Utilities

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Utilities

X x findplaces P 1 - : k 0 : 12 mat n 1 X length range X n el x ≡ P k k 1 + : el n : continue if for P 31 line :

X R removerows V 0 X cols matrix : r 1 X rows range R r findplaces 1 - ≡ V V X r row stack : continue if for V 31 line :

SVD Decomposition using dn library A tol MSVD S U V' 13 mat A dn_LinAlgSVD transpose : U - S V' - transpose 13 mat eval 21 line :

Null space A tol null U S V 13 mat A tol MSVD : r S tol > vectorize sum eval : V 1 V rows range r 1 + (V cols range el 31 line :

A null A TOL null 11 line :

rat

X# product P# 1 : x# X# P# x# P# * : for P# 31 line :

gcd of two numbers a b gcd x a abs : y b abs : 12 mat x 0 ≠ (y 0 ≠ (& x y > x x y mod : y y x mod : if while x y + 31 line :

gcd of an array. A gcd g A 1 el : k 2 A length range g g A k el gcd : for g 31 line :

lcm of two numbers a b lcm a b * a b gcd / 11 line :

lcm of an array A lcm l A 1 el : k 2 A length range l l A k el lcm : for l 31 line :

rat returns two integer matrices so that vectorize(N/D) is close to X in the sense that abs(N./D - X) <= tol*abs(X).
The rational approximations are generated by truncating continued fraction expansions. X tol rat N X X - : D N : T tol X normi * : 13 mat j 1 X length range x X j el : k 0 : C 2 identity : 13 mat Iters 110000 range k k 1 + : d x trunc : x x d - : C C d 121 mat * C 1 col augment eval : C 11 el C 21 el / X j el - abs T < (x 0 ≡ (| break x 1 x / : if 51 line for N j el C 21 el sign C 11 el * : D j el C 21 el abs : 12 mat 31 line for N D 12 mat eval 31 line :

X rat X TOL rat 11 line :

Try to find integers values from a vector of rationals. A tol ratint X A abs vectorize : m X min eval : (tol > 0 m X max eval : k 1 X length range m X k el > (X k el tol > (& m X k el : continue if for 21 line if N D 12 mat A m / rat : D lcm N D / vectorize * eval 41 line :

A ratint A TOL ratint 11 line :

Chem Bal

Molecular mass from a compound. R ChemMass R IsString X R ChemAtoms : M 0 : 12 mat k 1 X rows range M M X k 2 el MolW X k 1 el 1 findrows 2 el * + : for M g mol / * 31 line A R : k 1 A length range A k el A k el ChemMass : for A 31 line if 11 line :

MolW H 1.0079 He 4.0026 Li 6.941 Be 9.0122 B 10.81 C 12.011 N 14.0067 O 15.9994 F 18.9984 Ne 20.179 Na 22.9898 Mg 24.305 Al 26.9815 Si 28.086 P 30.9738 S 32.06 Cl 35.453 Ar 39.948 K 39.098 Ca 40.08 Sc 44.9559 Ti 47.9 V 50.9414 Cr 51.996 Mn 54.938 Fe 55.847 Co 58.9332 Ni 58.7 Cu 63.546 Zn 65.38 Ga 69.72 Ge 72.59 As 74.9216 Se 78.96 Br 79.904 Kr 83.8 Rb 85.4678 Sr 87.62 Yt 88.9059 Zr 91.22 Nb 92.9064 Mo 95.94 Tc 98.9062 Ru 101.07 Rh 102.9055 Pd 106.4 Ag 107.868 Cd 112.4 In 114.82 Sn 118.69 Sb 121.75 Te 127.6 I 126.9045 Xe 131.3 Cs 132.9054 Ba 137.34 La 138.9055 Ce 140.12 Pr 140.9077 Nd 144.24 Pm 147 Sm 150.4 Eu 151.96 Gd 157.25 Tb 158.9254 Dy 162.5 Ho 164.9304 Er 167.26 Tm 168.9342 Yt 173.04 Lu 174.97 Hf 178.49 Ta 180.9479 W 183.85 Re 186.207 Os 190.2 Ir 192.22 Pt 195.09 Au 196.9665 Hg 200.59 Tl 204.37 Pb 207.2 Bi 208.9804 Po 210 At 210 Rn 222 Fr 223 Ra 226.0254 Ac 227 Th 232.0381 Pa 231.0359 U 238.029 Np 237.0482 Pu 244 Am 243 Cm 247 Bk 247 Cf 251 Es 254 Fm 257 Md 258 No 259 Lr 262 Rf 261 Db 262 Sg 266 Bh 264 Hs 277 Mt 268 Q 01102 mat :

