Question

Calculate the energy produced per mole of fuel based on the bond energy chart. Convert the energy per mole of fuel to energy per full tank ofgas (30.0 L) OR one charge of an electric car (which is fueled by 100. pounds of coal for charging),

Answer 1

The energy produced per mole of fuel is 808 KJ

The energy produced per tank of fuel is 1082.14KJ

Step-by-step explanation

Given that;

`\text{ CH}_4\text{ + 2O}_(2(g))\text{ }\rightarrow\text{ CO}_(2(g))\text{ + 2H}_2O`

Follow the steps below to find the energy produced per mole

Step 1; Calculate the heat of formation of the fuel

`\text{ }\Delta H_f\text{ = }\Sigma\Delta H_(products)\text{ - }\Sigma\Delta H_(reactants)`
`\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}`

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

`\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}`

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

`\begin{gathered} \text{ 808 KJ }\rightarrow\text{ 22.4L} \\ \text{ xKJ }\rightarrow\text{ 30L} \\ \text{ Cross multiply} \\ \text{ 808 }*\text{ 30 = 22.4 }*\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}`

Therefore, the energy produced per tank of fuel is 1082.14KJ