Answer : The balanced chemical equation in a acidic solution are,
(a) ![2Pb+O_2+4H^+\rightarrow 2Pb^{2+}+2H_2O](https://tex.z-dn.net/?f=2Pb%2BO_2%2B4H%5E%2B%5Crightarrow%202Pb%5E%7B2%2B%7D%2B2H_2O)
(b) ![2Sn+NO_3^-+4H^+\rightarrow 2Sn^{2+}+NO+2H_2O](https://tex.z-dn.net/?f=2Sn%2BNO_3%5E-%2B4H%5E%2B%5Crightarrow%202Sn%5E%7B2%2B%7D%2BNO%2B2H_2O)
(c) ![2Cr^{3+}+7H_2O+3Cl_2\rightarrow Cr_2O_7^{2-}+14H^++6Cl^-](https://tex.z-dn.net/?f=2Cr%5E%7B3%2B%7D%2B7H_2O%2B3Cl_2%5Crightarrow%20Cr_2O_7%5E%7B2-%7D%2B14H%5E%2B%2B6Cl%5E-)
(d) ![2Mn^{2+}+8H_2O+5F_2\rightarrow 2MnO_4^-+16H^++10F^-](https://tex.z-dn.net/?f=2Mn%5E%7B2%2B%7D%2B8H_2O%2B5F_2%5Crightarrow%202MnO_4%5E-%2B16H%5E%2B%2B10F%5E-)
Explanation :
Redox reaction or Oxidation-reduction reaction : It is defined as the reaction in which the oxidation and reduction reaction takes place simultaneously.
Oxidation reaction : It is defined as the reaction in which a substance looses its electrons. In this, oxidation state of an element increases. Or we can say that in oxidation, the loss of electrons takes place.
Reduction reaction : It is defined as the reaction in which a substance gains electrons. In this, oxidation state of an element decreases. Or we can say that in reduction, the gain of electrons takes place.
<u>(a) The given chemical reaction is,</u>
![O_2(g)+Pb(s)\rightarrow H_2O(l)+Pb^{2+}(aq)](https://tex.z-dn.net/?f=O_2%28g%29%2BPb%28s%29%5Crightarrow%20H_2O%28l%29%2BPb%5E%7B2%2B%7D%28aq%29)
The oxidation-reduction half reaction will be :
Oxidation : ![Pb\rightarrow Pb^{2+}](https://tex.z-dn.net/?f=Pb%5Crightarrow%20Pb%5E%7B2%2B%7D)
Reduction : ![O_2\rightarrow H_2O](https://tex.z-dn.net/?f=O_2%5Crightarrow%20H_2O)
- Now balance oxygen atom on both side.
Oxidation : ![Pb\rightarrow Pb^{2+}](https://tex.z-dn.net/?f=Pb%5Crightarrow%20Pb%5E%7B2%2B%7D)
Reduction : ![O_2\rightarrow 2H_2O](https://tex.z-dn.net/?f=O_2%5Crightarrow%202H_2O)
- Now balance hydrogen atom on both side.
Oxidation : ![Pb\rightarrow Pb^{2+}](https://tex.z-dn.net/?f=Pb%5Crightarrow%20Pb%5E%7B2%2B%7D)
Reduction : ![O_2+4H^+\rightarrow 2H_2O](https://tex.z-dn.net/?f=O_2%2B4H%5E%2B%5Crightarrow%202H_2O)
Oxidation : ![Pb\rightarrow Pb^{2+}+2e^-](https://tex.z-dn.net/?f=Pb%5Crightarrow%20Pb%5E%7B2%2B%7D%2B2e%5E-)
Reduction : ![O_2+4H^++4e^-\rightarrow 2H_2O](https://tex.z-dn.net/?f=O_2%2B4H%5E%2B%2B4e%5E-%5Crightarrow%202H_2O)
In order to balance the electrons, we multiply the oxidation reaction by 2 and then added both equation, we get the balanced redox reaction.
Oxidation : ![2Pb\rightarrow 2Pb^{2+}+4e^-](https://tex.z-dn.net/?f=2Pb%5Crightarrow%202Pb%5E%7B2%2B%7D%2B4e%5E-)
Reduction : ![O_2+4H^++4e^-\rightarrow 2H_2O](https://tex.z-dn.net/?f=O_2%2B4H%5E%2B%2B4e%5E-%5Crightarrow%202H_2O)
The balanced chemical equation will be,
![2Pb+O_2+4H^+\rightarrow 2Pb^{2+}+2H_2O](https://tex.z-dn.net/?f=2Pb%2BO_2%2B4H%5E%2B%5Crightarrow%202Pb%5E%7B2%2B%7D%2B2H_2O)
<u>(b) The given chemical reaction is,</u>
![NO_3^-(aq)+Sn(s)\rightarrow NO(g)+Sn^{2+}(aq)](https://tex.z-dn.net/?f=NO_3%5E-%28aq%29%2BSn%28s%29%5Crightarrow%20NO%28g%29%2BSn%5E%7B2%2B%7D%28aq%29)
The oxidation-reduction half reaction will be :
Oxidation : ![Sn\rightarrow Sn^{2+}](https://tex.z-dn.net/?f=Sn%5Crightarrow%20Sn%5E%7B2%2B%7D)
Reduction : ![NO_3^-\rightarrow NO](https://tex.z-dn.net/?f=NO_3%5E-%5Crightarrow%20NO)
- Now balance oxygen atom on both side.
