Question

The enthalpy of combustion of propane (${{\text{C}}_{\text{3}}}{{\text{H}}_{\text{8}}}$ ) gas in terms of given data is:
Bond energy (kJ/mol)

$\varepsilon {\text{C - H}}$	${\text{ }}\varepsilon {\text{O = O}}$	${\text{ }}\varepsilon {\text{C = O}}$	$\varepsilon {\text{O - H }}$	${\text{ }}\varepsilon {\text{C - C}}$
${\text{ }} + {x_1}$	${\text{ }} + {x_2}$	${\text{ }} + {x_3}$	${\text{ }} + {x_4}$	${\text{ }} + {x_5}$

Resonance energy of ${\text{C}}{{\text{O}}_{\text{2}}}$ is $- z{\text{kJ/mol}}$ and $\Delta {\text{Hvaprization [}}{{\text{H}}_{\text{2}}}{\text{O(l)] is }}y{\text{ (kJ/mol)}}$
A. $8{x_1}{\text{ }} + 2{x_5}{\text{ }} + 5{x_2} - 6{x_3} - 8{x_4} - 4y - 3z$
B. $6{x_1}{\text{ }} + {x_5}{\text{ }} + 5{x_2} - 3{x_3} - 4{x_4} - 4y - 3z$
C. $8{x_1}{\text{ }} + 2{x_5}{\text{ }} + 5{x_2} - 6{x_3} - 8{x_4} - y - z$
D. $8{x_1}{\text{ }} + {x_5}{\text{ }} + 5{x_2} - 6{x_3} - 8{x_4} - 4y + 3z$

Answer 1

Write the balanced reaction for the combustion of propane. Determine the number of each type of bond present in reactants and products. Calculate the enthalpy combustion of propane using bond energy of reactants, bond energy of products, resonance energy of ${\text{C}}{{\text{O}}_{\text{2}}}$ and heat of vaporization of water.

Complete Step by step answer:

A combustion reaction is a type of reaction where hydrocarbon reacts with oxygen gas and gives carbon dioxide gas and water vapor.
So, the unbalanced combustion reaction of propane is:
${{\text{C}}_{\text{3}}}{{\text{H}}_{\text{8}}}{\text{ + }}{{\text{O}}_{\text{2}}}{\text{ }} \to {\text{ C}}{{\text{O}}_{\text{2}}}{\text{ + }}{{\text{H}}_{\text{2}}}{\text{O }}$
Now, the balanced reaction for the combustion of propane is:
${{\text{C}}_{\text{3}}}{{\text{H}}_{\text{8}}}{\text{ + 5}}{{\text{O}}_{\text{2}}}{\text{ }} \to {\text{ 3C}}{{\text{O}}_{\text{2}}}{\text{ + 4}}{{\text{H}}_{\text{2}}}{\text{O }}$
Now, using the given data calculates the bond energy of reactant (${\text{ B}}{{\text{E}}_{\text{r}}}$) and bond energy of product (${\text{B}}{{\text{E}}_{\text{P}}}$) as follows:
Structure of propane is:

So, in propane, there are 8 C-H bonds and 2C-C bonds present.
Structure of ${{\text{O}}_{\text{2}}}$is :

In oxygen gas, there is 1${\text{O = O}}$ double bond present.
Structure of ${\text{C}}{{\text{O}}_{\text{2}}}$ is :

In ${\text{C}}{{\text{O}}_{\text{2}}}$ there are 2 ${\text{C = O}}$ bonds present.
Structure of ${{\text{H}}_{\text{2}}}{\text{O }}$ is:

In water there are 2 O-H bonds present.
Now calculate the bond energy of reactant and product using balance combustion reaction of propane as follows:
${{\text{C}}_{\text{3}}}{{\text{H}}_{\text{8}}}{\text{ + 5}}{{\text{O}}_{\text{2}}}{\text{ }} \to {\text{ 3C}}{{\text{O}}_{\text{2}}}{\text{ + 4}}{{\text{H}}_{\text{2}}}{\text{O }}$
Here, 1 mole of propane is reacting with 5 moles of ${{\text{O}}_{\text{2}}}{\text{ }}$and gives 3 moles of ${\text{C}}{{\text{O}}_{\text{2}}}{\text{ }}$and 4 moles of${{\text{H}}_{\text{2}}}{\text{O }}$.
So, the bond energy of reactant (${\text{B}}{{\text{E}}_{\text{r}}}$) is as follows:
${\text{B}}{{\text{E}}_{\text{r}}} = 2{\text{C - C + 8 C - H + 5O = O}}$
Now, substitute the bond energy ${\text{ }} + {x_1}$ for ${\text{C - H}}$, ${\text{ }} + {x_5}$for ${\text{C - C}}$ and ${\text{ }} + {x_2}$ for ${\text{O = O}}$.

${\text{B}}{{\text{E}}_{\text{r}}} = 2{{\text{x}}_{\text{5}}}{\text{ + 8 }}{x_1}{\text{ + 5 }}{x_2}$
Calculate bond energy of reactant (${\text{B}}{{\text{E}}_{\text{P}}}$) is as follows:
${\text{B}}{{\text{E}}_{\text{P}}} = {\text{6C = O + 8O - H}}$
Now, substitute the bond energy ${\text{ }} + {x_3}$ for ${\text{C = O}}$ and ${\text{ }} + {x_4}$for ${\text{O - H}}$
${\text{B}}{{\text{E}}_{\text{P}}} = {\text{6 }}{x_3}{\text{ + 8}}{x_4}$
Now, calculate the enthalpy combustion of propane as follows:
${{\text{H}}_{\text{r}}} = {\text{ B}}{{\text{E}}_{\text{r}}} - {\text{B}}{{\text{E}}_{\text{P}}} + {\text{RE - }}\Delta {{\text{H}}_{{\text{vap}}}}$
RE = resonance energy of ${\text{C}}{{\text{O}}_{\text{2}}}$=$- z{\text{kJ/mol}}$
$\Delta {{\text{H}}_{{\text{vap}}}}$= heat of vaporization of water =$y{\text{ (kJ/mol)}}$
Since there are 3 moles of ${\text{C}}{{\text{O}}_{\text{2}}}{\text{ }}$and 4 moles of${{\text{H}}_{\text{2}}}{\text{O }}$.
${{\text{H}}_{\text{r}}} = {\text{ }}2{{\text{x}}_{\text{5}}}{\text{ + 8 }}{x_1}{\text{ + 5 }}{x_2} - ({\text{6 }}{x_3}{\text{ + 8}}{x_4}) - 3z - 4y$
${{\text{H}}_{\text{r}}} = {\text{ }}2{{\text{x}}_{\text{5}}}{\text{ + 8 }}{x_1}{\text{ + 5 }}{x_2} - {\text{6 }}{x_3}{\text{ - 8}}{x_4} - 3z - 4y$

Thus, the correct option is (A).

Note: It is very important to balance the reaction correctly. Also, count the number of types of bonds present correctly. After that we should take care that all the values should be added thoroughly with the proper corrected sign.