.23 9.46 CELL H 170.38 216.23 19.23 9.46 CELL H 190.38 216.23 19.23 9.46 CELL H 210.38 216.23 19.23 9.46 CELL H 230.38 216.23 19.23 9.46 CELL H 250.38 216.23 19.23 9.46 CELL H 270.38 216.23 19.23 9.46 CELL H 290.38 216.23 19.23 9.46 CELL H 310.38 216.23 19.23 9.46 CELL H 330.38 216.23 19.23 9.46 CELL R 350.38 216.23 19.23 9.46 CELL R 370.38 216.23 19.23 9.46 CELL R 390.38 216.23 19.23 9.46 CELL R 410.38 216.23 19.23 9.46 CELL R 430.38 216.23 19.23 9.46 CELL R 450.38 216.23 19.23 9.46 CELL R 470.38 216.23 19.23 9.46 CELL R 490.38 216.23 19.23 9.46 CELL R 510.38 216.23 19.23 9.46 CELL R 530.38 216.23 19.23 9.46 CELL R 550.38 216.23 19.23 9.46 CELL R 570.38 216.23 19.23 9.46 CELL H 70.38 206.39 19.23 9.46 CELL H 90.38 206.39 19.23 9.46 CELL H 110.38 206.39 19.23 9.46 CELL H 130.38 206.39 19.23 9.46 CELL H 150.38 206.39 19.23 9.46 CELL H 170.38 206.39 19.23 9.46 CELL H 190.38 206.39 19.23 9.46 CELL H 210.38 206.39 19.23 9.46 CELL H 230.38 206.39 19.23 9.46 CELL H 250.38 206.39 19.23 9.46 CELL H 270.38 206.39 19.23 9.46 CELL H 290.38 206.39 19.23 9.46 CELL H 310.38 206.39 19.23 9.46 CELL H 330.38 206.39 19.23 9.46 CELL R 350.38 206.39 19.23 9.46 CELL R 370.38 206.39 19.23 9.46 CELL R 390.38 206.39 19.23 9.46 CELL R 410.38 206.39 19.23 9.46 CELL R 430.38 206.39 19.23 9.46 CELL R 450.38 206.39 19.23 9.46 CELL R 470.38 206.39 19.23 9.46 CELL R 490.38 206.39 19.23 9.46 CELL R 510.38 206.39 19.23 9.46 CELL R 530.38 206.39 19.23 9.46 CELL R 550.38 206.39 19.23 9.46 CELL R 570.38 206.39 19.23 9.46 CELL H 70.38 196.55 19.23 9.46 CELL H 90.38 196.55 19.23 9.46 CELL H 110.38 196.55 19.23 9.46 CELL H 130.38 196.55 19.23 9.46 CELL H 150.38 196.55 19.23 9.46 CELL H 170.38 196.55 19.23 9.46 CELL H 190.38 196.55 19.23 9.46 CELL H 210.38 196.55 19.23 9.46 CELL H 230.38 196.55 19.23 9.46 CELL H 250.38 196.55 19.23 9.46 CELL H 270.38 196.55 19.23 9.46 CELL H 290.38 196.55 19.23 9.46 CELL H 310.38 196.55 19.23 9.46 CELL H 330.38 196.55 19.23 9.46 CELL R 350.38 196.55 19.23 9.46 CELL R 370.38 196.55 19.23 9.46 CELL R 390.38 196.55 19.23 9.46 CELL R 410.38 196.55 19.23 9.46 CELL R 430.38 196.55 19.23 9.46 CELL R 450.38 196.55 19.23 9.46 CELL R 470.38 196.55 19.23 9.46 CELL R 490.38 196.55 19.23 9.46 CELL R 510.38 196.55 19.23 9.46 CELL R 530.38 196.55 19.23 9.46 CELL R 550.38 196.55 19.23 9.46 CELL R 570.38 196.55 19.23 9.46 CELL H 70.38 186.71 19.23 9.46 CELL H 90.38 186.71 19.23 9.46 CELL H 110.38 186.71 19.23 9.46 CELL H 130.38 186.71 19.23 9.46 CELL H 150.38 