Chapter 11, Problem 61A

(a)

Interpretation Introduction

Interpretation: The balanced chemical equation for the combustion of ${\text{C}}_{\text{5}}{\text{H}}_{\text{12}}$ and ${\text{C}}_9{\text{H}}_{20}$ needs to be written using data given in the graph.

Concept Introduction: A chemical reaction is said to be balanced if there are an equal number of atoms of the same elements on both sides of the reaction arrow.

Explanation of Solution

The general equation for the combustion of alkanes is represented as follows:

  ${\text{C}}_n{\text{H}}_{2n+2}+\underset{¯}{}{\text{O}}_{\text{2}}\to \underset{¯}{}{\text{CO}}_{\text{2}}+\underset{¯}{}{\text{H}}_{\text{2}}\text{O}$

Now, the given graph shows the number of oxygen, carbon dioxide, and water molecules required to balance the equations for the combustion of alkanes.

In the case of ${\text{C}}_{\text{5}}{\text{H}}_{\text{12}}$ , the value of n is equal to 5. Now, from the graph, the number of oxygen, carbon dioxide, and water molecules required to balance for the combustion of alkane with carbon atoms 5 are 8, 5, and 6 respectively.

The balanced equation can be represented as follows:

  ${\text{C}}_{\text{5}}{\text{H}}_{\text{12}}+\underset{¯}{8}{\text{O}}_{\text{2}}\to \underset{¯}{5}{\text{CO}}_{\text{2}}+\underset{¯}{6}{\text{H}}_{\text{2}}\text{O}$

Similarly, for the combustion reaction of ${\text{C}}_9{\text{H}}_{20}$ , the number of oxygen, carbon dioxide, and water molecules needed to balance the reaction from the graph are 14, 9, and 10 respectively.

The balanced equation can be represented as follows:

  ${\text{C}}_9{\text{H}}_{20}+\underset{¯}{14}{\text{O}}_{\text{2}}\to \underset{¯}{9}{\text{CO}}_{\text{2}}+\underset{¯}{10}{\text{H}}_{\text{2}}\text{O}$

(b)

Interpretation Introduction

The graph needs to be extrapolated to write the balanced chemical equation for the combustion of ${\text{C}}_{\text{12}}{\text{H}}_{\text{26}}$ and ${\text{C}}_{\text{17}}{\text{H}}_{\text{36}}$ .

Concept Introduction: A chemical reaction is said to be balanced if there are an equal number of atoms of the same elements on both sides of the reaction arrow.

Explanation of Solution

The two given alkanes are ${\text{C}}_{\text{12}}{\text{H}}_{\text{26}}$ and ${\text{C}}_{\text{17}}{\text{H}}_{\text{36}}$ . Here, in ${\text{C}}_{\text{12}}{\text{H}}_{\text{26}}$ , the number of carbon atoms is 12 and that in ${\text{C}}_{\text{17}}{\text{H}}_{\text{36}}$ are 17. The graph can be extrapolated to get the number of oxygen, carbon dioxide, and water molecules needed to balance the combustion reactions of given alkenes.

After extrapolating the graph, the values will be as follows:

For ${\text{C}}_{\text{12}}{\text{H}}_{\text{26}}$ , the number of oxygen, carbon dioxide, and water molecules will be 18.5, 12, and 13 respectively. Thus, the balanced chemical reaction will be:

  $\begin{array}{l}{\text{C}}_{\text{12}}{\text{H}}_{\text{26}}+\underset{¯}{18.5}{\text{O}}_{\text{2}}\to \underset{¯}{12}{\text{CO}}_{\text{2}}+\underset{¯}{13}{\text{H}}_{\text{2}}\text{O}\\ \text{Or,}\\ {\text{2C}}_{\text{12}}{\text{H}}_{\text{26}}+\underset{¯}{37}{\text{O}}_{\text{2}}\to \underset{¯}{24}{\text{CO}}_{\text{2}}+\underset{¯}{26}{\text{H}}_{\text{2}}\text{O}\end{array}$

For ${\text{C}}_{\text{17}}{\text{H}}_{\text{36}}$ , the number of oxygen, carbon dioxide, and water molecules will be 26, 17, and 18 respectively. Thus, the balanced chemical reaction will be:

  ${\text{C}}_{\text{17}}{\text{H}}_{\text{36}}+\underset{¯}{26}{\text{O}}_{\text{2}}\to \underset{¯}{17}{\text{CO}}_{\text{2}}+\underset{¯}{18}{\text{H}}_{\text{2}}\text{O}$

(c)

Interpretation Introduction

Interpretation: The coefficients for carbon dioxide and water needs to be determined if the general equation for the coefficient of O₂is as follows:

  $n+\frac{n+1}{2}$

Concept Introduction: A chemical reaction is said to be balanced if there are an equal number of atoms of the same elements on both sides of the reaction arrow.

Explanation of Solution

The given general equation is as follows:

  ${\text{C}}_n{\text{H}}_{2n+2}+\underset{¯}{}{\text{O}}_{\text{2}}\to \underset{¯}{}{\text{CO}}_{\text{2}}+\underset{¯}{}{\text{H}}_{\text{2}}\text{O}$

For the above equation, the general equation for the coefficient of oxygen gas is as follows:

  $n+\frac{n+1}{2}$

Thus,

  ${\text{C}}_n{\text{H}}_{2n+2}+\underset{¯}{n+\frac{n+1}{2}}{\text{O}}_{\text{2}}\to \underset{¯}{}{\text{CO}}_{\text{2}}+\underset{¯}{}{\text{H}}_{\text{2}}\text{O}$

Now, it can be seen from the reaction that the number of carbon atoms on the reactant side is n thus, the number of atoms of carbon on the product side must be n. This gives coefficient n to carbon dioxide.

Thus,

  ${\text{C}}_n{\text{H}}_{2n+2}+\underset{¯}{n+\frac{n+1}{2}}{\text{O}}_{\text{2}}\to \underset{¯}{n}{\text{CO}}_{\text{2}}+\underset{¯}{}{\text{H}}_{\text{2}}\text{O}$

Now, the number of hydrogen atoms on the reactant side is 2n+2 and there are already 2 atoms of H on the product side. Thus, the coefficient of ${\text{H}}_{\text{2}}\text{O}$ must be:

  $\begin{array}{l}\frac{2n+2}{2}\\ \text{Or,}\\ n+1\end{array}$

Thus,

  ${\text{C}}_n{\text{H}}_{2n+2}+\underset{¯}{\left(n+\frac{n+1}{2}\right)}{\text{O}}_{\text{2}}\to \underset{¯}{\left(n\right)}{\text{CO}}_{\text{2}}+\underset{¯}{\left(n+1\right)}{\text{H}}_{\text{2}}\text{O}$

Check if the above general equation is balanced. The number of carbon atoms on the reactant side is n and that on the product side is n. The number of hydrogen atoms on the reactant side is $2n+2$ and that on the product side is $2\left(n+1\right)=2n+2$ . The number of oxygen atoms on the reactant side is $2\left(n+\frac{n+1}{2}\right)$ and that on the product side is calculated from carbon dioxide and water molecules as follows:

  $2n+n+1$

Taking 2 common,

  $2\left(n+\frac{n+1}{2}\right)$

Since the number of carbon, oxygen, and hydrogen atoms is equal on both sides of the reaction arrow, thus, the coefficients for carbon dioxide and water molecules are n and $n+1$ respectively.