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METALS AND ACIDS
METALS AND ACIDS Metals Magnesium Iron Sodium Calcium
METALS AND ACIDS Metals Magnesium Iron Sodium Calcium Acids Hydrochloric acid Sulphuric acid Nitric acid Ethanoic acid
METALS AND ACIDS Metal  +  Acid     Salt  +  Hydrogen Metals Magnesium Iron Sodium Calcium Acids Hydrochloric acid Sulphuric acid Nitric acid Ethanoic acid
FORMING SALTS METAL ACID SALT magnesium hydrochloric acid iron iron nitrate ethanoic acid sodium ethanoate calcium calcium sulphate copper nitric acid nitric acid iron nitrate sodium sodium chloride calcium ethanoic acid magnesium sulphuric acid
FORMING SALTS METAL ACID SALT magnesium hydrochloric acid magnesium chloride iron iron nitrate ethanoic acid sodium ethanoate calcium calcium sulphate copper nitric acid nitric acid iron nitrate sodium sodium chloride calcium ethanoic acid magnesium sulphuric acid
FORMING SALTS METAL ACID SALT magnesium hydrochloric acid magnesium chloride iron nitric acid iron nitrate ethanoic acid sodium ethanoate calcium calcium sulphate copper nitric acid nitric acid iron nitrate sodium sodium chloride calcium ethanoic acid magnesium sulphuric acid
FORMING SALTS METAL ACID SALT magnesium hydrochloric acid magnesium chloride iron nitric acid iron nitrate sodium ethanoic acid sodium ethanoate calcium calcium sulphate copper nitric acid nitric acid iron nitrate sodium sodium chloride calcium ethanoic acid magnesium sulphuric acid
FORMING SALTS METAL ACID SALT magnesium hydrochloric acid magnesium chloride iron nitric acid iron nitrate sodium ethanoic acid sodium ethanoate calcium sulphuric acid calcium sulphate copper nitric acid nitric acid iron nitrate sodium sodium chloride calcium ethanoic acid magnesium sulphuric acid
FORMING SALTS METAL ACID SALT magnesium hydrochloric acid magnesium chloride iron nitric acid iron nitrate sodium ethanoic acid sodium ethanoate calcium sulphuric acid calcium sulphate copper nitric acid No Reaction nitric acid iron nitrate sodium sodium chloride calcium ethanoic acid magnesium sulphuric acid
FORMING SALTS METAL ACID SALT magnesium hydrochloric acid magnesium chloride iron nitric acid iron nitrate sodium ethanoic acid sodium ethanoate calcium sulphuric acid calcium sulphate copper nitric acid copper nitrate iron nitric acid iron nitrate sodium sodium chloride calcium ethanoic acid magnesium sulphuric acid
FORMING SALTS METAL ACID SALT magnesium hydrochloric acid magnesium chloride iron nitric acid iron nitrate sodium ethanoic acid sodium ethanoate calcium sulphuric acid calcium sulphate copper nitric acid copper nitrate iron nitric acid iron nitrate sodium hydrochloric acid sodium chloride calcium ethanoic acid magnesium sulphuric acid
FORMING SALTS METAL ACID SALT magnesium hydrochloric acid magnesium chloride iron nitric acid iron nitrate sodium ethanoic acid sodium ethanoate calcium sulphuric acid calcium sulphate copper nitric acid copper nitrate iron nitric acid iron nitrate sodium hydrochloric acid sodium chloride calcium ethanoic acid calcium ethanoate magnesium sulphuric acid
FORMING SALTS METAL ACID SALT magnesium hydrochloric acid magnesium chloride iron nitric acid iron nitrate sodium ethanoic acid sodium ethanoate calcium sulphuric acid calcium sulphate copper nitric acid copper nitrate iron nitric acid iron nitrate sodium hydrochloric acid sodium chloride calcium ethanoic acid calcium ethanoate magnesium sulphuric acid magnesium sulphate
DISPLACEMENT REACTIONS Metal  soln Metal Iron (III) nitrate Magnesium nitrate Copper (II) sulphate Zinc sulphate Lead (II) nitrate Iron Magnesium Copper Zinc Lead
DISPLACEMENT REACTIONS ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