186.71 19.23 9.46 CELL H 170.38 186.71 19.23 9.46 CELL H 190.38 186.71 19.23 9.46 CELL H 210.38 186.71 19.23 9.46 CELL H 230.38 186.71 19.23 9.46 CELL H 250.38 186.71 19.23 9.46 CELL H 270.38 186.71 19.23 9.46 CELL H 290.38 186.71 19.23 9.46 CELL H 310.38 186.71 19.23 9.46 CELL H 330.38 186.71 19.23 9.46 CELL R 350.38 186.71 19.23 9.46 CELL R 370.38 186.71 19.23 9.46 CELL R 390.38 186.71 19.23 9.46 CELL R 410.38 186.71 19.23 9.46 CELL R 430.38 186.71 19.23 9.46 CELL R 450.38 186.71 19.23 9.46 CELL R 470.38 186.71 19.23 9.46 CELL R 490.38 186.71 19.23 9.46 CELL R 510.38 186.71 19.23 9.46 CELL R 530.38 186.71 19.23 9.46 CELL R 550.38 186.71 19.23 9.46 CELL R 570.38 186.71 19.23 9.46 CELL H 70.38 176.87 19.23 9.46 CELL H 90.38 176.87 19.23 9.46 CELL H 110.38 176.87 19.23 9.46 CELL H 130.38 176.87 19.23 9.46 CELL H 150.38 176.87 19.23 9.46 CELL H 170.38 176.87 19.23 9.46 CELL H 190.38 176.87 19.23 9.46 CELL H 210.38 176.87 19.23 9.46 CELL H 230.38 176.87 19.23 9.46 CELL H 250.38 176.87 19.23 9.46 CELL H 270.38 176.87 19.23 9.46 CELL H 290.38 176.87 19.23 9.46 CELL H 310.38 176.87 19.23 9.46 CELL H 330.38 176.87 19.23 9.46 CELL R 350.38 176.87 19.23 9.46 CELL R 370.38 176.87 19.23 9.46 CELL R 390.38 176.87 19.23 9.46 CELL R 410.38 176.87 19.23 9.46 CELL R 430.38 176.87 19.23 9.46 CELL R 450.38 176.87 19.23 9.46 CELL R 470.38 176.87 19.23 9.46 CELL R 490.38 176.87 19.23 9.46 CELL R 510.38 176.87 19.23 9.46 CELL R 530.38 176.87 19.23 9.46 CELL R 550.38 176.87 19.23 9.46 CELL R 570.38 176.87 19.23 9.46 CELL H 70.38 167.03 19.23 9.46 CELL H 90.38 167.03 19.23 9.46 CELL H 110.38 167.03 19.23 9.46 CELL H 130.38 167.03 19.23 9.46 CELL H 150.38 167.03 19.23 9.46 CELL H 170.38 167.03 19.23 9.46 CELL H 190.38 167.03 19.23 9.46 CELL H 210.38 167.03 19.23 9.46 CELL H 230.38 167.03 19.23 9.46 CELL H 250.38 167.03 19.23 9.46 CELL H 270.38 167.03 19.23 9.46 CELL H 290.38 167.03 19.23 9.46 CELL H 310.38 167.03 19.23 9.46 CELL H 330.38 167.03 19.23 9.46 CELL H 350.38 167.03 19.23 9.46 CELL R 370.38 167.03 19.23 9.46 CELL R 390.38 167.03 19.23 9.46 CELL R 410.38 167.03 19.23 9.46 CELL R 430.38 167.03 19.23 9.46 CELL R 450.38 167.03 19.23 9.46 CELL R 470.38 167.03 19.23 9.46 CELL R 490.38 167.03 19.23 9.46 CELL R 510.38 167.03 19.23 9.46 CELL R 530.38 167.03 19.23 9.46 CELL R 550.38 167.03 19.23 9.46 CELL R 570.38 167.03 19.23 9.46 CELL H 70.38 157.19 19.23 9.46 CELL H 90.38 157.19 19.23 9.46 CELL H 110.38 157.19 19.23 9.46 CELL H 130.38 157.19 19.23 9.46 CELL H 150.38 