ANSWER
The energy produced per mole of fuel is 808 KJ
The energy produced per tank of fuel is 1082.14KJ
EXPLANATION
Given that;
[tex]\text{ CH}_4\text{ + 2O}_{2(g)}\text{ }\rightarrow\text{ CO}_{2(g)}\text{ + 2H}_2O[/tex]Follow the steps below to find the energy produced per mole
Step 1; Calculate the heat of formation of the fuel
[tex]\text{ }\Delta H_f\text{ = }\Sigma\Delta H_{products}\text{ - }\Sigma\Delta H_{reactants}[/tex][tex]\text{ }\Delta H\text{ = \lbrack4\lparen O-H\rparen+ 2\lparen C=O\rparen- \lbrack4\lparen C- H\rparen+ 2\lparen O=O\rparen\rbrack}[/tex]
In the table provided,
C- H = 413 KJ/mol
O=O = 495 KJ/mol
C=O = 799 KJ/mol
O-H = 463 KJ/mol
Substitute the given data into the above formula
[tex]\begin{gathered} \text{ }\Delta H\text{ = 4\lparen463\rparen + 2\lparen799\rparen - \lbrack4\lparen413\rparen + 2\lparen495\rparen\rbrack} \\ \text{ }\Delta H\text{ = 1852 + 1598 - \lbrack1652 + 990\rbrack} \\ \text{ }\Delta H\text{ = 3450 - 2642} \\ \text{ }\Delta H\text{ = 808 KJ} \end{gathered}[/tex]Therefore, the energy produced per mole of fuel is 808 KJ
The next step is to find the energy produced per tank of fuel
Recall, that 1 mole of gas is 22.4L
[tex]\begin{gathered} \text{ 808 KJ }\rightarrow\text{ 22.4L} \\ \text{ xKJ }\rightarrow\text{ 30L} \\ \text{ Cross multiply} \\ \text{ 808 }\times\text{ 30 = 22.4 }\times\text{ x} \\ \text{ 24,240 = 22.4 x} \\ \text{ Divide both sides by 22.4} \\ \text{ }\frac{24,\text{ 240}}{\text{ 22.4}}\text{ = x} \\ \text{ x = 1082.14 KJ} \end{gathered}[/tex]Therefore, the energy produced per tank of fuel is 1082.14KJ