Balance each of the following equations according to the half- reaction method:
(a) zn + no3- --> zn2+ + n2 (in acid)
(b) zn + no3- --> zn2+ + nh3 (in base)
(c) cus + no3- --> cu2+ + s + no (in acid)
(d) nh3 + o2 --> no2 (gas phase)
(e) cl2 + oh- --> cl- + clo3-(in base)
(f) h2o2 + mno4- --> mn2+ o2 (in acid)
(g) no2 --> no3- + no2- (in base)
(h) fe3+ + i- --> fe2+ +i2

a) 12H+ + 6Zn + 2NO3 → 6Zn2+ + N2 + 6H2O

b) 12H2O + 9Zn + 2NO3 → 9Zn2+ + 2NH3 + 18OH-

c) 4H+ + 2CuS + NO3  → 2Cu2+ + 2S + NO + 2H2O

d) 7O2 + 4NH3 → 4NO2 + 6H2O

e) 13Cl2 + 26OH- + 10OH +  → 6ClO3- + 18H2O + 20Cl-

f) 5H2O2 + 2MnO4- + 6H+ → 5O2 + 2Mn2+ + 8H2O

g) 2NO2 + 2OH- → NO3- + NO2- + H2O

h) 2I- + 2Fe3+ → I2 + 2Fe2+

Explanation:

a) oxidation states :

⇒ Zn: 0 → 2+ : lose 2e-

⇒ N : +6 → 0 : win 6e-

half reaction:

⇒ ( 1 ) Zn → Zn2+ + 2e-

⇒ ( 2 ) 2NO3 + 12H+ 12e- → N2 + 6H2OThe O are balanced with H2O and the H with H +, then balanced the charges with e-.

( 1 ) * 6:

⇒ ( 7 ) 6Zn → 6Zn2+  +  12e-

( 7 ) + ( 2 ):

⇒ 12H+ + 6Zn + 2NO3 → 6Zn2+ + N2 + 6H2O

                  6 - Zn - 6

                  2 - N - 2

                  6 - O - 6

                  12 - H - 12

b) oxidation states:

⇒ Zn: 0 → 2+ ≡ 2e-

⇒ N: +3 → -3 ≡ 6e-

half reaction:

( 1 ) Zn → Zn2+ + 2e-

(2 ) 9H2O + 9e- + NO3 → NH3 + 3H2O + 9OH-each H + ion present in the equation is added a respective OH- ion to each side of the equation, and the combination of OH- and H + ions found on the same side of the equation is replaced with a water molecule.

∴ ( 1 ) * 9 and ( 2 ) * 2 and then i add them:

⇒ 18H2O + 9Zn + 2NO3 → 9Zn2+ + 2NH3 + 6H2O + 18OH-

                  9 - Zn - 9

                  2 - N - 2

                  24 - O - 24

                 36 - H - 36

c) oxidation states:

∴ S:  -2 → 0 ≡ 2e-

∴ N: +6 → +2 ≡ 4e-

half reaction:

( 1 ) CuS → Cu2+ + S + 2e-

( 2 ) NO3 + H2O + 4H+  + 4e- → NO + 3H2O

∴( ( 1 ) * 2 ) + ( 2 ):

⇒ 4H+ + 2CuS + NO3  → 2Cu2+ + 2S + NO + 2H2O

                      2 - Cu - 2

                      1 - N - 1

                      2 - S - 2

                      3 - O - 3

                      4 - H - 4

d) oxidation states:

∴ O: 0 → -2 ≡ 2e-

∴ N: -3 → +4 ≡ 7e-

half reaction:

( 1 ) O2 + 4H+ + 4e- → 2H2O

( 2 ) NH3 + 2H2O → NO2 + 7H+  + 7e-

∴  ( 1 ) * 7 and ( 2 ) * 4 and then i add them:

⇒ 7O2 + 4NH3 + 8H2O → 4NO2 + 14H2O

⇒ 7O2 + 4NH3 → 4NO2 + 6H2O

            4 - N - 4

            14 - O - 14

            12 - H - 12

e) oxidation states:

∴ Cl: 0 → -1 ≡ 1e-

∴ Cl: 0 → +5 ≡ 5e-

∴ O: -1 → -2 ≡ 1e-

half reaction:

( 1 ) Cl2 + 6H2O → 2ClO3- + 12H+

( 2 ) Cl2 + OH + H+ → Cl- + H2O

in base:

( 1 ) Cl2 + 6H2O + 12OH- → 2ClO3- + 12H2O

( 2 ) Cl2 + OH + H2O → 2Cl- + H2O + OH-

the charge are balanced:

( 1 ) Cl2 + 6H2O + 12OH- → 2ClO3- + 12H2O + 10e-

( 2 ) Cl2 + OH + H2O + 3e- → 2Cl- + H2O + OH-

∴ ( 1 ) * 3 and ( 2 ) * 10, then i add them:

⇒ 13Cl2 + 26OH- + 10OH +  → 6ClO3- + 18H2O + 20Cl-  

               26 - Cl - 26

               36 - O - 36

                36 - H - 36

f) oxidation states:

∴ O: -1 → 0 ≡ 1e-

∴ O: -2 → 0 ≡ 2e-

∴ Mn: +7 → +2 ≡ 5e-

half reaction:

( 1 ) H2O2 → O2 + 2H+ + 2e-

( 2 ) MnO4- + 8H+ + 5e- → Mn2+ + 4H2O

∴ ( 1 ) * 5 and ( 2 ) * 2, then i add them:

⇒5H2O2 + 2MnO4- + 6H+ → 5O2 + 2Mn2+ + 8H2O

               2 - Mn - 2

               18 - O - 18

               16 - H - 16

g) oxidation states:

∴ N: +4 → +5 ≡ 1e-

∴ N: +4 → +3 ≡ 1e-

half reaction:

( 1 ) NO2 + H2O + 2OH- → NO3- + 2H+

( 2 ) NO2 → NO2-

⇒ ( 1 ) NO2 + H2O + 2OH- →  NO3- + 2H2O + 1e-

⇒ ( 2 ) NO2 + 1e- → NO2-

( 1 ) + ( 2 ):

⇒ 2NO2 + 2OH- → NO3- + NO2- + H2O

                 2 - N - 2

                 6 - O - 6

                 2 - H - 2

h) oxidation states:

∴ Fe: +3 → +2 ≡ 1e-

∴ I: -1 → 0 ≡ 1e-

half reaction:

( 1 ) 2I- → I2 + 2e-

( 2 ) Fe3+ +1e- → Fe2+

∴ (( 2 ) * 2 ) + ( 1 ):

⇒ 2I- + 2Fe3+ → I2 + 2Fe2+

      2- I - 2

      2 - Fe - 2

solute : a solute is a substance that is dissolved in another substance is known as a solvent. it is mixed with a special mixture know as homogeneous mixture.

solvent: a solvent is a substance that dissolved a solute, which results in a solution is known as solvent.

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