Q10.82CP - Chemistry: Molecular Nature Of Matter And Change

Question

Methane burns in oxygen to form carbon dioxide and water vapor. Hydrogen sulfide burns in oxygen to form sulfur dioxide and water vapor. Use bond energies (Table 9.2, p. 353) to determine the heat of each reaction per mole of ${\mathbf{\text{O}}}_{\mathbf{\text{2}}}$  (assume Lewis structures with zero formal charges; BE of  $\mathbf{\text{S=O}}$  is 552 kJ/mol).

 

Step-by-Step Solution

Answer

When methane burns in oxygen, the heat of reaction per mole of oxygen is  $\mathbf{-}\mathbf{409}\mathbf{kJ}\mathbf{/}\mathbf{mol}$  and when hydrogen sulfide burns in oxygen, the heat of reaction per mole of oxygen is $\mathbf{-}\mathbf{398}\mathbf{kJ}\mathbf{/}\mathbf{mol}$ .

Step 1: Definition

The heat of combustion is the change that occurs in enthalpy when one mole of a substance is entirely burnt in the air.

 

The amount of heat absorbed or evolved when one molecule of a substance is formed is called heat of formation.

Step 2: The Heat of reaction of reaction per mole of Oxygen when Methane burns in oxygen.

Methane reacts with oxygen and forms one molecule of carbon dioxide and two molecules of water.

${\text{CH}}_{\text{4}}{\text{ + 2O}}_{\text{2}}\to {\text{CO}}_{\text{2}}{\text{ + 2H}}_{\text{2}}\text{O}$

The energy required when bonds broken

                                                            $\begin{array}{l}\text{= 4}\left(\text{C-H}\right)\text{ +2}\left(\text{O=O}\right)\text{ bonds}\\ \text{= 4}\left(\text{413}\right)\text{+ 2}\left(\text{498}\right)\text{ kJ/mol}\\ \text{= 2648 kJ/mol}\end{array}$

 

The energy released when bonds formed

 

                                                            $\begin{array}{l}\text{= 2}\left(\text{C=O}\right)\text{ + 2}\left(\text{O-H}\right)\text{ Bonds}\\ \text{= 2}\left(\text{799}\right)\text{ + 4}\left(\text{467}\right)\text{ kJ}\\ \text{= 3466kJ}\end{array}$

Therefore, the heat of reaction 

                                           $\begin{array}{l}\text{= }\left(\text{2648 - 3466}\right)\text{kJ/mol}\\ \text{= -818 kJ}\end{array}$            

 

The heat of reaction per mole of oxygen is

                                                    $\begin{array}{l}\text{= -}\frac{\text{818}}{\text{2}}\\ \text{= -409 kJ/mol}\end{array}$    

Step 3: The Heat of reaction of reaction per mole of Oxygen when Hydrogen sulfide burns in oxygen.

Two molecules of hydrogen sulfide react with three molecules of oxygen to produce two molecules of sulfur dioxide and two molecules of water.

${\text{2H}}_{\text{2}}{\text{S + 3O}}_{\text{2}}\to {\text{2SO}}_{\text{2}}{\text{ + 2H}}_{\text{2}}\text{O}$

The energy required when bonds broken

                                                           $\begin{array}{l}\text{= 4}\left(\text{S-H}\right)\text{ +3}\left(\text{O=O}\right)\text{ bonds}\\ \text{= 4}\left(\text{347}\right)\text{+ 3}\left(\text{498}\right)\text{ kJ}\\ \text{= 2882 kJ}\end{array}$

 

The energy released when bonds formed

                                                           $\begin{array}{l}\text{= 4}\left(\text{S=O}\right)\text{ + 4}\left(\text{O-H}\right)\text{ Bonds}\\ \text{= 4}\left(\text{552}\right)\text{ +4}\left(\text{467}\right)\text{ kJ}\\ \text{= 4076 kJ}\end{array}$  

 

Therefore, the heat of reaction

                                                   $\begin{array}{l}\text{= }\left(\text{2882-4076}\right)\text{kJ/mol}\\ \text{= -1194kJ}\end{array}$

Heat of reaction per mole of oxygen is

                                                             

        $\begin{array}{l}\text{= }\frac{\text{-1194}}{\text{3}}\\ \text{= -398kJ/mol}\end{array}$