157.19 19.23 9.46 CELL H 170.38 157.19 19.23 9.46 CELL H 190.38 157.19 19.23 9.46 CELL H 210.38 157.19 19.23 9.46 CELL H 230.38 157.19 19.23 9.46 CELL H 250.38 157.19 19.23 9.46 CELL H 270.38 157.19 19.23 9.46 CELL H 290.38 157.19 19.23 9.46 CELL H 310.38 157.19 19.23 9.46 CELL H 330.38 157.19 19.23 9.46 CELL H 350.38 157.19 19.23 9.46 CELL H 370.38 157.19 19.23 9.46 CELL R 390.38 157.19 19.23 9.46 CELL R 410.38 157.19 19.23 9.46 CELL R 430.38 157.19 19.23 9.46 CELL R 450.38 157.19 19.23 9.46 CELL R 470.38 157.19 19.23 9.46 CELL R 490.38 157.19 19.23 9.46 CELL R 510.38 157.19 19.23 9.46 CELL R 530.38 157.19 19.23 9.46 CELL R 550.38 157.19 19.23 9.46 CELL R 570.38 157.19 19.23 9.46 CELL H 70.38 147.35 19.23 9.46 CELL H 90.38 147.35 19.23 9.46 CELL H 110.38 147.35 19.23 9.46 CELL H 130.38 147.35 19.23 9.46 CELL H 150.38 147.35 19.23 9.46 CELL H 170.38 147.35 19.23 9.46 CELL H 190.38 147.35 19.23 9.46 CELL H 210.38 147.35 19.23 9.46 CELL H 230.38 147.35 19.23 9.46 CELL H 250.38 147.35 19.23 9.46 CELL H 270.38 147.35 19.23 9.46 CELL H 290.38 147.35 19.23 9.46 CELL H 310.38 147.35 19.23 9.46 CELL H 330.38 147.35 19.23 9.46 CELL H 350.38 147.35 19.23 9.46 CELL H 370.38 147.35 19.23 9.46 CELL H 390.38 147.35 19.23 9.46 CELL R 410.38 147.35 19.23 9.46 CELL R 430.38 147.35 19.23 9.46 CELL R 450.38 147.35 19.23 9.46 CELL R 470.38 147.35 19.23 9.46 CELL R 490.38 147.35 19.23 9.46 CELL R 510.38 147.35 19.23 9.46 CELL R 530.38 147.35 19.23 9.46 CELL R 550.38 147.35 19.23 9.46 CELL R 570.38 147.35 19.23 9.46 CELL H 70.38 137.51 19.23 9.46 CELL H 90.38 137.51 19.23 9.46 CELL H 110.38 137.51 19.23 9.46 CELL H 130.38 137.51 19.23 9.46 CELL H 150.38 137.51 19.23 9.46 CELL H 170.38 137.51 19.23 9.46 CELL H 190.38 137.51 19.23 9.46 CELL H 210.38 137.51 19.23 9.46 CELL H 230.38 137.51 19.23 9.46 CELL H 250.38 137.51 19.23 9.46 CELL H 270.38 137.51 19.23 9.46 CELL H 290.38 137.51 19.23 9.46 CELL H 310.38 137.51 19.23 9.46 CELL H 330.38 137.51 19.23 9.46 CELL H 350.38 137.51 19.23 9.46 CELL H 370.38 137.51 19.23 9.46 CELL H 390.38 137.51 19.23 9.46 CELL R 410.38 137.51 19.23 9.46 CELL R 430.38 137.51 19.23 9.46 CELL R 450.38 137.51 19.23 9.46 CELL R 470.38 137.51 19.23 9.46 CELL R 490.38 137.51 19.23 9.46 CELL R 510.38 137.51 19.23 9.46 CELL R 530.38 137.51 19.23 9.46 CELL R 550.38 137.51 19.23 9.46 CELL R 570.38 137.51 19.23 9.46 CELL H 70.38 127.67 19.23 9.46 CELL H 90.38 127.67 19.23 9.46 CELL H 110.38 127.67 19.23 9.46 CELL H 130.38 127.67 19.23 9.46 CELL