How To Find The Delta H Of A Reaction

The change in enthalpy, symbolized as ΔH, represents the heat absorbed or released during a chemical reaction at constant pressure. Determining ΔH is crucial for understanding the energy requirements and feasibility of various chemical processes. Several methods exist for finding the ΔH of a reaction, each relying on fundamental thermodynamic principles. Let’s delve into these methods in detail.

Calorimetry: Measuring Heat Flow Directly

Calorimetry is the most direct method for experimentally determining the ΔH of a reaction. It involves measuring the heat flow into or out of a system during a chemical or physical process. A calorimeter is an insulated container designed to capture and measure this heat exchange.

The Principles of Calorimetry

The basic principle behind calorimetry is the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred or converted from one form to another. In a calorimeter, the heat released or absorbed by the reaction (qreaction) is equal to the heat absorbed or released by the calorimeter and its contents (qcalorimeter).

• qreaction = -qcalorimeter

The heat absorbed or released by the calorimeter is calculated using the following equation:

• qcalorimeter = CΔT

Where:

• C is the heat capacity of the calorimeter, which is the amount of heat required to raise the temperature of the calorimeter by 1 degree Celsius (or 1 Kelvin).
• ΔT is the change in temperature of the calorimeter during the reaction (Tfinal - Tinitial).

Types of Calorimeters

Two main types of calorimeters are commonly used:

1. Constant-Volume Calorimeter (Bomb Calorimeter): This type is used for reactions that occur at constant volume, typically combustion reactions. The reaction takes place inside a sealed, rigid container (the "bomb") submerged in water. The heat released by the reaction raises the temperature of the water, and this temperature change is used to calculate the heat of combustion (qv). Because the volume is constant, no work is done (w = 0), and the change in internal energy (ΔU) is equal to the heat exchanged (ΔU = qv). To find ΔH from ΔU, the following equation is used:

   • ΔH = ΔU + Δ(PV) = ΔU + ΔnRT

   Where:

   • Δn is the change in the number of moles of gas during the reaction.
   • R is the ideal gas constant (8.314 J/mol·K).
   • T is the temperature in Kelvin.

2. Constant-Pressure Calorimeter (Coffee-Cup Calorimeter): This simpler type is often used for reactions in solution at atmospheric pressure. It typically consists of two nested Styrofoam cups, which provide good insulation. The reaction takes place in the inner cup, and the temperature change of the solution is measured. Since the pressure is constant, the heat exchanged (qp) is equal to the change in enthalpy (ΔH = qp).

Steps for Using Calorimetry to Determine ΔH

1. Calibrate the Calorimeter: Determine the heat capacity (C) of the calorimeter. This can be done by introducing a known amount of heat into the calorimeter (e.g., by passing an electric current through a resistor) and measuring the resulting temperature change.

2. Run the Reaction: Carefully measure the reactants and mix them inside the calorimeter. Ensure the calorimeter is sealed to prevent heat loss or gain.

3. Measure the Temperature Change: Monitor the temperature of the calorimeter contents over time. Record the initial and final temperatures accurately.

4. Calculate the Heat Exchange: Use the equation qcalorimeter = CΔT to calculate the heat absorbed or released by the calorimeter. Then, use the equation qreaction = -qcalorimeter to find the heat released or absorbed by the reaction.

5. Calculate ΔH: Divide the heat of reaction (qreaction) by the number of moles of the limiting reactant to obtain the change in enthalpy (ΔH) per mole of reaction. Be sure to include the correct sign: a negative ΔH indicates an exothermic reaction (heat released), and a positive ΔH indicates an endothermic reaction (heat absorbed).

Example of Calorimetry Calculation

Let's say you react 50.0 mL of 1.0 M HCl with 50.0 mL of 1.0 M NaOH in a coffee-cup calorimeter. The initial temperature of both solutions is 22.0 °C, and the final temperature after mixing is 28.5 °C. Assuming the density and specific heat capacity of the solution are the same as those of water (1.00 g/mL and 4.184 J/g·°C, respectively), calculate the ΔH of the neutralization reaction.

1. Calculate the mass of the solution: Total volume = 50.0 mL + 50.0 mL = 100.0 mL. Mass = volume x density = 100.0 mL x 1.00 g/mL = 100.0 g.

2. Calculate the heat absorbed by the solution: qsolution = mcΔT = (100.0 g)(4.184 J/g·°C)(28.5 °C - 22.0 °C) = 2719.6 J.

