Chemistry | Energy from fuels

Welcome to Reactivity 1.3: Energy from Fuels!

Hello future Chemists! This chapter, Energy from Fuels, sits squarely within our exploration of What Drives Chemical Reactions? (Thermodynamics). We've already looked at enthalpy changes and energy cycles (Hess's Law). Now, we apply this knowledge directly to the substances that power our world: fuels.

Understanding how much energy fuels contain and how efficiently we can use them is vital for solving real-world challenges, from transportation to climate change. Don't worry if the calculations seem complex—we’ll break them down into simple, manageable steps!

Section 1: Fuels and Exothermic Reactions (The Basics)

What is a Fuel?

A fuel is any substance that stores chemical potential energy and can release it relatively easily, usually through an exothermic reaction, to provide heat or power.

• Examples: Gasoline (octane), methane (natural gas), coal (carbon), hydrogen.
• The most common chemical reaction used to extract energy from traditional fuels is combustion (burning in oxygen).

Review: Exothermic Reactions

In an exothermic reaction, the chemical system releases energy into the surroundings (making the surroundings hotter).

• The total energy of the products is lower than the total energy of the reactants.
• The enthalpy change (\(\Delta H\)) is negative.
• Think of it this way: Fuels are like tiny chemical batteries. When they react (combust), they discharge, releasing stored energy as heat.

Section 2: Measuring the Energy Content of Fuels (Calorimetry)

We need a way to measure the heat released when a fuel burns. This process is called calorimetry.

What is Calorimetry?

Calorimetry is the experimental process of measuring the heat change (\(q\)) associated with a chemical reaction or physical process.

In fuel calorimetry, we burn a known mass of fuel and use the heat released to raise the temperature of a known mass of surrounding substance, typically water.

The Key Formula: The Heat Equation

The amount of heat energy (\(q\)) absorbed or released by a substance can be calculated using this essential formula:

\(q = mc\Delta T\)

• \(q\): Heat energy transferred (usually in Joules, J, or kilojoules, kJ).
• \(m\): Mass of the substance absorbing the heat (usually water, in grams, g, or kilograms, kg). Crucial: This is the mass of the substance being heated, not the mass of the fuel!
• \(c\): Specific Heat Capacity (The amount of energy needed to raise the temperature of 1 unit mass of a substance by 1 Kelvin/degree Celsius). For water, \(c \approx 4.18 \text{ J g}^{-1} \text{ K}^{-1}\).
• \(\Delta T\): The change in temperature (\(T_{\text{final}} - T_{\text{initial}}\)). Since we are dealing with temperature *change*, Kelvin (K) and degrees Celsius (\(^\circ\text{C}\)) are interchangeable.

Step-by-Step Calculation of Enthalpy of Combustion

Let’s see how we go from experimental data to the molar enthalpy change (\(\Delta H_{\text{combustion}}\)):

1. Calculate Heat Transferred (\(q\)):

   Use \(q = mc\Delta T\) for the water (the surroundings).

2. Convert \(q\) to Molar Enthalpy (\(\Delta H\)):

   The value \(q\) is the energy released by the *specific mass* of fuel burned. To get the standard molar enthalpy of combustion (\(\Delta H^\circ\)), you need to scale this to the energy released per *mole* of fuel.

   \( \Delta H = -\frac{q}{\text{moles of fuel}} \)

   Note the negative sign! If the water gained heat (\(q\) is positive), the reaction lost heat, so \(\Delta H\) must be negative (exothermic).

Common Mistake Alert!

Always ensure your units are consistent. If you use \(c\) in \(\text{J g}^{-1} \text{ K}^{-1}\) and \(m\) in grams, \(q\) will be in Joules (J). The final \(\Delta H\) should usually be given in \(\text{kJ mol}^{-1}\), so don't forget the J to kJ conversion (divide by 1000).