H 150.38 127.67 19.23 9.46 CELL H 170.38 127.67 19.23 9.46 CELL H 190.38 127.67 19.23 9.46 CELL H 210.38 127.67 19.23 9.46 CELL H 230.38 127.67 19.23 9.46 CELL H 250.38 127.67 19.23 9.46 CELL H 270.38 127.67 19.23 9.46 CELL H 290.38 127.67 19.23 9.46 CELL H 310.38 127.67 19.23 9.46 CELL H 330.38 127.67 19.23 9.46 CELL H 350.38 127.67 19.23 9.46 CELL H 370.38 127.67 19.23 9.46 CELL H 390.38 127.67 19.23 9.46 CELL H 410.38 127.67 19.23 9.46 CELL R 430.38 127.67 19.23 9.46 CELL R 450.38 127.67 19.23 9.46 CELL R 470.38 127.67 19.23 9.46 CELL R 490.38 127.67 19.23 9.46 CELL R 510.38 127.67 19.23 9.46 CELL R 530.38 127.67 19.23 9.46 CELL R 550.38 127.67 19.23 9.46 CELL R 570.38 127.67 19.23 9.46 CELL H 70.38 117.83 19.23 9.46 CELL H 90.38 117.83 19.23 9.46 CELL H 110.38 117.83 19.23 9.46 CELL H 130.38 117.83 19.23 9.46 CELL H 150.38 117.83 19.23 9.46 CELL H 170.38 117.83 19.23 9.46 CELL H 190.38 117.83 19.23 9.46 CELL H 210.38 117.83 19.23 9.46 CELL H 230.38 117.83 19.23 9.46 CELL H 250.38 117.83 19.23 9.46 CELL H 270.38 117.83 19.23 9.46 CELL H 290.38 117.83 19.23 9.46 CELL H 310.38 117.83 19.23 9.46 CELL H 330.38 117.83 19.23 9.46 CELL H 350.38 117.83 19.23 9.46 CELL H 370.38 117.83 19.23 9.46 CELL H 390.38 117.83 19.23 9.46 CELL H 410.38 117.83 19.23 9.46 CELL H 430.38 117.83 19.23 9.46 CELL R 450.38 117.83 19.23 9.46 CELL R 470.38 117.83 19.23 9.46 CELL R 490.38 117.83 19.23 9.46 CELL R 510.38 117.83 19.23 9.46 CELL R 530.38 117.83 19.23 9.46 CELL R 550.38 117.83 19.23 9.46 CELL R 570.38 117.83 19.23 9.46 CELL H 70.38 107.99 19.23 9.46 CELL H 90.38 107.99 19.23 9.46 CELL H 110.38 107.99 19.23 9.46 CELL H 130.38 107.99 19.23 9.46 CELL H 150.38 107.99 19.23 9.46 CELL H 170.38 107.99 19.23 9.46 CELL H 190.38 107.99 19.23 9.46 CELL H 210.38 107.99 19.23 9.46 CELL H 230.38 107.99 19.23 9.46 CELL H 250.38 107.99 19.23 9.46 CELL H 270.38 107.99 19.23 9.46 CELL H 290.38 107.99 19.23 9.46 CELL H 310.38 107.99 19.23 9.46 CELL H 330.38 107.99 19.23 9.46 CELL H 350.38 107.99 19.23 9.46 CELL H 370.38 107.99 19.23 9.46 CELL H 390.38 107.99 19.23 9.46 CELL H 410.38 107.99 19.23 9.46 CELL H 430.38 107.99 19.23 9.46 CELL H 450.38 107.99 19.23 9.46 CELL R 470.38 107.99 19.23 9.46 CELL R 490.38 107.99 19.23 9.46 CELL R 510.38 107.99 19.23 9.46 CELL R 530.38 107.99 19.23 9.46 CELL R 550.38 107.99 19.23 9.46 CELL R 570.38 107.99 19.23 9.46 CELL H 70.38 98.15 19.23 9.46 CELL H 90.38 98.15 19.23 9.46 CELL H 110.38 98.15 19.23 9.46 CELL H 130.38 98.15 19.23 9.46 