How To Find Change In Enthalpy

Understanding enthalpy change is crucial for comprehending energy transformations in chemical reactions and physical processes. This article provides a comprehensive guide to finding enthalpy change, covering theoretical underpinnings, practical methods, and common applications. Whether you're a student, a researcher, or simply curious about thermodynamics, this resource will equip you with the knowledge to confidently tackle enthalpy change calculations.

The Fundamentals of Enthalpy

Enthalpy, denoted by the symbol H, is a thermodynamic property of a system, defined as the sum of the internal energy (U) of the system plus the product of its pressure (P) and volume (V):

H = U + PV

Enthalpy is a state function, meaning its value depends only on the current state of the system, not on the path taken to reach that state. This makes it particularly useful for analyzing processes where the initial and final conditions are known.

Enthalpy Change (ΔH)

The change in enthalpy (ΔH) is the heat absorbed or released by a system during a process at constant pressure. It is a measure of the heat exchanged with the surroundings. By convention:

• Exothermic reactions: Release heat into the surroundings (ΔH < 0).
• Endothermic reactions: Absorb heat from the surroundings (ΔH > 0).

Understanding the sign and magnitude of ΔH provides valuable insights into the energy requirements and spontaneity of a reaction.

Methods for Determining Enthalpy Change

Several methods can be employed to determine the enthalpy change of a reaction or process, each with its own advantages and limitations.

1. Calorimetry

Calorimetry is the most direct experimental method for measuring enthalpy change. It involves measuring the heat absorbed or released during a reaction in a calorimeter, a device designed to isolate the reaction from the surroundings and measure the temperature change.

Types of Calorimeters:

• Constant-pressure calorimeter (coffee-cup calorimeter): Used for reactions in solution at atmospheric pressure.
• Constant-volume calorimeter (bomb calorimeter): Used for combustion reactions where the volume is held constant.

Procedure:

1. Calibrate the calorimeter: Determine the heat capacity of the calorimeter by introducing a known amount of heat and measuring the temperature change. This is typically done by burning a known mass of a standard substance with a well-defined enthalpy of combustion.

2. Conduct the reaction: Perform the reaction inside the calorimeter and measure the temperature change (ΔT).

3. Calculate the heat absorbed or released (q):

   • For a constant-pressure calorimeter: q = mcΔT, where m is the mass of the solution, c is the specific heat capacity of the solution, and ΔT is the temperature change. Then, ΔH ≈ q (at constant pressure).
   • For a constant-volume calorimeter: q = CΔT, where C is the heat capacity of the calorimeter. To find ΔH, further calculations are required to account for the volume change, which is typically negligible for solid and liquid reactants.

4. Calculate the enthalpy change (ΔH): Relate the heat (q) to the number of moles of reactants involved in the reaction.

Example:

Suppose you dissolve 5.0 g of potassium hydroxide (KOH) in 100.0 g of water in a coffee-cup calorimeter. The temperature of the solution rises from 22.0 °C to 35.5 °C. Assuming the specific heat capacity of the solution is 4.184 J/g°C, calculate the enthalpy change for the dissolution of KOH.

1. Calculate the heat absorbed by the solution:

   q = mcΔT = (105.0 g) * (4.184 J/g°C) * (35.5 °C - 22.0 °C) = 5949.5 J = 5.95 kJ

2. Calculate the number of moles of KOH:

   Molar mass of KOH = 56.11 g/mol Moles of KOH = 5.0 g / 56.11 g/mol = 0.089 mol

3. Calculate the enthalpy change (ΔH):

   ΔH = -q / moles of KOH = -5.95 kJ / 0.089 mol = -66.85 kJ/mol

   The negative sign indicates that the dissolution of KOH is exothermic.

2. Hess's Law

Hess's Law states that the enthalpy change for a reaction is independent of the path taken. In other words, if a reaction can be carried out in a series of steps, the sum of the enthalpy changes for each step will equal the enthalpy change for the overall reaction.

Applications of Hess's Law:

• Calculating the enthalpy change for reactions that are difficult or impossible to measure directly.
• Using known enthalpy changes of formation to calculate the enthalpy change for a reaction.