UChars ABCDEFGHIJKLMNOPQRSTUVWXYZ :

LChars abcdefghijklmnopqrstuvwxyz :

NChars 1234567890 :

Compostion from a chemical formula Σ ChemAtoms Σ IsString k 1 : r 0 : M 0 : S Σ strrep concat : 14 mat S S + Q strrep - Qn strrep : str (aq) (s) (l) (g) 14 mat S S str strrep : for a b s S a b substr : S (findstr 1 - ≡ k S strlen < UChars k 1 s findstr 1 - ≡ j 1 : NChars k j + 1 s findstr 1 - ≠ j j 1 + : while Digits M r 2 el k j s str2num : k k j + : 13 mat 31 line LChars k 1 + 1 s findstr 1 - ≡ UChar M r r 1 + : 1 el k 1 s : M r 2 el 1 : k k 1 + : 14 mat LChar M r r 1 + : 1 el k 2 s : M r 2 el 1 : k k 2 + : 14 mat if if while r 1 M rows range M r 1 el Qn ≡ Neg charges M r 1 el Q : M r 2 el M r 2 el - : 13 mat continue if for 21 line α S (findstr 1 el : β S) findstr 1 el : 12 mat j 0 : NChars β j + 1 + 1 s findstr 1 - ≠ j j 1 + : while M α 1 + β α - 1 - s ChemAtoms : j 0 ≡ 0 M M 1 col β 1 + j s str2num M 2 col * augment : if str β j + 1 + S strlen β - j - s : M M 1 α 1 - s str concat ChemAtoms stack eval : 71 line if r 0 : r M rows < Combine duplicates r r 1 + : 12 mat P M 1 col M r 1 el findplaces : (r 11 mat ≠ M r 2 el M P 2 el sum : M M P 2 P length range el removerows : 21 line continue if 21 line while 71 line M Σ augment : k 1 Σ length range A Σ k el ChemAtoms : r 1 A rows range R 1 M rows 1 + (range R M rows > (M R 1 el A r 1 el ≡ (| break continue if for M R 1 el A r 1 el : M R k 1 + el A r 2 el : 31 line for 21 line for 21 line if M 21 line :

Balance a chemical equation R ra ChemBal R rows 1 ≡ A R ChemAtoms : A R : if B A 2 A rows 2 A cols submatrix : C B null : 12 mat ra 0 ≡ C C ratint : C C ra * 0 round vectorize eval : if S C cols 1 matrix C transpose augment : r c N C r c el abs 1 ≡ C r c el abs num2str concat if : c 1 C cols range check 0 : b 12 mat : 12 mat χ 2 A cols range r 2 A rows range A r χ el A r χ el S χ el * : for check check A 2 A rows range χ el sum (+ eval : 21 line for b k str b k el 1 b k el strlen 3 - substr : r 1 C rows range ChemSign C r c el * 0 < b 1 el b 1 el r c N A 1 r 1 + el + concat : b 2 el b 2 el r c N A 1 r 1 + el + concat : if for S c 1 el b 1 str -> b 2 str concat strrep : check 0 ≡ 0 S c 1 el ERROR: S c 1 el concat : if 61 line for S 71 line :

Last is for charges Q

R ChemBal R 0 ChemBal 11 line :

ChemSign 1 :

TOL 1012 -^:

Examples

Balancing equations using null space

R Fe O2 Fe2O3 13 mat :

R ChemMass g mol / 55.847 31.9988 159.6922 13 mat

R ChemAtoms Fe O2 Fe2O3 Fe 102 O 02334 mat

R ChemBal 2 Fe2O3 -> 4 Fe + 3 O2 432 - 14 mat

ChemAtoms give the matrix for solve for the null space, which can be rounded to integer values. Positive values are products, negative are reactants. You can change this with 'ChemSign:=-1.

General procedure is, given a list of compounds

R NH4ClO4(s) Al(s) Al2O3(s) AlCl3(s) H2O(g) N2(g) 16 mat :

Find the Atoms in one compound

R 1 el NH4ClO4(s)

R 1 el ChemAtoms N 1 H 4 Cl 1 O 442 mat

Doing that for each compound, we get a Matrix with compositions

A R ChemAtoms : NH4ClO4(s) Al(s) Al2O3(s) AlCl3(s) H2O(g) N2(g) N 100002 H 400020 Cl 100300 O 403010 Al 01210067 mat

Basis for the Null splace of the compositions

B A 2 A rows range 2 A cols range el null : 0.3413 0.5689 0.2276 - 0.1138 - 0.6827 - 0.1707 - 61 mat

B are the coefficients for balance the equation. Final step is try to convert it to integers. rat returns Num and Den as the best rational aproximation for B, and lcm is the Euclidean least common multiplier.

