Balancing Really HardBalancing Really HardChemical ReactionsChemical Reactions

TAMOBETAMOBEToburen’s Algebraic Method of Toburen’s Algebraic Method of

Balancing EquationsBalancing Equations

Reactants: Zn + IReactants: Zn + I22 Product: Zn IProduct: Zn I22

Balancing Really Hard Equations:Balancing Really Hard Equations:At the conclusion of our time together, At the conclusion of our time together,

you should be able to:you should be able to:

1.1. Use TAMOBE to solve even the Use TAMOBE to solve even the most difficult equations.most difficult equations.

Happy Birthday DirgeHappy Birthday Dirge

Happy Birthday, Happy Happy Birthday, Happy Birthday,Birthday,

When you’ve reached this When you’ve reached this age you know, age you know,

that the mind is first to go.that the mind is first to go. Happy Birthday, Happy Happy Birthday, Happy

Birthday!Birthday!

Steps to TAMOBESteps to TAMOBE

Use this method for very difficult Use this method for very difficult equations to balance.equations to balance.

Place a different letter coefficient Place a different letter coefficient in front of each formula on both in front of each formula on both sides of the equation. Use letters sides of the equation. Use letters that are not commonly used in that are not commonly used in Chemistry.Chemistry.

Example AExample A

HCl + KMnOHCl + KMnO44 H H22O + KCl + MnClO + KCl + MnCl22 + + ClCl22  

X HCl + Y KMnOX HCl + Y KMnO44 Z H Z H22O + W KCl + O + W KCl + Q MnClQ MnCl22 + R Cl + R Cl22

Complexity Complexity H, H, K, K, Mn, Mn, O, O, ClCl

X HCl + Y KMnOX HCl + Y KMnO44 Z H Z H22O + W KCl + O + W KCl + Q MnClQ MnCl22 + R Cl + R Cl22 Eliminate H:Eliminate H:

X = 2ZX = 2Z 2Z HCl + Y KMnO2Z HCl + Y KMnO44 Z HZ H22O + W KCl + Q MnClO + W KCl + Q MnCl22 + R Cl + R Cl22 Eliminate K:Eliminate K: Y = WY = W 2Z HCl + W KMnO2Z HCl + W KMnO44 Z HZ H22O + W KCl + Q MnClO + W KCl + Q MnCl22 + R Cl + R Cl22

2Z HCl + W KMnO2Z HCl + W KMnO44 Z HZ H22O + W KCl + Q MnClO + W KCl + Q MnCl22 + R + R

ClCl22

Eliminate Mn:Eliminate Mn: W = QW = Q 2Z HCl + Q KMnO2Z HCl + Q KMnO44 Z HZ H22O + Q KCl + Q MnClO + Q KCl + Q MnCl22 + R + R

ClCl22

  2Z HCl + Q KMnO2Z HCl + Q KMnO44 Z HZ H22O + Q KCl + Q MnClO + Q KCl + Q MnCl22 + R + R

ClCl22Eliminate O:Eliminate O:

4Q = Z4Q = Z 8Q HCl + Q KMnO8Q HCl + Q KMnO44 4Q H4Q H22O + Q KCl + Q MnClO + Q KCl + Q MnCl22 + R + R

ClCl22

  8Q HCl + Q KMnO8Q HCl + Q KMnO44 4Q H4Q H22O + Q KCl + Q MnClO + Q KCl + Q MnCl22 + R + R

ClCl22Eliminate Cl:Eliminate Cl:

8Q = Q + 2Q + 2R8Q = Q + 2Q + 2R 5Q = 2R5Q = 2R 5/2Q = R5/2Q = R 8Q HCl + Q KMnO8Q HCl + Q KMnO44 4Q H4Q H22O + Q KCl + Q MnClO + Q KCl + Q MnCl22 + 5/2Q + 5/2Q

