Measuring Enthalpy Change: How We Track Energy in Reactions
Welcome to the start of our journey into Reactivity! This chapter, "Measuring enthalpy change," is where we connect the abstract idea of energy inside a chemical system to concrete, measurable results in the lab.
In simple terms, we are learning how to become energy detectives: measuring exactly how much heat is released or absorbed when a chemical reaction takes place. This concept is central to understanding What drives chemical reactions?, as energy is the ultimate driving force for change.
1. Understanding Enthalpy and Enthalpy Change
First, let's define our key concept: Enthalpy (\(H\)).
Enthalpy is essentially the total heat content of a substance or system measured at constant pressure. We can't measure the absolute enthalpy of a substance, but luckily, we only care about the change!
a. Defining Enthalpy Change (\(\Delta H\))
The Enthalpy Change (\(\Delta H\)) is the heat absorbed or released during a chemical reaction or physical process, assuming the pressure remains constant (which is usually true in an open laboratory setting).
Key Equation Reminder:
\[\Delta H = H_{\text{products}} - H_{\text{reactants}}\]
b. Exothermic vs. Endothermic Reactions
Every reaction fits into one of two categories based on its heat exchange with the surroundings:
1. Exothermic Reactions
- Definition: Reactions that release heat energy to the surroundings.
- Observation: The surroundings (like the water in a calorimeter) get hotter.
- Sign Convention: Since the system (the reaction) is losing energy, the enthalpy change, \(\Delta H\) is negative (–).
- Analogy: Think of "Exiting" heat. Burning fuel, condensation, or neutralizing an acid with a base are common exothermic processes.
2. Endothermic Reactions
- Definition: Reactions that absorb heat energy from the surroundings.
- Observation: The surroundings get colder as heat flows into the system.
- Sign Convention: Since the system is gaining energy, the enthalpy change, \(\Delta H\) is positive (+).
- Analogy: Think of "Entering" heat. Melting ice, evaporating liquid water, or the cold pack used for sports injuries are endothermic processes.
Quick Review Box:
Exo = Heat Out = Negative \(\Delta H\)
Endo = Heat In = Positive \(\Delta H\)
2. Standard Enthalpy Changes (\(\Delta H^{\theta}\))
To compare the energy output of different reactions accurately, chemists must measure them under specific, agreed-upon conditions. These are called Standard Conditions.
a. Defining Standard State
When you see the superscript symbol (\(\theta\)) next to \(\Delta H\), it means the measurement was taken under standard conditions:
- Pressure: 100 kPa (kilopascals). (Note: This used to be 101.3 kPa, but the current IB definition uses 100 kPa.)
- Temperature: 298 K (25\({}^\circ\text{C}\)).
- Concentration (for solutions): 1.0 mol dm\({}^{-3}\).
- Physical State: Substances must be in their standard states (the most stable physical state under 100 kPa and 298 K, e.g., Br\(_2\) is a liquid, C (graphite) is a solid).
Did you know? The standard temperature (298 K) is purely for convenience in the lab, not related to STP (Standard Temperature and Pressure for gases).
Key Takeaway: Using the standard state allows scientists worldwide to compare values like the Standard Enthalpy of Combustion or the Standard Enthalpy of Formation reliably.
3. Measuring Heat Change: Calorimetry
Calorimetry is the experimental technique used to measure the heat changes (\(q\)) associated with a chemical or physical process. The apparatus used is called a calorimeter.
a. The Principle of Calorimetry
Calorimetry relies on the principle of conservation of energy:
\[\text{Heat released by reaction} = \text{Heat absorbed by surroundings (e.g., water)}\]
In a simple experiment (often called a coffee cup calorimeter), the reaction occurs in an insulated container containing a known mass of water. We monitor the temperature change (\(\Delta T\)) of the water.
b. Specific Heat Capacity (\(c\))
To translate a temperature change into a heat energy value, we need to know the substance's specific heat capacity (\(c\)).
- Definition: The amount of energy (in Joules, J) required to raise the temperature of 1 gram of a substance by 1 Kelvin (or 1\({}^\circ\text{C}\)).
- Value for Water: The specific heat capacity of water is approximately \(4.18 \text{ J g}^{-1}\text{ K}^{-1}\). This value is extremely high, which is why water is so effective at moderating temperature changes.
- Analogy: Think of specific heat capacity as the "thermal inertia." Water has high inertia—it takes a lot of effort (energy) to change its speed (temperature). Metals, with low specific heat, heat up much faster.