Section 3: Quantifying Fuel Efficiency

Not all fuels are created equal. When comparing different fuels, chemists use two specific metrics based on mass and volume.

1. Specific Energy (Energy per Mass)

Specific energy is the heat energy released when a unit mass of fuel undergoes complete combustion.

• Units: \(\text{J g}^{-1}\) or \(\text{kJ g}^{-1}\) (or sometimes \(\text{MJ kg}^{-1}\)).
• Why it matters: This is crucial when mass is a limiting factor, such as in aerospace or long-distance transport (e.g., how far can a plane fly with 1 tonne of fuel?).
• Did You Know? Hydrogen gas (\(\text{H}_2\)) has the highest specific energy of any known fuel, which is why it is often touted as a potential clean energy source.

2. Energy Density (Energy per Volume)

Energy density is the heat energy released when a unit volume of fuel undergoes complete combustion.

• Units: \(\text{J cm}^{-3}\) or \(\text{kJ dm}^{-3}\) (or \(\text{MJ L}^{-1}\)).
• Why it matters: This is crucial when space is a limiting factor, such as in cars or domestic heating systems (e.g., how much energy can fit into a 50 L fuel tank?).

Memory Aid: Density

Remember the definition of physical density (\(D = m/V\)). If you see "Energy Density," immediately think Volume (V). If you see "Specific Energy," think Mass (m).

Section 4: Estimating Enthalpy Using Bond Enthalpies

While calorimetry gives us experimental values (often inaccurate due to heat loss), we can estimate the theoretical enthalpy of combustion using average bond enthalpies. This method is incredibly important because it connects energy changes directly to the breaking and forming of chemical bonds.

Understanding Bond Enthalpies

A bond enthalpy (or bond energy) is the energy required to break one mole of a specific type of bond in the gaseous state.

• Breaking bonds is always Endothermic (\(\Delta H > 0\)). Energy must be put into the system.
• Forming bonds is always Exothermic (\(\Delta H < 0\)). Energy is released when stable bonds are formed.

We can estimate the overall enthalpy change (\(\Delta H\)) for a reaction using the following relationship, which is a variation of Hess’s Law:

\(\Delta H = \sum (\text{Energy Required to Break Bonds}) - \sum (\text{Energy Released to Form Bonds})\)

\(\Delta H = \sum (\text{Bonds Broken, Reactants}) - \sum (\text{Bonds Formed, Products})\)

Step-by-Step Example: Combustion of Methane (\(\text{CH}_4\))

Let’s use the reaction: \(\text{CH}_4 (g) + 2\text{O}_2 (g) \rightarrow \text{CO}_2 (g) + 2\text{H}_2\text{O} (g)\)

This requires drawing the Lewis structures to count the bonds correctly!

1. Identify and Count Bonds BROKEN (Reactants):
   • Methane (\(\text{CH}_4\)) has 4 C-H single bonds.
   • Oxygen (\(2\text{O}_2\)) has 2 O=O double bonds.
   • Total energy input (Endothermic): \(4 \times E(\text{C-H}) + 2 \times E(\text{O=O})\)
2. Identify and Count Bonds FORMED (Products):
   • Carbon Dioxide (\(\text{CO}_2\)) has 2 C=O double bonds.
   • Water (\(2\text{H}_2\text{O}\)) has 4 O-H single bonds (2 per molecule, multiplied by 2).
   • Total energy released (Exothermic): \(2 \times E(\text{C=O}) + 4 \times E(\text{O-H})\)
3. Calculate \(\Delta H_{\text{combustion}}\):

   \(\Delta H = [4 E(\text{C-H}) + 2 E(\text{O=O})] - [2 E(\text{C=O}) + 4 E(\text{O-H})]\)

Why is this only an estimate?

The values used are average bond enthalpies, derived from many different molecules. They are not the exact energy required to break that specific bond in that specific molecule in that specific reaction. Therefore, calculations using bond enthalpy are typically approximations, though often close to the true value.