DISPLACEMENT REACTIONS Metal ion soln Metal Iron (III) nitrate Magnesium nitrate Copper (II) sulphate Zinc sulphate Lead (II) nitrate Iron Magnesium Copper Zinc Lead
DISPLACEMENT REACTIONS Metal ion soln Metal Iron (III) nitrate Magnesium nitrate Copper (II) sulphate Zinc sulphate Lead (II) nitrate Iron X X  X  Magnesium Copper Zinc Lead
DISPLACEMENT REACTIONS Metal ion soln Metal Iron (III) nitrate Magnesium nitrate Copper (II) sulphate Zinc sulphate Lead (II) nitrate Iron X X  X  Magnesium  X    Copper Zinc Lead
DISPLACEMENT REACTIONS Metal ion soln Metal Iron (III) nitrate Magnesium nitrate Copper (II) sulphate Zinc sulphate Lead (II) nitrate Iron X X  X  Magnesium  X    Copper X X X X X Zinc Lead
DISPLACEMENT REACTIONS Metal ion soln Metal Iron (III) nitrate Magnesium nitrate Copper (II) sulphate Zinc sulphate Lead (II) nitrate Iron X X  X  Magnesium  X    Copper X X X X X Zinc  X  X  Lead
DISPLACEMENT REACTIONS Metal ion soln Metal Iron (III) nitrate Magnesium nitrate Copper (II) sulphate Zinc sulphate Lead (II) nitrate Iron X X  X  Magnesium  X    Copper X X X X X Zinc  X  X  Lead X X  X X
DISPLACEMENT REACTIONS Summary More reactive metals can displace less reactive metals from their solutions
DISPLACEMENT REACTIONS Summary More reactive metals can displace less reactive metals from their solutions e.g. magnesium  +  iron (II) nitrate  
DISPLACEMENT REACTIONS Summary More reactive metals can displace less reactive metals from their solutions e.g. magnesium  +  iron (II) nitrate     magnesium nitrate  +  iron
DISPLACEMENT REACTIONS Summary More reactive metals can displace less reactive metals from their solutions e.g. magnesium  +  iron (II) nitrate     magnesium nitrate  +  iron  magnesium is more reactive than iron
DISPLACEMENT REACTIONS Summary More reactive metals can displace less reactive metals from their solutions e.g. magnesium  +  iron (II) nitrate     magnesium nitrate  +  iron  magnesium is more reactive than iron and lead  +  copper (II) sulphate  
DISPLACEMENT REACTIONS Summary More reactive metals can displace less reactive metals from their solutions e.g. magnesium  +  iron (II) nitrate     magnesium nitrate  +  iron  magnesium is more reactive than iron and lead  +  copper (II) sulphate     lead (II) sulphate  +  copper
DISPLACEMENT REACTIONS Summary More reactive metals can displace less reactive metals from their solutions e.g. magnesium  +  iron (II) nitrate     magnesium nitrate  +  iron  magnesium is more reactive than iron and lead  +  copper (II) sulphate     lead (II) sulphate  +  copper lead is more reactive than copper
DISPLACEMENT REACTIONS Summary More reactive metals can displace less reactive metals from their solutions e.g. magnesium  +  iron (II) nitrate     magnesium nitrate  +  iron  magnesium is more reactive than iron and lead  +  copper (II) sulphate     lead (II) sulphate  +  copper lead is more reactive than copper but copper + lead (II) sulphate  
DISPLACEMENT REACTIONS Summary More reactive metals can displace less reactive metals from their solutions e.g. magnesium  +  iron (II) nitrate     magnesium nitrate  +  iron  magnesium is more reactive than iron and lead  +  copper (II) sulphate     lead (II) sulphate  +  copper lead is more reactive than copper but copper + lead (II) sulphate     no reaction
DISPLACEMENT REACTIONS Summary More reactive metals can displace less reactive metals from their solutions e.g. magnesium  +  iron (II) nitrate     magnesium nitrate  +  iron  magnesium is more reactive than iron and lead  +  copper (II) sulphate     lead (II) sulphate  +  copper lead is more reactive than copper but copper + lead (II) sulphate     no reaction   copper   is not more reactive than lead