Procedure:

1. Identify the target reaction: The reaction for which you want to determine the enthalpy change.
2. Identify a series of reactions: A series of reactions that, when added together, give the target reaction.
3. Manipulate the reactions:
   • If a reaction needs to be reversed, change the sign of its ΔH.
   • If a reaction needs to be multiplied by a factor, multiply its ΔH by the same factor.
4. Add the manipulated reactions: Ensure that all intermediate species cancel out, leaving only the reactants and products of the target reaction.
5. Sum the enthalpy changes: Add the enthalpy changes of the manipulated reactions to obtain the enthalpy change for the target reaction.

Example:

Calculate the enthalpy change for the reaction:

C(s) + 2H₂(g) → CH₄(g)

Given the following reactions and their enthalpy changes:

1. C(s) + O₂(g) → CO₂(g) ΔH₁ = -393.5 kJ/mol
2. H₂(g) + ½O₂(g) → H₂O(l) ΔH₂ = -285.8 kJ/mol
3. CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l) ΔH₃ = -890.4 kJ/mol

Solution:

1. Keep reaction 1 as is: C(s) + O₂(g) → CO₂(g) ΔH₁ = -393.5 kJ/mol
2. Multiply reaction 2 by 2: 2H₂(g) + O₂(g) → 2H₂O(l) 2ΔH₂ = -571.6 kJ/mol
3. Reverse reaction 3: CO₂(g) + 2H₂O(l) → CH₄(g) + 2O₂(g) -ΔH₃ = +890.4 kJ/mol

Add the manipulated reactions:

C(s) + O₂(g) + 2H₂(g) + O₂(g) + CO₂(g) + 2H₂O(l) → CO₂(g) + 2H₂O(l) + CH₄(g) + 2O₂(g)

Simplify the equation:

C(s) + 2H₂(g) → CH₄(g)

Sum the enthalpy changes:

ΔH = ΔH₁ + 2ΔH₂ - ΔH₃ = -393.5 kJ/mol - 571.6 kJ/mol + 890.4 kJ/mol = -74.7 kJ/mol

Therefore, the enthalpy change for the formation of methane is -74.7 kJ/mol.

3. Standard Enthalpies of Formation

The standard enthalpy of formation (ΔH°f) is the enthalpy change when one mole of a compound is formed from its elements in their standard states (usually 298 K and 1 atm). Standard enthalpies of formation are tabulated for many compounds and can be used to calculate the enthalpy change for a reaction using the following equation:

ΔH°reaction = ΣnΔH°f(products) - ΣnΔH°f(reactants)

Where:

• ΔH°reaction is the standard enthalpy change of the reaction.
• n is the stoichiometric coefficient for each product and reactant in the balanced chemical equation.
• ΔH°f(products) is the standard enthalpy of formation of each product.
• ΔH°f(reactants) is the standard enthalpy of formation of each reactant.

Important Considerations:

• The standard enthalpy of formation of an element in its standard state is zero.
• Ensure the chemical equation is balanced before applying the formula.

Example:

Calculate the standard enthalpy change for the reaction:

2Al(s) + Fe₂O₃(s) → Al₂O₃(s) + 2Fe(s)

Given the following standard enthalpies of formation:

• ΔH°f(Al₂O₃(s)) = -1676 kJ/mol
• ΔH°f(Fe₂O₃(s)) = -824.2 kJ/mol
• ΔH°f(Al(s)) = 0 kJ/mol
• ΔH°f(Fe(s)) = 0 kJ/mol

Solution:

ΔH°reaction = [ΔH°f(Al₂O₃(s)) + 2ΔH°f(Fe(s))] - [2ΔH°f(Al(s)) + ΔH°f(Fe₂O₃(s))]

ΔH°reaction = [-1676 kJ/mol + 2(0 kJ/mol)] - [2(0 kJ/mol) + (-824.2 kJ/mol)]

ΔH°reaction = -1676 kJ/mol + 824.2 kJ/mol = -851.8 kJ/mol

Therefore, the standard enthalpy change for the reaction is -851.8 kJ/mol.

4. Bond Enthalpies

Bond enthalpy is the average energy required to break one mole of a particular bond in the gaseous phase. Bond enthalpies can be used to estimate the enthalpy change for a reaction, especially when standard enthalpies of formation are not available.