CELL H 150.38 98.15 19.23 9.46 CELL H 170.38 98.15 19.23 9.46 CELL H 190.38 98.15 19.23 9.46 CELL H 210.38 98.15 19.23 9.46 CELL H 230.38 98.15 19.23 9.46 CELL H 250.38 98.15 19.23 9.46 CELL H 270.38 98.15 19.23 9.46 CELL H 290.38 98.15 19.23 9.46 CELL H 310.38 98.15 19.23 9.46 CELL H 330.38 98.15 19.23 9.46 CELL H 350.38 98.15 19.23 9.46 CELL H 370.38 98.15 19.23 9.46 CELL H 390.38 98.15 19.23 9.46 CELL H 410.38 98.15 19.23 9.46 CELL H 430.38 98.15 19.23 9.46 CELL H 450.38 98.15 19.23 9.46 CELL H 470.38 98.15 19.23 9.46 CELL R 490.38 98.15 19.23 9.46 CELL R 510.38 98.15 19.23 9.46 CELL R 530.38 98.15 19.23 9.46 CELL R 550.38 98.15 19.23 9.46 CELL R 570.38 98.15 19.23 9.46 CELL H 70.38 88.31 19.23 9.46 CELL H 90.38 88.31 19.23 9.46 CELL H 110.38 88.31 19.23 9.46 CELL H 130.38 88.31 19.23 9.46 CELL H 150.38 88.31 19.23 9.46 CELL H 170.38 88.31 19.23 9.46 CELL H 190.38 88.31 19.23 9.46 CELL H 210.38 88.31 19.23 9.46 CELL H 230.38 88.31 19.23 9.46 CELL H 250.38 88.31 19.23 9.46 CELL H 270.38 88.31 19.23 9.46 CELL H 290.38 88.31 19.23 9.46 CELL H 310.38 88.31 19.23 9.46 CELL H 330.38 88.31 19.23 9.46 CELL H 350.38 88.31 19.23 9.46 CELL H 370.38 88.31 19.23 9.46 CELL H 390.38 88.31 19.23 9.46 CELL H 410.38 88.31 19.23 9.46 CELL H 430.38 88.31 19.23 9.46 CELL H 450.38 88.31 19.23 9.46 CELL H 470.38 88.31 19.23 9.46 CELL R 490.38 88.31 19.23 9.46 CELL R 510.38 88.31 19.23 9.46 CELL R 530.38 88.31 19.23 9.46 CELL R 550.38 88.31 19.23 9.46 CELL R 570.38 88.31 19.23 9.46 CELL H 70.38 78.47 19.23 9.46 CELL H 90.38 78.47 19.23 9.46 CELL H 110.38 78.47 19.23 9.46 CELL H 130.38 78.47 19.23 9.46 CELL H 150.38 78.47 19.23 9.46 CELL H 170.38 78.47 19.23 9.46 CELL H 190.38 78.47 19.23 9.46 CELL H 210.38 78.47 19.23 9.46 CELL H 230.38 78.47 19.23 9.46 CELL H 250.38 78.47 19.23 9.46 CELL H 270.38 78.47 19.23 9.46 CELL H 290.38 78.47 19.23 9.46 CELL H 310.38 78.47 19.23 9.46 CELL H 330.38 78.47 19.23 9.46 CELL H 350.38 78.47 19.23 9.46 CELL H 370.38 78.47 19.23 9.46 CELL H 390.38 78.47 19.23 9.46 CELL H 410.38 78.47 19.23 9.46 CELL H 430.38 78.47 19.23 9.46 CELL H 450.38 78.47 19.23 9.46 CELL H 470.38 78.47 19.23 9.46 CELL H 490.38 78.47 19.23 9.46 CELL R 510.38 78.47 19.23 9.46 CELL R 530.38 78.47 19.23 9.46 CELL R 550.38 78.47 19.23 9.46 CELL R 570.38 78.47 19.23 9.46 CELL H 70.38 68.63 19.23 9.46 CELL H 90.38 68.63 19.23 9.46 CELL H 110.38 68.63 19.23 9.46 CELL H 130.38 68.63 19.23 9.46 CELL H 150.38 68.63 19.23 9.46 CELL H 170.38 68.63 19.23 9.46 CELL H 190.38 