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Metals Acids Displacement Reactions

  • 2. METALS AND ACIDS Metals Magnesium Iron Sodium Calcium
  • 3. METALS AND ACIDS Metals Magnesium Iron Sodium Calcium Acids Hydrochloric acid Sulphuric acid Nitric acid Ethanoic acid
  • 4. METALS AND ACIDS Metal + Acid  Salt + Hydrogen Metals Magnesium Iron Sodium Calcium Acids Hydrochloric acid Sulphuric acid Nitric acid Ethanoic acid
  • 5. FORMING SALTS METAL ACID SALT magnesium hydrochloric acid iron iron nitrate ethanoic acid sodium ethanoate calcium calcium sulphate copper nitric acid nitric acid iron nitrate sodium sodium chloride calcium ethanoic acid magnesium sulphuric acid
  • 6. FORMING SALTS METAL ACID SALT magnesium hydrochloric acid magnesium chloride iron iron nitrate ethanoic acid sodium ethanoate calcium calcium sulphate copper nitric acid nitric acid iron nitrate sodium sodium chloride calcium ethanoic acid magnesium sulphuric acid
  • 7. FORMING SALTS METAL ACID SALT magnesium hydrochloric acid magnesium chloride iron nitric acid iron nitrate ethanoic acid sodium ethanoate calcium calcium sulphate copper nitric acid nitric acid iron nitrate sodium sodium chloride calcium ethanoic acid magnesium sulphuric acid
  • 8. FORMING SALTS METAL ACID SALT magnesium hydrochloric acid magnesium chloride iron nitric acid iron nitrate sodium ethanoic acid sodium ethanoate calcium calcium sulphate copper nitric acid nitric acid iron nitrate sodium sodium chloride calcium ethanoic acid magnesium sulphuric acid
  • 9. FORMING SALTS METAL ACID SALT magnesium hydrochloric acid magnesium chloride iron nitric acid iron nitrate sodium ethanoic acid sodium ethanoate calcium sulphuric acid calcium sulphate copper nitric acid nitric acid iron nitrate sodium sodium chloride calcium ethanoic acid magnesium sulphuric acid
  • 10. FORMING SALTS METAL ACID SALT magnesium hydrochloric acid magnesium chloride iron nitric acid iron nitrate sodium ethanoic acid sodium ethanoate calcium sulphuric acid calcium sulphate copper nitric acid No Reaction nitric acid iron nitrate sodium sodium chloride calcium ethanoic acid magnesium sulphuric acid
  • 11. FORMING SALTS METAL ACID SALT magnesium hydrochloric acid magnesium chloride iron nitric acid iron nitrate sodium ethanoic acid sodium ethanoate calcium sulphuric acid calcium sulphate copper nitric acid copper nitrate iron nitric acid iron nitrate sodium sodium chloride calcium ethanoic acid magnesium sulphuric acid
  • 12. FORMING SALTS METAL ACID SALT magnesium hydrochloric acid magnesium chloride iron nitric acid iron nitrate sodium ethanoic acid sodium ethanoate calcium sulphuric acid calcium sulphate copper nitric acid copper nitrate iron nitric acid iron nitrate sodium hydrochloric acid sodium chloride calcium ethanoic acid magnesium sulphuric acid
  • 13. FORMING SALTS METAL ACID SALT magnesium hydrochloric acid magnesium chloride iron nitric acid iron nitrate sodium ethanoic acid sodium ethanoate calcium sulphuric acid calcium sulphate copper nitric acid copper nitrate iron nitric acid iron nitrate sodium hydrochloric acid sodium chloride calcium ethanoic acid calcium ethanoate magnesium sulphuric acid
  • 14. FORMING SALTS METAL ACID SALT magnesium hydrochloric acid magnesium chloride iron nitric acid iron nitrate sodium ethanoic acid sodium ethanoate calcium sulphuric acid calcium sulphate copper nitric acid copper nitrate iron nitric acid iron nitrate sodium hydrochloric acid sodium chloride calcium ethanoic acid calcium ethanoate magnesium sulphuric acid magnesium sulphate
  • 15. DISPLACEMENT REACTIONS Metal soln Metal Iron (III) nitrate Magnesium nitrate Copper (II) sulphate Zinc sulphate Lead (II) nitrate Iron Magnesium Copper Zinc Lead
  • 16.
