Chapter 18, Problem 18.1P

Interpretation Introduction

Interpretation:

The balanced form of given redox reaction in acidic solution is to be stated.

Concept introduction: In balanced form of redox reaction number of atoms and total charge of reactants and products are same.

To determine: The balanced form of given redox reaction in acidic solution.

Answer to Problem 18.1P

Solution:

The balanced form of given redox reaction in acidic solution is,

$\text{Cr}\left(s\right)+2{\text{H}}^{+}\left(aq\right)\to {\text{Cr}}^{2+}\left(aq\right)+{\text{H}}_2\left(g\right)$

Explanation of Solution

The redox reaction in acidic solution is,

${\text{H}}^{+}\left(aq\right)+\text{Cr}\left(s\right)\to {\text{H}}_{\text{2}}\left(g\right)+{\text{Cr}}^{2+}\left(aq\right)$     .....(1)

The above redox reaction is unbalanced.

In balanced form of redox reaction number of atoms and total charge of reactants and products are same.

To balance the above equation (1) following steps are followed.

Step 1:

Calculate the oxidation state of each atom.
${\text{H}}^{+}$

The oxidation state of ${\text{H}}^{+}$ is $+1$ .
$\text{Cr}$

The oxidation state of $\text{Cr}$ is $0$ .
${\text{H}}_{\text{2}}$

The oxidation state of ${\text{H}}_{\text{2}}$ is $0$ .
${\text{Cr}}^{2+}$

The oxidation state of ${\text{Cr}}^{2+}$ is $+2$ .

Step 2:

Identify the oxidation and reduction reaction and separate them as half reactions.

In oxidation process, positive oxidation state of atoms increased by some number.
In reduction process, positive oxidation state of atoms decreased by some number.

$\begin{array}{c}\begin{array}{cccc}\text{Oxidation:}& \text{Cr}\left(s\right)& \to & {\text{Cr}}^{2+}\left(aq\right)\\ & 0& & +2\end{array}\\ \begin{array}{cccc}\text{Reduction:}& {\text{H}}^{+}\left(aq\right)& \to & {\text{H}}_{\text{2}}\left(g\right)\\ & +1& & 0\end{array}\end{array}$

Step 3:

Balance the atoms of reactant and product.
To balance ${\text{H}}^{+}$ ,multiply ${\text{H}}^{+}$ with two in reduction half reaction on the left side.
$\text{Reduction:}2{\text{H}}^{+}\left(aq\right)\to {\text{H}}_2\left(g\right)$

Step 4:

Balance each half reaction with respect to charge.
Balance the charge of oxidation half reaction by the addition of $2e^{-}$ on the right side.
Balance the charge of reduction half reaction by the addition of $2e^{-}$ on the left side.

$\begin{array}{c}\text{Oxidation:}\text{Cr}\left(s\right)\to {\text{Cr}}^{2+}\left(aq\right)+2e^{-}\\ \text{Reduction:}2{\text{H}}^{+}\left(aq\right)+2e^{-}\to {\text{H}}_2\left(g\right)\end{array}$

Step 6:
To get overall reaction add the half reactions together and remove common terms.

$\begin{array}{l}\text{Oxidation:}\text{Cr}\left(s\right)\to {\text{Cr}}^{2+}\left(aq\right)+2e^{-}\\ \text{Reduction:}2{\text{H}}^{+}\left(aq\right)+2e^{-}\to {\text{H}}_2\left(g\right)\\ \overline{\underset{\_}{\text{Overall:}\text{Cr}\left(s\right)+2{\text{H}}^{+}\left(aq\right)\to {\text{Cr}}^{2+}\left(aq\right)+{\text{H}}_2\left(g\right)}}\end{array}$

Thus, the balanced form of given redox reaction in acidic solution is,

$\text{Cr}\left(s\right)+2{\text{H}}^{+}\left(aq\right)\to {\text{Cr}}^{2+}\left(aq\right)+{\text{H}}_2\left(g\right)$

Conclusion

The balanced form of given redox reaction in acidic solution is,

$\text{Cr}\left(s\right)+2{\text{H}}^{+}\left(aq\right)\to {\text{Cr}}^{2+}\left(aq\right)+{\text{H}}_2\left(g\right)$