Equation:

ΔH°reaction ≈ ΣBond enthalpies(reactants) - ΣBond enthalpies(products)

Procedure:

1. Draw the Lewis structures: Draw the Lewis structures of all reactants and products to identify all the bonds present.
2. Identify the bonds broken and formed: Determine which bonds are broken in the reactants and which bonds are formed in the products.
3. Look up bond enthalpies: Find the bond enthalpies for each type of bond in a table.
4. Calculate the enthalpy change: Apply the equation above, summing the bond enthalpies of the bonds broken and subtracting the sum of the bond enthalpies of the bonds formed.

Limitations:

• Bond enthalpies are average values, so the calculated enthalpy change is an estimate.
• Bond enthalpies are only applicable to reactions in the gaseous phase.
• This method is less accurate than using standard enthalpies of formation or calorimetry.

Example:

Estimate the enthalpy change for the reaction:

H₂(g) + Cl₂(g) → 2HCl(g)

Given the following bond enthalpies:

• H-H bond: 436 kJ/mol
• Cl-Cl bond: 242 kJ/mol
• H-Cl bond: 431 kJ/mol

Solution:

Bonds broken: 1 H-H bond and 1 Cl-Cl bond Bonds formed: 2 H-Cl bonds

ΔH°reaction ≈ [Bond enthalpy(H-H) + Bond enthalpy(Cl-Cl)] - [2 * Bond enthalpy(H-Cl)]

ΔH°reaction ≈ [436 kJ/mol + 242 kJ/mol] - [2 * 431 kJ/mol]

ΔH°reaction ≈ 678 kJ/mol - 862 kJ/mol = -184 kJ/mol

Therefore, the estimated enthalpy change for the reaction is -184 kJ/mol.

Factors Affecting Enthalpy Change

Several factors can influence the enthalpy change of a reaction:

• Temperature: Enthalpy change is temperature-dependent. The effect of temperature on ΔH is described by Kirchhoff's Law.
• Pressure: While enthalpy is defined at constant pressure, changes in pressure can affect the enthalpy change, especially for reactions involving gases.
• Physical state: The physical state of reactants and products (solid, liquid, or gas) significantly affects the enthalpy change due to differences in intermolecular forces.
• Concentration: For reactions in solution, the concentration of reactants and products can influence the enthalpy change.
• Purity: Impurities in the reactants or products can affect the enthalpy change.

Applications of Enthalpy Change

Understanding and determining enthalpy change has numerous applications in various fields:

• Chemical engineering: Designing and optimizing chemical processes, including heat management and energy efficiency.
• Materials science: Predicting the stability and reactivity of materials.
• Environmental science: Assessing the environmental impact of chemical reactions, such as combustion and pollution.
• Biochemistry: Studying the energetics of biochemical reactions in living organisms.
• Pharmaceutical science: Determining the heat of solution and stability of drug formulations.
• Everyday life: Understanding the heat released by burning fuels (like wood or propane) or the heat absorbed during melting (like ice).

Common Mistakes to Avoid

When calculating enthalpy change, avoid these common mistakes:

• Incorrect balancing of chemical equations: Ensure the chemical equation is balanced before applying any formula.
• Using incorrect signs: Remember that exothermic reactions have negative ΔH values, while endothermic reactions have positive ΔH values.
• Forgetting stoichiometric coefficients: Include the stoichiometric coefficients in the calculations when using standard enthalpies of formation or bond enthalpies.
• Using incorrect units: Ensure all values are in consistent units (e.g., kJ/mol).
• Not accounting for phase changes: Consider the enthalpy changes associated with phase transitions (melting, boiling, sublimation) if they occur during the reaction.
• Confusing heat and enthalpy: Heat (q) and enthalpy change (ΔH) are related but not identical. Enthalpy change is specifically defined at constant pressure.

Conclusion

Finding the enthalpy change of a reaction or process is a fundamental task in chemistry and related fields. By mastering the methods of calorimetry, Hess's Law, standard enthalpies of formation, and bond enthalpies, you can confidently determine the energy changes associated with chemical and physical transformations. Understanding the factors that affect enthalpy change and avoiding common mistakes will further enhance your accuracy and understanding. Whether you're predicting the heat released by a combustion reaction or analyzing the energetics of a biochemical process, the ability to determine enthalpy change is an invaluable skill.