  • 17. DISPLACEMENT REACTIONS Metal ion soln Metal Iron (III) nitrate Magnesium nitrate Copper (II) sulphate Zinc sulphate Lead (II) nitrate Iron Magnesium Copper Zinc Lead
  • 18. DISPLACEMENT REACTIONS Metal ion soln Metal Iron (III) nitrate Magnesium nitrate Copper (II) sulphate Zinc sulphate Lead (II) nitrate Iron X X  X  Magnesium Copper Zinc Lead
  • 19. DISPLACEMENT REACTIONS Metal ion soln Metal Iron (III) nitrate Magnesium nitrate Copper (II) sulphate Zinc sulphate Lead (II) nitrate Iron X X  X  Magnesium  X    Copper Zinc Lead
  • 20. DISPLACEMENT REACTIONS Metal ion soln Metal Iron (III) nitrate Magnesium nitrate Copper (II) sulphate Zinc sulphate Lead (II) nitrate Iron X X  X  Magnesium  X    Copper X X X X X Zinc Lead
  • 21. DISPLACEMENT REACTIONS Metal ion soln Metal Iron (III) nitrate Magnesium nitrate Copper (II) sulphate Zinc sulphate Lead (II) nitrate Iron X X  X  Magnesium  X    Copper X X X X X Zinc  X  X  Lead
  • 22. DISPLACEMENT REACTIONS Metal ion soln Metal Iron (III) nitrate Magnesium nitrate Copper (II) sulphate Zinc sulphate Lead (II) nitrate Iron X X  X  Magnesium  X    Copper X X X X X Zinc  X  X  Lead X X  X X
  • 23. DISPLACEMENT REACTIONS Summary More reactive metals can displace less reactive metals from their solutions
  • 24. DISPLACEMENT REACTIONS Summary More reactive metals can displace less reactive metals from their solutions e.g. magnesium + iron (II) nitrate 
  • 25. DISPLACEMENT REACTIONS Summary More reactive metals can displace less reactive metals from their solutions e.g. magnesium + iron (II) nitrate  magnesium nitrate + iron
  • 26. DISPLACEMENT REACTIONS Summary More reactive metals can displace less reactive metals from their solutions e.g. magnesium + iron (II) nitrate  magnesium nitrate + iron magnesium is more reactive than iron
  • 27. DISPLACEMENT REACTIONS Summary More reactive metals can displace less reactive metals from their solutions e.g. magnesium + iron (II) nitrate  magnesium nitrate + iron magnesium is more reactive than iron and lead + copper (II) sulphate 
  • 28. DISPLACEMENT REACTIONS Summary More reactive metals can displace less reactive metals from their solutions e.g. magnesium + iron (II) nitrate  magnesium nitrate + iron magnesium is more reactive than iron and lead + copper (II) sulphate  lead (II) sulphate + copper
  • 29. DISPLACEMENT REACTIONS Summary More reactive metals can displace less reactive metals from their solutions e.g. magnesium + iron (II) nitrate  magnesium nitrate + iron magnesium is more reactive than iron and lead + copper (II) sulphate  lead (II) sulphate + copper lead is more reactive than copper
  • 30. DISPLACEMENT REACTIONS Summary More reactive metals can displace less reactive metals from their solutions e.g. magnesium + iron (II) nitrate  magnesium nitrate + iron magnesium is more reactive than iron and lead + copper (II) sulphate  lead (II) sulphate + copper lead is more reactive than copper but copper + lead (II) sulphate 
  • 31. DISPLACEMENT REACTIONS Summary More reactive metals can displace less reactive metals from their solutions e.g. magnesium + iron (II) nitrate  magnesium nitrate + iron magnesium is more reactive than iron and lead + copper (II) sulphate  lead (II) sulphate + copper lead is more reactive than copper but copper + lead (II) sulphate  no reaction
  • 32. DISPLACEMENT REACTIONS Summary More reactive metals can displace less reactive metals from their solutions e.g. magnesium + iron (II) nitrate  magnesium nitrate + iron magnesium is more reactive than iron and lead + copper (II) sulphate  lead (II) sulphate + copper lead is more reactive than copper but copper + lead (II) sulphate  no reaction copper is not more reactive than lead

Hinweis der Redaktion

  1. Electrons can spin. In a similar way, all nuclei can spin (except those with an even atomic number and an even mass number). These positively charged spheres behave like magnets. When placed into a strong magnetic field, each nucleus can either align with the external magnetic field or against it. The lower energy state occurs when the nucleus is spinning in alignment with the magnetic field, and the high energy state occurs when the nucleus is spinning out of alignment with the magnetic field Given sufficient energy, the nuclei can ‘flip’ between the two states. In an NMR spectrometer, the magnetic field strength can be varied. The magnetic field strength at which the nucleus flips can thus be measured. The strength of magnetic field at which a particular nucleus flips is dependant upon the environment of that nucleus.