ClCl22  

8Q HCl + Q KMnO8Q HCl + Q KMnO44 4Q H4Q H22O + Q KCl + Q MnClO + Q KCl + Q MnCl22 + 5/2Q Cl + 5/2Q Cl22

Double EverythingDouble Everything 16Q HCl + 2Q KMnO16Q HCl + 2Q KMnO44 8Q H8Q H22O + 2Q KCl + 2Q MnClO + 2Q KCl + 2Q MnCl22 + 5Q Cl + 5Q Cl22

Divide Everything by QDivide Everything by Q 16 HCl + 2 KMnO16 HCl + 2 KMnO44 8 H8 H22O + 2 KCl + 2 MnClO + 2 KCl + 2 MnCl22 + 5 Cl + 5 Cl22

Example of TAMOBE BExample of TAMOBE B

CC33HH77S + OS + O22 COCO22 + H + H22OO + SO + SO22

X CX C33HH77S + Y OS + Y O22 Z COZ CO22 + Q H + Q H22OO + R + R

SOSO22

Example of TAMOBE BExample of TAMOBE B

X CX C33HH77S + Y OS + Y O22 Z COZ CO22 + Q H + Q H22OO + R + R

SOSO22

Complexity Complexity S, S, C, C, H, H, OO

X CX C33HH77S + Y OS + Y O22 Z COZ CO22 + Q H + Q H22OO + R + R

SOSO22 Complexity Complexity S, S, C, C, H, H, OO

Eliminate S:Eliminate S: X = RX = R R CR C33HH77S + Y OS + Y O22 Z COZ CO22 + Q H + Q H22OO + R + R

SOSO22

R CR C33HH77S + Y OS + Y O22 Z COZ CO22 + Q H + Q H22OO + R + R

SOSO22

Eliminate C:Eliminate C: 3R = Z3R = Z R CR C33HH77S + Y OS + Y O22 3R CO3R CO22 + Q H + Q H22OO + R + R

SOSO22

R CR C33HH77S + Y OS + Y O22 3R CO3R CO22 + Q H + Q H22OO + R + R

SOSO22 Eliminate H:Eliminate H: 7R = 2Q; 7R = 2Q; 7/2R = Q7/2R = Q R CR C33HH77S + Y OS + Y O22 3R CO3R CO22 + 7/2R H + 7/2R H22OO + R + R

SOSO22

R CR C33HH77S + Y OS + Y O22 3R CO3R CO22 + 7/2R H + 7/2R H22OO + R + R

SOSO22

Eliminate O:Eliminate O:2Y 2Y = 6R + 7/2 R + 2R = 6R + 7/2 R + 2R

= 23/2 R= 23/2 R Y Y = 23/4R= 23/4R R CR C33HH77S + 23/4R OS + 23/4R O22 3R CO3R CO22 + 7/2R H + 7/2R H22OO + R + R

SOSO22

R CR C33HH77S + 23/4R OS + 23/4R O22 3R CO3R CO22 + 7/2R H + 7/2R H22OO + R + R

SOSO22

Multiply Everything by 4Multiply Everything by 4 4R C4R C33HH77S + 23R OS + 23R O22 12R CO12R CO22 + 14R H + 14R H22OO + 4R + 4R

SOSO22

4R C4R C33HH77S + 23R OS + 23R O22 12R CO12R CO22 + 14R H + 14R H22OO + 4R + 4R

SOSO22

Divide by R Divide by R  4 C4 C33HH77S + 23 OS + 23 O22 12 CO12 CO22 + 14 H + 14 H22OO + 4 SO + 4 SO22

Interesting Signs:

Balancing Really Hard Equations:Balancing Really Hard Equations:Let’s see if you can:Let’s see if you can:

1.1. Use TAMOBE to solve even the Use TAMOBE to solve even the most difficult equations.most difficult equations.

The Scientific MethodThe Scientific Methodbegins with begins with

Questions about the World Around Questions about the World Around You.You.

