Chapter 5, Problem 115SCQ

Methane, CH₄, can be converted to methanol, which, like ethanol, can be used as a fuel. The energy level diagram shown here presents relationships between energies of the fuels and their oxidation products. Use the information in the diagram to answer the following questions. (The energy terms are per mol-rxn.)

1. (a) Which fuel, methanol or methane, yields the most energy per mole when burned?
2. (b) Which fuel yields the most energy per gram when burned?
3. (c) What is the enthalpy change for the conversion of methane to methanol by reaction with O₂(g)?
4. (d) Each arrow on the diagram represents a chemical reaction. Write the equation for the reaction that converts methane to methanol.

Interpretation Introduction

Interpretation:

The fuel that yields the most energy per mole when burned has to be determined

Concept Introduction:

Heat energy required to raise the temperature of 1g of substance by 1K.Energy gained or lost can be calculated using the below equation.

  $\text{q=C×m×ΔT}$

Where, q= energy gained or lost for a given mass of substance (m), C =specific heat capacity,$\Delta T$= change in temperature.

The standard molar enthalpy of formation is the enthalpy change ${\text{Δ}}_{\text{f}}{\text{H}}^{\text{0}}$ is the enthalpy change for the formation of $\text{1mol}$ of a compound directly from its component elements in their standard states. And is given by

  ${\text{Δ}}_{\text{r}}{\text{H}}^{\text{0}}$${\text{ΣnΔ}}_{\text{f}}{\text{H}}^{\text{0}}\text{(products)}\text{-}{\text{ΣnΔ}}_{\text{f}}{\text{H}}^{\text{0}}\text{(reactants)}$

Explanation of Solution

From the energy level diagram,

Methane liberates at $\text{955}\text{.1kJ/mol}$

Methanol liberates at $\text{676}\text{.1kJ/mol}$

So, methane yields most energy per mole when it’s burned.

Interpretation Introduction

Interpretation:

The fuel yields the most energy per gram when burned has to be calculated.

Concept Introduction:

Heat energy required to raise the temperature of 1g of substance by 1K.Energy gained or lost can be calculated using the below equation.

  $\text{q=C×m×ΔT}$

Where, q= energy gained or lost for a given mass of substance (m), C =specific heat capacity,$\Delta T$= change in temperature.

The standard molar enthalpy of formation is the enthalpy change ${\text{Δ}}_{\text{f}}{\text{H}}^{\text{0}}$ is the enthalpy change for the formation of $\text{1mol}$ of a compound directly from its component elements in their standard states. And is given by

  ${\text{Δ}}_{\text{r}}{\text{H}}^{\text{0}}$${\text{ΣnΔ}}_{\text{f}}{\text{H}}^{\text{0}}\text{(products)}\text{-}{\text{ΣnΔ}}_{\text{f}}{\text{H}}^{\text{0}}\text{(reactants)}$

Explanation of Solution

The fuel yields the most energy per gram when burned

Molar mass of methane is $\text{16}\text{.04}\text{g/mol}$

For methane=$\frac{\text{-955}\text{.1kJ}}{\text{1mol}}\text{×}\frac{\text{1mol}}{\text{16}\text{.04g}}$ =$\text{-59}\text{.54kJ/g}$

Molar mass of methanol is $\text{32}\text{.04}\text{g/mol}$

For methanol=$\frac{\text{-676}\text{.1kJ}}{\text{1mol}}\text{×}\frac{\text{1mol}}{\text{32}\text{.04g}}$=$\text{-21}\text{.10kJ/g}$

So, the fuel that yields the most energy per gram when burned is methane

Interpretation Introduction

Interpretation:

The enthalpy change for the conversion of methane by reaction with ${\text{O}}_{\text{2}}\left(\text{g}\right)$ has to be determined.

Concept Introduction:

Heat energy required to raise the temperature of 1g of substance by 1K. Energy gained or lost can be calculated using the below equation.

  $\text{q=C×m×ΔT}$

Where, q= energy gained or lost for a given mass of substance (m), C =specific heat capacity, $\text{ΔT}$= change in temperature.

The standard enthalpy change of combustion of a compound is the enthalpy change which occurs when one gram of the compound is burned completely in oxygen under standard conditions, and with everything in its standard state.

  ${\text{Δ}}_{\text{r}}{\text{H}}^{\text{0}}$=${\text{ΣnΔ}}_{\text{f}}{\text{H}}^{\text{0}}\text{(products)}\text{-}{\text{ΣnΔ}}_{\text{f}}{\text{H}}^{\text{0}}\text{(reactants)}$

Explanation of Solution

From the energy level diagram the values obtained are

Methane liberates at $\text{955}\text{.1kJ/mol}$

Methanol liberates at $\text{676}\text{.1kJ/mol}$

  ${\text{Δ}}_{\text{r}}{\text{H}}^{\text{0}}$=${\text{ΣnΔ}}_{\text{f}}{\text{H}}^{\text{0}}\text{(products)}\text{-}{\text{ΣnΔ}}_{\text{f}}{\text{H}}^{\text{0}}\text{(reactants)}$

  ${\text{Δ}}_{\text{r}}\text{H}$ = $\text{-955}\text{.1kJ/mol}\text{-(-676}\text{.1kJ/mol)}$ =$\text{-278}\text{.9kJ/mol}$

Interpretation Introduction

Interpretation:

The equation for the reaction that converts methane to methanol has to be identified.

Concept Introduction:

Heat energy required to raise the temperature of 1g of substance by 1K. Energy gained or lost can be calculated using the below equation.

  $\text{q=C×m×ΔT}$

Where, q= energy gained or lost for a given mass of substance (m), C =specific heat capacity, $\text{ΔT}$= change in temperature.

The standard enthalpy change of combustion of a compound is the enthalpy change which occurs when one gram of the compound is burned completely in oxygen under standard conditions, and with everything in its standard state.

  ${\text{Δ}}_{\text{r}}{\text{H}}^{\text{0}}$=${\text{ΣnΔ}}_{\text{f}}{\text{H}}^{\text{0}}\text{(products)}\text{-}{\text{ΣnΔ}}_{\text{f}}{\text{H}}^{\text{0}}\text{(reactants)}$

Explanation of Solution

From the energy level diagram the obtained equation for the conversion of methane to methanol is ${\text{CH}}_{\text{4}}\text{+}{\text{2O}}_{\text{2}}\to {\text{CH}}_{\text{3}}\text{OH}$