3. Calculate the heat released by the reaction: qreaction = -qsolution = -2719.6 J.

4. Calculate the number of moles of reactants: Moles of HCl = (1.0 M)(0.050 L) = 0.050 mol. Moles of NaOH = (1.0 M)(0.050 L) = 0.050 mol. Since HCl and NaOH react in a 1:1 ratio, the limiting reactant is either HCl or NaOH (they are present in equal amounts).

5. Calculate ΔH: ΔH = qreaction / moles = -2719.6 J / 0.050 mol = -54392 J/mol = -54.4 kJ/mol.

Therefore, the ΔH of the neutralization reaction is -54.4 kJ/mol. The negative sign indicates that the reaction is exothermic.

Hess's Law: Adding Enthalpies of Reactions

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 single step or in a series of steps, the sum of the enthalpy changes for the individual steps will be equal to the enthalpy change for the overall reaction.

Principles of Hess's Law

Hess's Law is a consequence of the fact that enthalpy is a state function. A state function is a property that depends only on the initial and final states of the system, not on the path taken to get from one state to the other. Examples of other state functions include internal energy (U), entropy (S), and Gibbs free energy (G).

Applying Hess's Law

To use Hess's Law to determine the ΔH of a reaction, you need to manipulate a series of known reactions (with known ΔH values) so that they add up to the desired reaction. This may involve:

• Reversing a reaction: When you reverse a reaction, the sign of ΔH changes. If the forward reaction is exothermic (ΔH < 0), the reverse reaction is endothermic (ΔH > 0), and vice versa.
• Multiplying a reaction by a coefficient: When you multiply a reaction by a coefficient, you must also multiply the ΔH value by the same coefficient. This is because enthalpy is an extensive property, meaning that it depends on the amount of substance.

Steps for Using Hess's Law

1. Identify the Target Reaction: Write down the reaction for which you want to determine the ΔH.

2. Find Suitable Reactions: Look for a set of reactions with known ΔH values that, when added together, will give you the target reaction. These reactions are often called "intermediate reactions."

3. Manipulate the Intermediate Reactions: Reverse or multiply the intermediate reactions as needed to match the target reaction. Remember to adjust the ΔH values accordingly.

4. Add the Reactions and ΔH Values: Add the manipulated intermediate reactions together. Cancel out any species that appear on both sides of the equation. The resulting reaction should be the same as the target reaction. Add the adjusted ΔH values together to obtain the ΔH for the target reaction.

Example of Hess's Law Calculation

Let's say you want to determine the ΔH for the reaction:

• C(s) + 2H2(g) → CH4(g)

You have the following information:

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

Here's how to use Hess's Law to find the ΔH for the target reaction:

1. Target Reaction: C(s) + 2H2(g) → CH4(g)

2. Manipulate the Intermediate Reactions:

   • Reaction 1: C(s) + O2(g) → CO2(g) ΔH1 = -393.5 kJ (Keep as is)
   • Reaction 2: H2(g) + 1/2 O2(g) → H2O(l) ΔH2 = -285.8 kJ (Multiply by 2)
     • 2H2(g) + O2(g) → 2H2O(l) 2ΔH2 = -571.6 kJ
   • Reaction 3: CH4(g) + 2O2(g) → CO2(g) + 2H2O(l) ΔH3 = -890.4 kJ (Reverse the reaction)
     • CO2(g) + 2H2O(l) → CH4(g) + 2O2(g) -ΔH3 = +890.4 kJ

3. Add the Reactions and ΔH Values:

   • C(s) + O2(g) → CO2(g) ΔH1 = -393.5 kJ
   • 2H2(g) + O2(g) → 2H2O(l) 2ΔH2 = -571.6 kJ
   • CO2(g) + 2H2O(l) → CH4(g) + 2O2(g) -ΔH3 = +890.4 kJ
   • Overall: C(s) + 2H2(g) → CH4(g) ΔH = -393.5 kJ - 571.6 kJ + 890.4 kJ = -74.7 kJ

Therefore, the ΔH for the reaction C(s) + 2H2(g) → CH4(g) is -74.7 kJ.

Standard Enthalpies of Formation: A Tabular Approach

The standard enthalpy of formation (ΔHf°) is the change in enthalpy when one mole of a compound is formed from its elements in their standard states. The standard state is defined as the most stable form of the substance at 298 K (25 °C) and 1 atm pressure. Standard enthalpies of formation are typically tabulated for a wide range of compounds.

Using Standard Enthalpies of Formation to Calculate ΔH

The ΔH for a reaction can be calculated using the following equation:

• ΔHreaction = ΣnΔHf°(products) - ΣnΔHf°(reactants)

Where:

• Σ represents the sum of.
• n is the stoichiometric coefficient of each substance in the balanced chemical equation.
• ΔHf°(products) is the standard enthalpy of formation of each product.
• ΔHf°(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 defined as zero. For example, ΔHf°(O2(g)) = 0, ΔHf°(C(graphite)) = 0, and ΔHf°(H2(g)) = 0.
• Make sure the chemical equation is balanced before applying the equation.
• Pay attention to the phases of the reactants and products, as the enthalpy of formation can vary depending on the phase.

