Chapter 20, Problem 21QRT

Interpretation Introduction

Interpretation:

Given redox reaction has to be balanced.

    $\text{Fe}(s)+{\text{NO}}_3{}^{-}(aq)\to {\text{Fe}}^{3+}(aq)+{\text{NO}}_{\text{2}}(g)$

Concept Introduction:

Redox reaction is the one where oxidation and reduction takes place simultaneously.  In order to balance the redox reaction, the half reactions has to be balanced first and they have to be added in order to obtain the balanced equation for the redox reaction.

Explanation of Solution

Given reaction is shown below.

    $\text{Fe}(s)+{\text{NO}}_3{}^{-}(aq)\to {\text{Fe}}^{3+}(aq)+{\text{NO}}_{\text{2}}(g)$

Balancing first half reaction:

The first half reaction is given below.

    $\text{Fe}(s)\to {\text{Fe}}^{3+}(aq)$        (1)

The charge has to be balanced in the above equation.  Therefore, three electrons are added to the right side of the equation.  This balances out the first half reaction.  The balanced equation for half reaction is shown below.

    $\text{Fe}(s)\to {\text{Fe}}^{3+}(aq)+3e^{-}$        (2)

Balancing second half reaction:

The second half reaction is given below.

    ${\text{NO}}_3{}^{-}(aq)\to {\text{NO}}_{\text{2}}(g)$        (3)

The number of oxygen atom is not same on both sides of the equation.  Therefore, in order to balance oxygen atom, a molecule of water is added on the right side of the equation.  This can be given as shown below.

    ${\text{NO}}_3{}^{-}(aq)\to {\text{NO}}_{\text{2}}(g)+{\text{H}}_{\text{2}}\text{O}$        (4)

In order to balance the hydrogen atom on both sides of the above equation, two ${\text{H}}^{\text{+}}$ ions are added on the left side of the equation.  The equation obtained can be given as shown below.

    ${\text{2H}}^{\text{+}}{\text{(aq) +NO}}_3{}^{-}(aq)\to {\text{NO}}_{\text{2}}(g)+{\text{H}}_{\text{2}}\text{O}$        (5)

Now all the atoms on both sides are balanced.  The charge on both sides of the equation has to be balanced.  Therefore, adding one electron to the left side of the equation balances the half reaction.  Balanced equation for the second half reaction can be given as shown below.

    ${\text{2H}}^{\text{+}}{\text{(aq) +NO}}_3{}^{-}(aq){\text{+ e}}^{-}\to {\text{NO}}_{\text{2}}(g)+{\text{H}}_{\text{2}}\text{O}$        (6)

Multiplying the equation (6) by 3, the equation is obtained as shown.

    ${\text{6H}}^{\text{+}}{\text{(aq) +3NO}}_3{}^{-}(aq){\text{+ 3e}}^{-}\to 3{\text{NO}}_{\text{2}}(g)+3{\text{H}}_{\text{2}}\text{O}$        (7)

Adding equation (2) and (7), the balanced redox equation can be obtained as shown.

    $\begin{array}{c}\text{Fe}(s)\to {\text{Fe}}^{3+}(aq)+3e^{-}\\ \underset{\_}{{\text{ 6H}}^{\text{+}}{\text{(aq) +3NO}}_3{}^{-}(aq){\text{+ 3e}}^{-}\to 3{\text{NO}}_{\text{2}}(g)+3{\text{H}}_{\text{2}}\text{O }}\\ \underset{\_}{{\text{6H}}^{\text{+}}{\text{(aq) +3NO}}_3{}^{-}(aq)\text{+ Fe}(s)\to 3{\text{NO}}_{\text{2}}(g)+3{\text{H}}_{\text{2}}{\text{O+Fe}}^{3+}(aq)}\end{array}$

The balanced redox equation is obtained as above because the atoms and charges are equal on both sides of the equation.