68.63 19.23 9.46 CELL H 210.38 68.63 19.23 9.46 CELL H 230.38 68.63 19.23 9.46 CELL H 250.38 68.63 19.23 9.46 CELL H 270.38 68.63 19.23 9.46 CELL H 290.38 68.63 19.23 9.46 CELL H 310.38 68.63 19.23 9.46 CELL H 330.38 68.63 19.23 9.46 CELL H 350.38 68.63 19.23 9.46 CELL H 370.38 68.63 19.23 9.46 CELL H 390.38 68.63 19.23 9.46 CELL H 410.38 68.63 19.23 9.46 CELL H 430.38 68.63 19.23 9.46 CELL H 450.38 68.63 19.23 9.46 CELL H 470.38 68.63 19.23 9.46 CELL H 490.38 68.63 19.23 9.46 CELL H 510.38 68.63 19.23 9.46 CELL R 530.38 68.63 19.23 9.46 CELL R 550.38 68.63 19.23 9.46 CELL R 570.38 68.63 19.23 9.46 CELL H 70.38 58.79 19.23 9.46 CELL H 90.38 58.79 19.23 9.46 CELL H 110.38 58.79 19.23 9.46 CELL H 130.38 58.79 19.23 9.46 CELL H 150.38 58.79 19.23 9.46 CELL H 170.38 58.79 19.23 9.46 CELL H 190.38 58.79 19.23 9.46 CELL H 210.38 58.79 19.23 9.46 CELL H 230.38 58.79 19.23 9.46 CELL H 250.38 58.79 19.23 9.46 CELL H 270.38 58.79 19.23 9.46 CELL H 290.38 58.79 19.23 9.46 CELL H 310.38 58.79 19.23 9.46 CELL H 330.38 58.79 19.23 9.46 CELL H 350.38 58.79 19.23 9.46 CELL H 370.38 58.79 19.23 9.46 CELL H 390.38 58.79 19.23 9.46 CELL H 410.38 58.79 19.23 9.46 CELL H 430.38 58.79 19.23 9.46 CELL H 450.38 58.79 19.23 9.46 CELL H 470.38 58.79 19.23 9.46 CELL H 490.38 58.79 19.23 9.46 CELL H 510.38 58.79 19.23 9.46 CELL R 530.38 58.79 19.23 9.46 CELL R 550.38 58.79 19.23 9.46 CELL R 570.38 58.79 19.23 9.46 CELL H 70.38 48.95 19.23 9.46 CELL H 90.38 48.95 19.23 9.46 CELL H 110.38 48.95 19.23 9.46 CELL H 130.38 48.95 19.23 9.46 CELL H 150.38 48.95 19.23 9.46 CELL H 170.38 48.95 19.23 9.46 CELL H 190.38 48.95 19.23 9.46 CELL H 210.38 48.95 19.23 9.46 CELL H 230.38 48.95 19.23 9.46 CELL H 250.38 48.95 19.23 9.46 CELL H 270.38 48.95 19.23 9.46 CELL H 290.38 48.95 19.23 9.46 CELL H 310.38 48.95 19.23 9.46 CELL H 330.38 48.95 19.23 9.46 CELL H 350.38 48.95 19.23 9.46 CELL H 370.38 48.95 19.23 9.46 CELL H 390.38 48.95 19.23 9.46 CELL H 410.38 48.95 19.23 9.46 CELL H 430.38 48.95 19.23 9.46 CELL H 450.38 48.95 19.23 9.46 CELL H 470.38 48.95 19.23 9.46 CELL H 490.38 48.95 19.23 9.46 CELL H 510.38 48.95 19.23 9.46 CELL H 530.38 48.95 19.23 9.46 CELL R 550.38 48.95 19.23 9.46 CELL R 570.38 48.95 19.23 9.46 CELL H 70.38 39.11 19.23 9.46 CELL H 90.38 39.11 19.23 9.46 CELL H 110.38 39.11 19.23 9.46 CELL H 130.38 39.11 19.23 9.46 CELL H 150.38 39.11 19.23 9.46 CELL H 170.38 39.11 19.23 9.46 CELL H 190.38 39.11 19.23 9.46 CELL H 210.38 39.11 19.23 9.46 CELL H 230.38 39.11 