  2. Electrons can spin. In a similar way, all nuclei can spin (except those with an even atomic number and an even mass number). These positively charged spheres behave like magnets. When placed into a strong magnetic field, each nucleus can either align with the external magnetic field or against it. The lower energy state occurs when the nucleus is spinning in alignment with the magnetic field, and the high energy state occurs when the nucleus is spinning out of alignment with the magnetic field Given sufficient energy, the nuclei can ‘flip’ between the two states. In an NMR spectrometer, the magnetic field strength can be varied. The magnetic field strength at which the nucleus flips can thus be measured. The strength of magnetic field at which a particular nucleus flips is dependant upon the environment of that nucleus.
  3. Electrons can spin. In a similar way, all nuclei can spin (except those with an even atomic number and an even mass number). These positively charged spheres behave like magnets. When placed into a strong magnetic field, each nucleus can either align with the external magnetic field or against it. The lower energy state occurs when the nucleus is spinning in alignment with the magnetic field, and the high energy state occurs when the nucleus is spinning out of alignment with the magnetic field Given sufficient energy, the nuclei can ‘flip’ between the two states. In an NMR spectrometer, the magnetic field strength can be varied. The magnetic field strength at which the nucleus flips can thus be measured. The strength of magnetic field at which a particular nucleus flips is dependant upon the environment of that nucleus.
  4. Electrons can spin. In a similar way, all nuclei can spin (except those with an even atomic number and an even mass number). These positively charged spheres behave like magnets. When placed into a strong magnetic field, each nucleus can either align with the external magnetic field or against it. The lower energy state occurs when the nucleus is spinning in alignment with the magnetic field, and the high energy state occurs when the nucleus is spinning out of alignment with the magnetic field Given sufficient energy, the nuclei can ‘flip’ between the two states. In an NMR spectrometer, the magnetic field strength can be varied. The magnetic field strength at which the nucleus flips can thus be measured. The strength of magnetic field at which a particular nucleus flips is dependant upon the environment of that nucleus.
  5. We say that these show different chemical shifts - ie they flip at different field strengths. The observed chemical shift is measured against a standard - usually tetramethylsilane (TMS). The example above shows methanol. Methanol has three H nuclei which have an identical environment (labelled 1) and one hydrogen in a different environnment (labelled 2). Two peaks due to methanol can be observed. The smallest is due to the hydrogen labelled 1. The second is due to the three other hydrogens. It is three times the size of the first.
  6. We say that these show different chemical shifts - ie they flip at different field strengths. The observed chemical shift is measured against a standard - usually tetramethylsilane (TMS). The example above shows methanol. Methanol has three H nuclei which have an identical environment (labelled 1) and one hydrogen in a different environnment (labelled 2). Two peaks due to methanol can be observed. The smallest is due to the hydrogen labelled 1. The second is due to the three other hydrogens. It is three times the size of the first.
  7. We say that these show different chemical shifts - ie they flip at different field strengths. The observed chemical shift is measured against a standard - usually tetramethylsilane (TMS). The example above shows methanol. Methanol has three H nuclei which have an identical environment (labelled 1) and one hydrogen in a different environnment (labelled 2). Two peaks due to methanol can be observed. The smallest is due to the hydrogen labelled 1. The second is due to the three other hydrogens. It is three times the size of the first.
  8. We say that these show different chemical shifts - ie they flip at different field strengths. The observed chemical shift is measured against a standard - usually tetramethylsilane (TMS). The example above shows methanol. Methanol has three H nuclei which have an identical environment (labelled 1) and one hydrogen in a different environnment (labelled 2). Two peaks due to methanol can be observed. The smallest is due to the hydrogen labelled 1. The second is due to the three other hydrogens. It is three times the size of the first.