N D 12 mat B B abs vectorize min / rat : 352 - 1 - 6 - 3 - 61 mat 11111261 mat 12 mat

D lcm N D / vectorize * 6104 - 2 - 12 - 3 - 61 mat

R transpose NH4ClO4(s) Al(s) Al2O3(s) AlCl3(s) H2O(g) N2(g) 61 mat

coeffs of

R ChemBal 4 Al2O3(s) + 2 AlCl3(s) + 12 H2O(g) + 3 N2(g) -> 6 NH4ClO4(s) + 10 Al(s) 11 mat

Examples

R (NH4)2Cr2O7(s) Cr2O3(s) N2(g) H2O(g) 14 mat :

R ChemBal (NH4)2Cr2O7(s) -> Cr2O3(s) + N2(g) + 4 H2O(g) 1 - 1114 mat

R Al(s) NH4ClO4(s) Al2O3(s) AlCl3(s) H2O(g) N2(g) 16 mat :

R ChemBal 4 Al2O3(s) + 2 AlCl3(s) + 12 H2O(g) + 3 N2(g) -> 10 Al(s) + 6 NH4ClO4(s) 11 mat

R C8H18(g) O2(g) CO2(g) H2O(l) 14 mat :

R ChemBal 16 CO2(g) + 18 H2O(l) -> 2 C8H18(g) + 25 O2(g) 22516 - 14 mat

R C7H16(g) O2(g) CO2(g) H2O(l) 14 mat :

R ChemBal 7 CO2(g) + 8 H2O(l) -> C7H16(g) + 11 O2(g) 1117 - 8 - 15 mat

R Pb(NO3)2(aq) NaCl(aq) NaNO3(aq) PbCl2(s) 14 mat :

R ChemBal Pb(NO3)2(aq) + 2 NaCl(aq) -> 2 NaNO3(aq) + PbCl2(s) 1 - 12 mat

R C2H5OH(l) O2(g) CO2(g) H2O(l) 14 mat :

R ChemBal 2 CO2(g) + 3 H2O(l) -> C2H5OH(l) + 3 O2(g) 132 - 3 - 15 mat

Reactions with ions

R Fe+2 Cr2O7-2 H+ Fe+3 Cr+3 H2O 16 mat :

R ChemAtoms Fe+2 Cr2O7-2 H+ Fe+3 Cr+3 H2O Fe 100100 Q 22 - 1330 Cr 020010 O 070001 H 00100267 mat

<- Q are the charges.

R ChemBal 6 Fe+3 + 2 Cr+3 + 7 H2O -> 6 Fe+2 + Cr2O7-2 + 14 H+ 612 mat

R Cr2O7-2 H+ I- Cr+3 I2 H2O 16 mat :

R ChemAtoms Cr2O7-2 H+ I- Cr+3 I2 H2O Cr 200100 O 700001 Q 2 - 11 - 300 H 010002 I 00102067 mat

R ChemBal Cr2O7-2 + 14 H+ + 6 I- -> 2 Cr+3 + 3 I2 + 7 H2O 1 - 14 - 13 mat

R MnO4- SnO2-2 MnO2 SnO3-2 OH- H2O 16 mat :

R ChemBal 2 MnO2 + 3 SnO3-2 + 2 OH- -> 2 MnO4- + 3 SnO2-2 + H2O 11 mat

R H+ Cr2O7-2 C2H5OH Cr+3 CO2 H2O 16 mat :

R ChemBal 4 Cr+3 + 2 CO2 + 11 H2O -> 16 H+ + 2 Cr2O7-2 + C2H5OH 11 mat

Miscellaneous samples

R C2H6 O2 CO2 H2O 14 mat :

R ChemBal 4 CO2 + 6 H2O -> 2 C2H6 + 7 O2 274 - 6 - 15 mat

R C2H6 O2 CO2 H2O 14 mat :

R ChemBal 4 CO2 + 6 H2O -> 2 C2H6 + 7 O2 274 - 6 - 15 mat

R NaOH H2SO4 Na2SO4 H2O 14 mat :

R ChemBal Na2SO4 + 2 H2O -> 2 NaOH + H2SO4 211 - 2 - 15 mat

R NaCl SO2 H2O O2 Na2SO4 HCl 16 mat :