Oxidation : ![Sn\rightarrow Sn^{2+}](https://tex.z-dn.net/?f=Sn%5Crightarrow%20Sn%5E%7B2%2B%7D)
Reduction : ![NO_3^-\rightarrow NO+2H_2O](https://tex.z-dn.net/?f=NO_3%5E-%5Crightarrow%20NO%2B2H_2O)
- Now balance hydrogen atom on both side.
Oxidation : ![Sn\rightarrow Sn^{2+}](https://tex.z-dn.net/?f=Sn%5Crightarrow%20Sn%5E%7B2%2B%7D)
Reduction : ![NO_3^-+4H^+\rightarrow NO+2H_2O](https://tex.z-dn.net/?f=NO_3%5E-%2B4H%5E%2B%5Crightarrow%20NO%2B2H_2O)
Oxidation : ![Sn\rightarrow Sn^{2+}+2e^-](https://tex.z-dn.net/?f=Sn%5Crightarrow%20Sn%5E%7B2%2B%7D%2B2e%5E-)
Reduction : ![NO_3^-+4H^++4e^-\rightarrow NO+2H_2O](https://tex.z-dn.net/?f=NO_3%5E-%2B4H%5E%2B%2B4e%5E-%5Crightarrow%20NO%2B2H_2O)
In order to balance the electrons, we multiply the oxidation reaction by 2 and then added both equation, we get the balanced redox reaction.
Oxidation : ![2Sn\rightarrow 2Sn^{2+}+4e^-](https://tex.z-dn.net/?f=2Sn%5Crightarrow%202Sn%5E%7B2%2B%7D%2B4e%5E-)
Reduction : ![NO_3^-+4H^++4e^-\rightarrow NO+2H_2O](https://tex.z-dn.net/?f=NO_3%5E-%2B4H%5E%2B%2B4e%5E-%5Crightarrow%20NO%2B2H_2O)
The balanced chemical equation will be,
![2Sn+NO_3^-+4H^+\rightarrow 2Sn^{2+}+NO+2H_2O](https://tex.z-dn.net/?f=2Sn%2BNO_3%5E-%2B4H%5E%2B%5Crightarrow%202Sn%5E%7B2%2B%7D%2BNO%2B2H_2O)
<u>(c) The given chemical reaction is,</u>
![Cl_2(g)+Cr^{3+}(aq)\rightarrow Cl^-(aq)+Cr_2O_7^{2-}(aq)](https://tex.z-dn.net/?f=Cl_2%28g%29%2BCr%5E%7B3%2B%7D%28aq%29%5Crightarrow%20Cl%5E-%28aq%29%2BCr_2O_7%5E%7B2-%7D%28aq%29)
The oxidation-reduction half reaction will be :
Oxidation : ![2Cr^{3+}\rightarrow Cr_2O_7^{2-}](https://tex.z-dn.net/?f=2Cr%5E%7B3%2B%7D%5Crightarrow%20Cr_2O_7%5E%7B2-%7D)
Reduction : ![Cl_2\rightarrow 2Cl^-](https://tex.z-dn.net/?f=Cl_2%5Crightarrow%202Cl%5E-)
- Now balance oxygen atom on both side.
Oxidation : ![2Cr^{3+}+7H_2O\rightarrow Cr_2O_7^{2-}](https://tex.z-dn.net/?f=2Cr%5E%7B3%2B%7D%2B7H_2O%5Crightarrow%20Cr_2O_7%5E%7B2-%7D)
Reduction : ![Cl_2\rightarrow 2Cl^-](https://tex.z-dn.net/?f=Cl_2%5Crightarrow%202Cl%5E-)
- Now balance hydrogen atom on both side.