  9. We say that these show different chemical shifts - ie they flip at different field strengths. The observed chemical shift is measured against a standard - usually tetramethylsilane (TMS). The example above shows methanol. Methanol has three H nuclei which have an identical environment (labelled 1) and one hydrogen in a different environnment (labelled 2). Two peaks due to methanol can be observed. The smallest is due to the hydrogen labelled 1. The second is due to the three other hydrogens. It is three times the size of the first.
  10. We say that these show different chemical shifts - ie they flip at different field strengths. The observed chemical shift is measured against a standard - usually tetramethylsilane (TMS). The example above shows methanol. Methanol has three H nuclei which have an identical environment (labelled 1) and one hydrogen in a different environnment (labelled 2). Two peaks due to methanol can be observed. The smallest is due to the hydrogen labelled 1. The second is due to the three other hydrogens. It is three times the size of the first.
  11. We say that these show different chemical shifts - ie they flip at different field strengths. The observed chemical shift is measured against a standard - usually tetramethylsilane (TMS). The example above shows methanol. Methanol has three H nuclei which have an identical environment (labelled 1) and one hydrogen in a different environnment (labelled 2). Two peaks due to methanol can be observed. The smallest is due to the hydrogen labelled 1. The second is due to the three other hydrogens. It is three times the size of the first.
  12. We say that these show different chemical shifts - ie they flip at different field strengths. The observed chemical shift is measured against a standard - usually tetramethylsilane (TMS). The example above shows methanol. Methanol has three H nuclei which have an identical environment (labelled 1) and one hydrogen in a different environnment (labelled 2). Two peaks due to methanol can be observed. The smallest is due to the hydrogen labelled 1. The second is due to the three other hydrogens. It is three times the size of the first.
  13. We say that these show different chemical shifts - ie they flip at different field strengths. The observed chemical shift is measured against a standard - usually tetramethylsilane (TMS). The example above shows methanol. Methanol has three H nuclei which have an identical environment (labelled 1) and one hydrogen in a different environnment (labelled 2). Two peaks due to methanol can be observed. The smallest is due to the hydrogen labelled 1. The second is due to the three other hydrogens. It is three times the size of the first.
  14. We say that these show different chemical shifts - ie they flip at different field strengths. The observed chemical shift is measured against a standard - usually tetramethylsilane (TMS). The example above shows methanol. Methanol has three H nuclei which have an identical environment (labelled 1) and one hydrogen in a different environnment (labelled 2). Two peaks due to methanol can be observed. The smallest is due to the hydrogen labelled 1. The second is due to the three other hydrogens. It is three times the size of the first.
  15. Balance the following half-equations using either H+ or H2O (and, of course, e-) on either side of the equation.
  16. Balance the following half-equations using either H+ or H2O (and, of course, e-) on either side of the equation.
  17. Balance the following half-equations using either H+ or H2O (and, of course, e-) on either side of the equation.
  18. Balance the following half-equations using either H+ or H2O (and, of course, e-) on either side of the equation.
  19. Balance the following half-equations using either H+ or H2O (and, of course, e-) on either side of the equation.
  20. Balance the following half-equations using either H+ or H2O (and, of course, e-) on either side of the equation.
  21. Balance the following half-equations using either H+ or H2O (and, of course, e-) on either side of the equation.
  22. Balance the following half-equations using either H+ or H2O (and, of course, e-) on either side of the equation.
  23. Balance the following half-equations using either H+ or H2O (and, of course, e-) on either side of the equation.
  24. Balance the following half-equations using either H+ or H2O (and, of course, e-) on either side of the equation.
  25. Balance the following half-equations using either H+ or H2O (and, of course, e-) on either side of the equation.
  26. Balance the following half-equations using either H+ or H2O (and, of course, e-) on either side of the equation.
  27. Balance the following half-equations using either H+ or H2O (and, of course, e-) on either side of the equation.
  28. Balance the following half-equations using either H+ or H2O (and, of course, e-) on either side of the equation.
  29. Balance the following half-equations using either H+ or H2O (and, of course, e-) on either side of the equation.
  30. Balance the following half-equations using either H+ or H2O (and, of course, e-) on either side of the equation.
  31. Balance the following half-equations using either H+ or H2O (and, of course, e-) on either side of the equation.
  32. Balance the following half-equations using either H+ or H2O (and, of course, e-) on either side of the equation.