Steps for Using Standard Enthalpies of Formation

1. Write the Balanced Chemical Equation: Ensure the equation is balanced correctly.

2. Look Up Standard Enthalpies of Formation: Find the standard enthalpies of formation (ΔHf°) for all reactants and products in a table of thermodynamic data.

3. Apply the Formula: Use the equation ΔHreaction = ΣnΔHf°(products) - ΣnΔHf°(reactants) to calculate the ΔH for the reaction.

Example of Calculation Using Standard Enthalpies of Formation

Calculate the standard enthalpy change for the combustion of methane:

• CH4(g) + 2O2(g) → CO2(g) + 2H2O(g)

Using the following standard enthalpies of formation:

• ΔHf°(CH4(g)) = -74.8 kJ/mol
• ΔHf°(O2(g)) = 0 kJ/mol
• ΔHf°(CO2(g)) = -393.5 kJ/mol
• ΔHf°(H2O(g)) = -241.8 kJ/mol

Calculation:

• ΔHreaction = [ΔHf°(CO2(g)) + 2ΔHf°(H2O(g))] - [ΔHf°(CH4(g)) + 2ΔHf°(O2(g))]
• ΔHreaction = [(-393.5 kJ/mol) + 2(-241.8 kJ/mol)] - [(-74.8 kJ/mol) + 2(0 kJ/mol)]
• ΔHreaction = [-393.5 kJ/mol - 483.6 kJ/mol] - [-74.8 kJ/mol]
• ΔHreaction = -877.1 kJ/mol + 74.8 kJ/mol
• ΔHreaction = -802.3 kJ/mol

Therefore, the standard enthalpy change for the combustion of methane is -802.3 kJ/mol.

Bond Energies: Estimating Enthalpies of Reaction

Bond energy is the average energy required to break one mole of a particular bond in the gas phase. It's an approximate method, as bond energies are average values and can vary slightly depending on the molecular environment.

Using Bond Energies to Estimate ΔH

The ΔH for a reaction can be estimated using the following equation:

• ΔH ≈ ΣBond Energies(reactants) - ΣBond Energies(products)

This equation essentially states that the enthalpy change is approximately equal to the energy required to break all the bonds in the reactants minus the energy released when forming all the bonds in the products.

Steps for Using Bond Energies

1. Draw Lewis Structures: Draw the Lewis structures for all reactants and products to identify all the bonds present.

2. List Bonds and Their Energies: List all the bonds broken in the reactants and all the bonds formed in the products, along with their corresponding bond energies (obtained from a table of average bond energies).

3. Calculate Total Energy Required to Break Bonds: Sum the bond energies of all the bonds broken in the reactants.

4. Calculate Total Energy Released When Forming Bonds: Sum the bond energies of all the bonds formed in the products.

5. Apply the Formula: Use the equation ΔH ≈ ΣBond Energies(reactants) - ΣBond Energies(products) to estimate the ΔH for the reaction.

Example Using Bond Energies

Estimate the enthalpy change for the reaction:

• H2(g) + Cl2(g) → 2HCl(g)

Using the following average bond energies:

• H-H bond: 436 kJ/mol
• Cl-Cl bond: 243 kJ/mol
• H-Cl bond: 432 kJ/mol

Calculation:

1. Bonds broken: 1 mol H-H (436 kJ/mol) and 1 mol Cl-Cl (243 kJ/mol)
2. Bonds formed: 2 mol H-Cl (2 x 432 kJ/mol = 864 kJ/mol)

• ΔH ≈ [Bond Energy(H-H) + Bond Energy(Cl-Cl)] - [2 x Bond Energy(H-Cl)]
• ΔH ≈ [436 kJ/mol + 243 kJ/mol] - [864 kJ/mol]
• ΔH ≈ 679 kJ/mol - 864 kJ/mol
• ΔH ≈ -185 kJ/mol

Therefore, the estimated enthalpy change for the reaction is -185 kJ/mol.

Summary Table of Methods

Understanding how to determine the ΔH of a reaction is fundamental to thermodynamics and has significant implications for various fields, including chemistry, engineering, and materials science. Each method has its strengths and limitations, and the choice of method depends on the specific reaction and the available resources. By mastering these techniques, one can gain valuable insights into the energy changes associated with chemical processes.