19.23 9.46 CELL H 250.38 39.11 19.23 9.46 CELL H 270.38 39.11 19.23 9.46 CELL H 290.38 39.11 19.23 9.46 CELL H 310.38 39.11 19.23 9.46 CELL H 330.38 39.11 19.23 9.46 CELL H 350.38 39.11 19.23 9.46 CELL H 370.38 39.11 19.23 9.46 CELL H 390.38 39.11 19.23 9.46 CELL H 410.38 39.11 19.23 9.46 CELL H 430.38 39.11 19.23 9.46 CELL H 450.38 39.11 19.23 9.46 CELL H 470.38 39.11 19.23 9.46 CELL H 490.38 39.11 19.23 9.46 CELL H 510.38 39.11 19.23 9.46 CELL H 530.38 39.11 19.23 9.46 CELL R 550.38 39.11 19.23 9.46 CELL R 570.38 39.11 19.23 9.46 CELL H 70.38 29.27 19.23 9.46 CELL H 90.38 29.27 19.23 9.46 CELL H 110.38 29.27 19.23 9.46 CELL H 130.38 29.27 19.23 9.46 CELL H 150.38 29.27 19.23 9.46 CELL H 170.38 29.27 19.23 9.46 CELL H 190.38 29.27 19.23 9.46 CELL H 210.38 29.27 19.23 9.46 CELL H 230.38 29.27 19.23 9.46 CELL H 250.38 29.27 19.23 9.46 CELL H 270.38 29.27 19.23 9.46 CELL H 290.38 29.27 19.23 9.46 CELL H 310.38 29.27 19.23 9.46 CELL H 330.38 29.27 19.23 9.46 CELL H 350.38 29.27 19.23 9.46 CELL H 370.38 29.27 19.23 9.46 CELL H 390.38 29.27 19.23 9.46 CELL H 410.38 29.27 19.23 9.46 CELL H 430.38 29.27 19.23 9.46 CELL H 450.38 29.27 19.23 9.46 CELL H 470.38 29.27 19.23 9.46 CELL H 490.38 29.27 19.23 9.46 CELL H 510.38 29.27 19.23 9.46 CELL H 530.38 29.27 19.23 9.46 CELL H 550.38 29.27 19.23 9.46 CELL R 570.38 29.27 19.23 9.46 MARK 303.92 280.00 --- Fig 5 SVG points: MC convergence, n (log) -> x-pixel [80,580], running SE -> y-pixel [280,34] --- SE 80.00, 90.91 SE 89.90, 116.27 SE 105.51, 34.00 SE 117.63, 50.22 SE 129.74, 65.71 SE 143.14, 63.60 SE 156.60, 89.85 SE 169.50, 110.51 SE 182.44, 132.33 SE 194.88, 137.92 SE 208.16, 158.87 SE 220.89, 167.72 SE 233.81, 179.59 SE 246.55, 188.74 SE 259.32, 197.46 SE 272.23, 206.63 SE 285.06, 215.51 SE 297.94, 223.35 SE 310.71, 229.57 SE 323.55, 234.89 SE 336.39, 239.81 SE 349.23, 244.66 SE 362.03, 248.88 SE 374.86, 252.36 SE 387.69, 255.31 SE 400.51, 258.18 SE 413.33, 260.66 SE 426.15, 262.70 SE 438.97, 264.81 SE 451.79, 266.60 SE 464.61, 268.13 SE 477.43, 269.50 SE 490.25, 270.65 SE 503.08, 271.69 SE 515.90, 272.59 SE 528.72, 273.42 SE 541.54, 274.16 SE 554.36, 274.82 SE 567.18, 275.40 SE 580.00, 275.91 MEAN 80.00, 183.87 MEAN 89.90, 181.48 MEAN 105.51, 168.08 MEAN 117.63, 166.15 MEAN 129.74, 151.96 MEAN 143.14, 164.26 MEAN 156.60, 162.07 MEAN 169.50, 153.78 MEAN 182.44, 149.44 MEAN 194.88, 151.35 MEAN 208.16, 149.58 MEAN 220.89, 140.59 MEAN 233.81, 141.74 MEAN 246.55, 136.53 MEAN 259.32, 132.77 MEAN 272.23, 