Expressing Enthalpy Changes Study Guide

Overview of Communicating Enthalpy Changes

• Enthalpy changes are communicated in four primary ways within the study of chemistry:

  1. By stating the molar enthalpy of a specific reactant in a reaction.

  2. By stating the enthalpy change ($\Delta H$) for a balanced reaction equation.

  3. By including an energy value as a term in a balanced reaction (thermochemical equations).

  4. By drawing a chemical potential energy diagram.

Method 1: Molar Enthalpy of a Specific Reactant

• Standard Conditions (SATP): Chemists use a standard set of conditions (Standard Ambient Temperature and Pressure) so that scientists can create tables of precise, standard values and compare other values easily.

  • For enthalpy measurements, liquids and solid compounds must have the same initial and final temperature, which is most often $25^\circ C$.

• Notation for Standard Conditions: Standard conditions are communicated using a ${^\circ}$ superscript.

  • Examples include: $\Delta_f H_m^\circ$ (Standard molar enthalpy of formation) or $\Delta_c H_m^\circ$ (Standard molar enthalpy of combustion).

• Well-known Reactions: For specific reactions like formation ($\Delta_f$) or combustion ($\Delta_c$), a chemical equation is not strictly necessary because the subscript refers to a universally understood specific reaction.

• Other Reactions: For equations that are not well known or obvious, the chemical equation must be explicitly stated alongside the molar enthalpy value.

• Directionality and Signage: The sign for the molar enthalpy of formation ($\Delta_f H_m^\circ$) is the opposite of the sign for the molar enthalpy of decomposition ($\Delta_d H_m^\circ$).

Method 2: Enthalpy Change Beside a Balanced Equation

• Definition and Calculation: The enthalpy change ($\Delta H$) for a reaction can be determined by multiplying the chemical amount ($n$) by the molar enthalpy of reaction ($\Delta H_m$) for a specific chemical: $\Delta H = n \times \Delta H_m$.

• Coefficients: The chemical amount used in the calculation is derived from the coefficient in the balanced chemical equation. This coefficient is considered an exact number and is not used to determine significant digits.

• Example Calculation - Sulfur Dioxide Combustion:

  • Reaction: Sulfur dioxide and oxygen react to form sulfur trioxide.

  • Given: The standard molar enthalpy of combustion of sulfur dioxide ($SO_{2(g)}$) is $-98.9\,kJ/mol$.

  1. Balanced Equation: $2SO_{2(g)} + O_{2(g)} \rightarrow 2SO_{3(g)}$

  2. Determine Amount: According to the equation, there are $2\,mol$ of $SO_2$.

  3. Calculate Change: $\Delta H = 2\,mol \times (-98.9\,kJ/mol) = -197.8\,kJ$.

  4. Report Enthalpy: The enthalpy change is reported next to the balanced equation: $2SO_{2(g)} + O_{2(g)} \rightarrow 2SO_{3(g)} \quad \Delta H = -197.8\,kJ$.

Method 3: Energy Value as a Term in a Balanced Equation

• Endothermic Reactions: These reactions require additional energy to proceed. In a thermochemical equation, the energy value is listed on the reactant side (left side).

• Exothermic Reactions: These reactions release energy as they proceed. In a thermochemical equation, the energy value is listed on the product side (right side).

• Conditions: To specify initial and final conditions for the enthalpy change, the temperature and pressure may be noted at the end of the equation.

• Example - Formation of Methanol:

  • Goal: Write the thermochemical equation for the formation of $2\,moles$ of methanol ($CH_3OH_{(l)}$) from its elements.

  • Given: Molar enthalpy of formation ($\Delta_f H_m$) is $-108.6\,kJ/mol$.

  • Calculation: $\Delta H = 2\,mol \times (-108.6\,kJ/mol) = -217.2\,kJ$ (Reaction is exothermic).

  • Equation: $2C_{(s)} + 4H_{2(g)} + O_{2(g)} \rightarrow 2CH_3OH_{(l)} + 217.2\,kJ$

Method 4: Chemical Potential Energy Diagrams

• Theory of Chemical Potential Energy: Observed energy changes during chemical reactions are due to changes in chemical potential energy ($E_p$). This is a stored form of energy related to the relative positions of particles and the strengths of the bonds between them.

• Mechanisms of Change: As bonds break and re-form and atom positions are altered, potential energy changes occur. Evidence for a change in the enthalpy of a chemical system is provided by a temperature change in the surroundings.

• Diagram Components:

  • Vertical Axis: Represents Potential Energy ($E_p$).

  • Horizontal Axis: Represents the Reaction Coordinate or Reaction Progress.

  • Layout: Reactants are written on the left; products are written on the right.

  • Enthalpy Change: The difference between the potential energy of the reactants and the products is the enthalpy change (often obtained via calorimetry).

• