Chapter 10, Problem 124QRT

(a)

Interpretation Introduction

Interpretation:

The enthalpy of combustion of propane, nonane, and hexadecane has to be predicted with help of graphical method.

Concept Introduction:

The amount of energy which is produced or absorbed during the reaction is the enthalpy change of a chemical reaction.  When bonds get break, some amount of energy is absorbed by the system.  When bonds are formed, some amount of energy is produced by the system.

Answer to Problem 124QRT

The enthalpy of combustion of propane $\left({\text{C}}_{\text{3}}{\text{H}}_{\text{8}}\right)$, nonane $\left({\text{C}}_9{\text{H}}_{20}\right)$, and hexadecane $\left({\text{C}}_{16}{\text{H}}_{34}\right)$ are $22000\text{kJ}/\text{mol}$, $61000\text{kJ}/\text{mol}$, and $10700\text{kJ}/\text{mol}$.

Explanation of Solution

The given data table is shown below.

Hydrocarbon	Formula	Enthalpy if combustion (kJ/mol)
Butane	${\text{C}}_{\text{4}}{\text{H}}_{\text{10}}$
Pentane	${\text{C}}_{\text{5}}{\text{H}}_{12}$
Hexane	${\text{C}}_{\text{6}}{\text{H}}_{\text{14}}$
Heptane	${\text{C}}_{\text{7}}{\text{H}}_{\text{16}}$
Octane	${\text{C}}_{\text{8}}{\text{H}}_{\text{18}}$

The graph has been plotted between enthalpy of combustion on the $y\text{-}$ axis and number of carbon atoms on the $x\text{-}$ axis as shown below.

Figure 1

When the number of carbon atom is $3$, the enthalpy of combustion approximately $22000\text{kJ}/\text{mol}$.

Therefore, the enthalpy of combustion of propane $\left({\text{C}}_{\text{3}}{\text{H}}_{\text{8}}\right)$ is $22000\text{kJ}/\text{mol}$.

When the number of carbon atom is $9$, the enthalpy of combustion approximately $61000\text{kJ}/\text{mol}$.

Therefore, the enthalpy of combustion of nonane $\left({\text{C}}_9{\text{H}}_{20}\right)$ is $61000\text{kJ}/\text{mol}$.

When the number of carbon atom is $16$, the enthalpy of combustion approximately $10700\text{kJ}/\text{mol}$.

Therefore, the enthalpy of combustion of hexadecane $\left({\text{C}}_{16}{\text{H}}_{34}\right)$ is $10700\text{kJ}/\text{mol}$.

(b)

Interpretation Introduction

Interpretation:

The reason as to why the slope of graph enthalpy of combustion on the $y\text{-}$ axis and number of carbon atoms on the $x\text{-}$ axis is positive has to be explained on the basis of bond enthalpies.

Concept Introduction:

Refer to part (a).

Answer to Problem 124QRT

The graph has positive slope because bond enengy increases as the number of carbon increases.

Explanation of Solution

The given data table is shown below.

Hydrocarbon	Formula	Enthalpy if combustion (kJ/mol)
Butane	${\text{C}}_{\text{4}}{\text{H}}_{\text{10}}$
Pentane	${\text{C}}_{\text{5}}{\text{H}}_{12}$
Hexane	${\text{C}}_{\text{6}}{\text{H}}_{\text{14}}$
Heptane	${\text{C}}_{\text{7}}{\text{H}}_{\text{16}}$
Octane	${\text{C}}_{\text{8}}{\text{H}}_{\text{18}}$

The graph has been plotted between enthalpy of combustion on the $y\text{-}$ axis and number of carbon atoms on the $x\text{-}$ axis as shown below.

Figure 1

This graph has positive value.

The combustion of hydrocarbons involves breaking of $\text{C}-\text{H}$ and $\text{C}-\text{C}$ bonds.

The bond enthalpy for $\text{C}-\text{H}$ is $416\text{kJ}/\text{mol}$.

The bond enthalpy for $\text{C}-\text{C}$ is $356\text{kJ}/\text{mol}$.

The number of bonds $\text{C}-\text{H}$ and $\text{C}-\text{C}$ increases as number carbon atom increases.  The bond energies also increases as number carbon atom increases.  Therefore, the graph has positive value.