134.25 MEAN 285.06, 132.67 MEAN 297.94, 134.74 MEAN 310.71, 136.68 MEAN 323.55, 133.66 MEAN 336.39, 131.49 MEAN 349.23, 130.94 MEAN 362.03, 130.32 MEAN 374.86, 130.31 MEAN 387.69, 130.81 MEAN 400.51, 131.52 MEAN 413.33, 131.22 MEAN 426.15, 131.22 MEAN 438.97, 131.47 MEAN 451.79, 130.50 MEAN 464.61, 130.13 MEAN 477.43, 131.21 MEAN 490.25, 130.85 MEAN 503.08, 131.49 MEAN 515.90, 131.26 MEAN 528.72, 131.10 MEAN 541.54, 131.43 MEAN 554.36, 131.72 MEAN 567.18, 131.59 MEAN 580.00, 131.47 --- Additional headline numbers for the article text --- Deterministic (nominal-constant) enhancement ratio x(5 M)/x(minimum): 15912.8 Naive rule at 5 M: 3.5400e-11 M; exact: 4.9564e-03 M; naive is low by a factor of 1.400e+08 Naive rule within +-10% of exact for C in [3.915e-05, 1.059e-04] M Naive rule within +-20% of exact for C in [2.810e-05, 2.055e-04] M Pure-water solubility (no common ion): 1.3499e-05 M -- the naive rule is undefined there (C=0). Ratio of minimum-concentration to pure-water solubility itself: 223.05 x CaF2 solubility (C=1e-3 M NaF) exceeds 2x its high-pH value below pH ~ 3.45 CaF2 solubility (C=1e-3 M NaF) exceeds 10x its high-pH value below pH ~ 2.55 CaF2 solubility (C=1e-3 M NaF) exceeds 100x its high-pH value below pH ~ 1.27 CaF2 at pH 0: solubility is 816.3x the high-pH (pH>=7) plateau of 3.4102e-05 M. --- Species breakdown: at the minimum, and at 5 M chloride --- at the minimum (C=3.0108e-03 M): total x=3.1147e-07 M Ag = 5.8788e-08 M (18.87% of total) AgCl0 = 1.9408e-07 M (62.31% of total) AgCl2 = 5.8433e-08 M (18.76% of total) AgCl3 = 1.7593e-10 M (0.06% of total) AgCl4 = 9.6390e-13 M (0.00% of total) at 5 M NaCl: total x=4.9564e-03 M Ag = 3.5501e-11 M (0.00% of total) AgCl0 = 1.9408e-07 M (0.00% of total) AgCl2 = 9.6763e-05 M (1.95% of total) AgCl3 = 4.8244e-04 M (9.73% of total) AgCl4 = 4.3770e-03 M (88.31% of total) Exact solver x(5 M) / pure-water solubility x(0): 367.2x --- V4b (objection check): how wrong would log beta2 need to be for the reversal to vanish within the real solubility range of NaCl (about 6.1 mol/L at 25C)? --- Nominal log10(beta2) = 5.04 (beta2 = 1.096e+05) No positive beta2 pushes the minimum that far with beta3, beta4 held fixed: the higher complexes alone already guarantee a minimum inside the real concentration range. ============================================================================== DONE ============================================================================== Total wall-clock time: 7.21 s