4. Calorimetry Calculations (The Math!)
This is where we put the measurements into practice to find the heat change, \(q\).
a. Calculating Heat Absorbed/Released (\(q\))
The fundamental formula for calculating the heat exchanged is:
\[q = m \times c \times \Delta T\]
- \(q\): Heat energy (usually in Joules, J).
- \(m\): Mass of the substance absorbing the heat (usually the mass of water in the calorimeter, in grams, g).
- \(c\): Specific heat capacity (usually of water, \(4.18 \text{ J g}^{-1}\text{ K}^{-1}\)).
- \(\Delta T\): Temperature change (\(T_{\text{final}} - T_{\text{initial}}\)) in Kelvin (K) or degrees Celsius (\({}^\circ\text{C}\)). Since we are dealing with a change, the magnitude is the same in K or \({}^\circ\text{C}\).
b. Step-by-Step: Converting \(q\) to Molar Enthalpy Change (\(\Delta H^{\theta}\))
The calculated value \(q\) is the heat released/absorbed by the specific amount of substance used in the experiment. To compare this value universally, we must convert it to a molar value (\(\text{kJ mol}^{-1}\)).
Step 1: Calculate \(q\) in Joules (J)
Use the formula \(q = mc\Delta T\). Remember that \(m\) is the mass of the surrounding substance (usually water).
Step 2: Convert \(q\) to Kilojoules (kJ)
Divide the result from Step 1 by 1000: \(q_{\text{kJ}} = q_{\text{J}} / 1000\).
Step 3: Calculate the Moles (\(n\)) of the Reactant
Calculate the number of moles of the substance (solute or fuel) that reacted.
Step 4: Determine Molar Enthalpy (\(\Delta H\))
Divide the heat energy by the moles reacted, and APPLY THE SIGN CONVENTION.
\[\Delta H = \frac{-q}{\text{moles}}\]
The negative sign is CRITICAL! If the water heated up (exothermic, positive \(q\)), the reaction must have lost heat (negative \(\Delta H\)). We flip the sign of the measured \(q\) to reflect the change from the system's perspective.
c. Common Mistakes to Avoid
- Units: Ensure that \(q\) is in kJ and moles are correct before calculating \(\Delta H\).
- Mass (\(m\)): If a solution (like 100 cm\({}^3\) of water) is used, assume the density is \(1.00 \text{ g cm}^{-3}\). Therefore, \(100 \text{ cm}^3 = 100 \text{ g}\).
- The Sign: Forgetting to apply the negative sign for an exothermic reaction (or failing to use the correct sign if the reaction is endothermic) is the most common error.
5. Experimental Considerations and Limitations
Calorimetry, especially using simple equipment, involves several inherent limitations that lead to experimental errors. Evaluating these is a key skill in the IB curriculum.
a. Assumptions Made in Simple Calorimetry
When calculating enthalpy change using \(q = mc\Delta T\), we make several important assumptions:
- Perfect Insulation: We assume no heat is lost to the surroundings (the air) or absorbed by the container (the coffee cup/glass beaker). In reality, heat loss is unavoidable.
- Solution Properties: We assume that the specific heat capacity (\(c\)) and density of the solution (e.g., a salt dissolved in water) are exactly the same as pure water (\(4.18 \text{ J g}^{-1}\text{ K}^{-1}\) and \(1.00 \text{ g cm}^{-3}\)).
- Complete Reaction: We assume that all the reactant measured underwent the desired chemical change.
b. Improving Accuracy (HL Extension/Practical Skills)
For more accurate work (e.g., high-level combustion experiments), more sophisticated calorimeters are used, such as the Bomb Calorimeter.
- Bomb calorimeters measure heat at constant volume (not pressure, which is slightly different from \(\Delta H\)) and are highly insulated.
- Crucially, these advanced calorimeters require determining the Heat Capacity of the Calorimeter (C\(_\text{cal}\)) itself.
- In these cases, the total heat absorbed \(q_{\text{total}}\) includes both the water and the apparatus: \[q_{\text{total}} = (m_{\text{water}}c_{\text{water}}\Delta T) + (C_{\text{cal}}\Delta T)\] (Don't worry, you typically won't have to calculate \(C_{\text{cal}}\) unless the value is provided in the data).
Key Takeaway: Simple coffee cup calorimetry is a great introductory method, but it tends to underestimate the true enthalpy change because of inevitable heat loss to the surroundings. Therefore, experimental \(\Delta H\) values are often less negative (closer to zero) than theoretical values.