Oxidation : ![2Cr^{3+}+7H_2O\rightarrow Cr_2O_7^{2-}+14H^+](https://tex.z-dn.net/?f=2Cr%5E%7B3%2B%7D%2B7H_2O%5Crightarrow%20Cr_2O_7%5E%7B2-%7D%2B14H%5E%2B)
Reduction : ![Cl_2\rightarrow 2Cl^-](https://tex.z-dn.net/?f=Cl_2%5Crightarrow%202Cl%5E-)
Oxidation : ![2Cr^{3+}+7H_2O\rightarrow Cr_2O_7^{2-}+14H^++6e^-](https://tex.z-dn.net/?f=2Cr%5E%7B3%2B%7D%2B7H_2O%5Crightarrow%20Cr_2O_7%5E%7B2-%7D%2B14H%5E%2B%2B6e%5E-)
Reduction : ![Cl_2+2e^-\rightarrow 2Cl^-](https://tex.z-dn.net/?f=Cl_2%2B2e%5E-%5Crightarrow%202Cl%5E-)
In order to balance the electrons, we multiply the reduction reaction by 3 and then added both equation, we get the balanced redox reaction.
Oxidation : ![2Cr^{3+}+7H_2O\rightarrow Cr_2O_7^{2-}+14H^++6e^-](https://tex.z-dn.net/?f=2Cr%5E%7B3%2B%7D%2B7H_2O%5Crightarrow%20Cr_2O_7%5E%7B2-%7D%2B14H%5E%2B%2B6e%5E-)
Reduction : ![3Cl_2+6e^-\rightarrow 6Cl^-](https://tex.z-dn.net/?f=3Cl_2%2B6e%5E-%5Crightarrow%206Cl%5E-)
The balanced chemical equation will be,
![2Cr^{3+}+7H_2O+3Cl_2\rightarrow Cr_2O_7^{2-}+14H^++6Cl^-](https://tex.z-dn.net/?f=2Cr%5E%7B3%2B%7D%2B7H_2O%2B3Cl_2%5Crightarrow%20Cr_2O_7%5E%7B2-%7D%2B14H%5E%2B%2B6Cl%5E-)
<u>(d) The given chemical reaction is,</u>
![F_2(g)+Mn^{2+}(aq)\rightarrow F^-(aq)+MnO_4^-(aq)](https://tex.z-dn.net/?f=F_2%28g%29%2BMn%5E%7B2%2B%7D%28aq%29%5Crightarrow%20F%5E-%28aq%29%2BMnO_4%5E-%28aq%29)
The oxidation-reduction half reaction will be :
Oxidation : ![Mn^{2+}\rightarrow MnO_4^-](https://tex.z-dn.net/?f=Mn%5E%7B2%2B%7D%5Crightarrow%20MnO_4%5E-)
Reduction : ![F_2\rightarrow 2F^-](https://tex.z-dn.net/?f=F_2%5Crightarrow%202F%5E-)
- Now balance oxygen atom on both side.
Oxidation : ![Mn^{2+}+4H_2O\rightarrow MnO_4^-](https://tex.z-dn.net/?f=Mn%5E%7B2%2B%7D%2B4H_2O%5Crightarrow%20MnO_4%5E-)
Reduction : ![F_2\rightarrow 2F^-](https://tex.z-dn.net/?f=F_2%5Crightarrow%202F%5E-)
- Now balance hydrogen atom on both side.
Oxidation : ![Mn^{2+}+4H_2O\rightarrow MnO_4^-+8H^+](https://tex.z-dn.net/?f=Mn%5E%7B2%2B%7D%2B4H_2O%5Crightarrow%20MnO_4%5E-%2B8H%5E%2B)
Reduction : ![F_2\rightarrow 2F^-](https://tex.z-dn.net/?f=F_2%5Crightarrow%202F%5E-)
Oxidation : ![Mn^{2+}+4H_2O\rightarrow MnO_4^-+8H^+5e^-](https://tex.z-dn.net/?f=Mn%5E%7B2%2B%7D%2B4H_2O%5Crightarrow%20MnO_4%5E-%2B8H%5E%2B5e%5E-)
Reduction : ![F_2+2e^-\rightarrow 2F^-](https://tex.z-dn.net/?f=F_2%2B2e%5E-%5Crightarrow%202F%5E-)
In order to balance the electrons, we multiply the oxidation reaction by 2 and reduction reaction by 5 and then added both equation, we get the balanced redox reaction.
Oxidation : ![2Mn^{2+}+8H_2O\rightarrow 2MnO_4^-+16H^+10e^-](https://tex.z-dn.net/?f=2Mn%5E%7B2%2B%7D%2B8H_2O%5Crightarrow%202MnO_4%5E-%2B16H%5E%2B10e%5E-)
Reduction : ![5F_2+10e^-\rightarrow 10F^-](https://tex.z-dn.net/?f=5F_2%2B10e%5E-%5Crightarrow%2010F%5E-)
The balanced chemical equation will be,
![2Mn^{2+}+8H_2O+5F_2\rightarrow 2MnO_4^-+16H^++10F^-](https://tex.z-dn.net/?f=2Mn%5E%7B2%2B%7D%2B8H_2O%2B5F_2%5Crightarrow%202MnO_4%5E-%2B16H%5E%2B%2B10F%5E-)