R ChemBal 2 Na2SO4 + 4 HCl -> 4 NaCl + 2 SO2 + 2 H2O + O2 422115 mat

R H3PO4 (NH4)2MoO4 HNO3 (NH4)3PO4(MoO3)12 N2H4O3 H2O 16 mat :

R ChemBal (NH4)3PO4(MoO3)12 + 21 N2H4O3 + 12 H2O -> H3PO4 + 12 (NH4)2MoO4 + 21 HNO3 112211 - 15 mat

R MgN2O6 Mg N2 O2 14 mat :

R ChemBal Mg + N2 + 3 O2 -> MgN2O6 11 - 1 - 3 - 15 mat

R K4Fe(CN)6 H2SO4 H2O K2SO4 FeSO4 (NH4)2SO4 CO 17 mat :

A R ChemAtoms : K4Fe(CN)6 H2SO4 H2O K2SO4 FeSO4 (NH4)2SO4 CO C 6000001 N 6000020 K 4002000 Fe 1000100 H 0220080 S 0101110 O 041444188 mat

R ChemBal 2 K2SO4 + FeSO4 + 3 (NH4)2SO4 + 6 CO -> K4Fe(CN)6 + 6 H2SO4 + 6 H2O 1662 - 15 mat

R K4FeC6N6 KMnO4 H2SO4 KHSO4 Fe2S3O12 MnSO4 HNO3 CO2 H2O 19 mat :

B R ChemBal :

B 29 range el transpose 10122299162 - 5 - 122 - 60 - 60 - 18 mat

B 1 el 162 KHSO4 + 5 Fe2S3O12 + 122 MnSO4 + 60 HNO3 + 60 CO2 + 188 H2O -> 10 K4FeC6N6 + 122 KMnO4 + 299 H2SO4

A R ChemAtoms : K4FeC6N6 KMnO4 H2SO4 KHSO4 Fe2S3O12 MnSO4 HNO3 CO2 H2O K 410100000 Fe 100020000 C 600000010 N 600000100 Mn 010001000 O 0444124321 H 002100102 S 001131000910 mat

R1 H2 Ca(CN)2 NaAlF4 FeSO4 MgSiO3 KI H3PO4 PbCrO4 BrCl CF2Cl2 SO2 111 mat :

R2 PbBr2 CrCl3 MgCO3 KAl(OH)4 Fe(SCN)3 PI3 NaSiO3 CaF2 H2O 19 mat :

R R1 R2 augment :

B R ChemBal :

B 12 B cols range el 11918612662122462412 - 12 - 6 - 6 - 12 - 2 - 6 - 18 - 110 - 120 mat

B 1 el 198 substr 12 PbBr2 + 12 CrCl3 + 6 MgCO3 + 6 KAl(OH)4 + 12 Fe(SCN)3 + 2 PI3 + 6 NaSiO3 + 18 CaF2 + 110 H2O ->

B 1 el 97114 substr -> 119 H2 + 18 Ca(CN)2 + 6 NaAlF4 + 12 FeSO4 + 6 MgSiO3 + 6 KI + 2 H3PO4 + 12 PbCrO4 + 24 BrCl + 6 CF2Cl2 + 24 SO2

Issues

Two solutions: I don't know what can do here very well because usually it means that can be more than one reaction, but I don't uderstand this case..

R CO CO2 H2 CH4 H2O 15 mat :

A R ChemAtoms : CO CO2 H2 CH4 H2O C 11010 O 12001 H 0024246 mat

R ChemBal ERROR: 4422811581856390000000000000000000000000000000000 CO2 + 3914082389556230000000000000000000000000000000000 CH4 -> 8336893971415580000000000000000000000000000000000 CO + 7319435586815260000000000000000000000000000000000 H2 + 508729192300159000000000000000000000000000000000 H2O 8.3369 1048^* 4.4228 1048^* - 7.3194 1048^* 3.9141 1048^* - ERROR: 4443805230603310000000000000000000000000000000000 CO + 952602252280213000000000000000000000000000000000 CH4 + 6349009735168490000000000000000000000000000000000 H2O -> 5396407482872730000000000000000000000000000000000 CO2 + 8254214239720680000000000000000000000000000000000 H2 4.4438 1048^* - 5.3964 1048^* 8.2542 1048^* 9.526 1047^* - 25 mat

No solutions: Here the error msg it's ok, can't be reactions with this compounds.

R FeS2 HNO3 Fe2S3O12 NO H2SO4 15 mat :

R ChemBal #

R ChemAtoms FeS2 HNO3 Fe2S3O12 NO H2SO4 Fe 10200 S 20301 H 01002 N 01010 O 03121466 mat

Alvaro