Ever Wonder Why?...Ever Wonder Why?...

Superman sticks out his chest to block bullets but he ducks when the gun is

thrown at him?

Try TAMOBE AgainTry TAMOBE Again

AsAs22SS33 + HNO + HNO33 + H + H22O O HH33AsOAsO44 + H + H22SOSO4 4 + NO + NO

X AsX As22SS33 + Y HNO + Y HNO33 + Z H + Z H22O O Q HQ H33AsOAsO44 + R H + R H22SOSO4 4 + W NO + W NO

Complexity Complexity N, N, As, As, S, S, H, H, OO

Eliminate N:Eliminate N: Y = WY = W X AsX As22SS33 + W HNO + W HNO33 + Z H + Z H22O O Q HQ H33AsOAsO44 + R H + R H22SOSO4 4 + W NO + W NO

Eliminate As:Eliminate As: 2X = Q2X = Q X AsX As22SS33 + W HNO + W HNO33 + Z H + Z H22O O 2X H2X H33AsOAsO44 + R H + R H22SOSO4 4 + W NO + W NO

Eliminate S:Eliminate S: 3X = R3X = R X AsX As22SS33 + W HNO + W HNO33 + Z H + Z H22O O 2X H2X H33AsOAsO44 + 3X H + 3X H22SOSO4 4 + W NO + W NO

X AsX As22SS33 + W HNO + W HNO33 + Z H + Z H22O O 2X H2X H33AsOAsO44 + 3X H + 3X H22SOSO4 4 + W NO + W NO

Eliminate H:Eliminate H: W + 2Z = 6X + 6X = 12XW + 2Z = 6X + 6X = 12X X AsX As22SS33 + (12X-2Z) HNO + (12X-2Z) HNO33 + Z H + Z H22O O 2X H2X H33AsOAsO44 + 3X H + 3X H22SOSO4 4 + (12X-2Z) NO + (12X-2Z) NO

Eliminate O: 36X-6Z + Z = 8X + 12X + 12X-2ZEliminate O: 36X-6Z + Z = 8X + 12X + 12X-2Z 36X-5Z = 32X-2Z36X-5Z = 32X-2Z 4/3X = Z4/3X = Z X AsX As22SS33 + (12X-8/3X) HNO + (12X-8/3X) HNO33 + 4/3X H + 4/3X H22O O 2X H2X H33AsOAsO44 + 3X H + 3X H22SOSO4 4 + (12X-8/3X) NO + (12X-8/3X) NO   

X AsX As22SS33 + (12X-8/3X) HNO + (12X-8/3X) HNO33 + 4/3X H + 4/3X H22O O 2X H2X H33AsOAsO44 + 3X H + 3X H22SOSO4 4 + (12X-8/3X) NO + (12X-8/3X) NO

Multiply Everything by 3Multiply Everything by 3 3X As3X As22SS33 + (36X-8X) HNO + (36X-8X) HNO33 + 4X H + 4X H22O O 6X H6X H33AsOAsO44 + 9X H + 9X H22SOSO4 4 + (36X-8X) NO + (36X-8X) NOCombine Like Terms:Combine Like Terms: 3X As3X As22SS33 + 28X HNO + 28X HNO33 + 4X H + 4X H22O O 6X H6X H33AsOAsO44 + 9X H + 9X H22SOSO4 4 + 28X NO + 28X NODivide by X Divide by X  3 As3 As22SS33 + 28 HNO + 28 HNO33 + 4 H + 4 H22O O 6 H6 H33AsOAsO44 + 9 H + 9 H22SOSO4 4 + 28 NO + 28 NO

“Disorder in the American Courts”

These are statements people actually said in court, word for word, taken down and now published by court

reporters.ATTORNEY:  Now doctor, isn't it true that when a person dies in his

sleep, he doesn't know about it until the next morning?WITNESS:  Did you actually pass the bar exam?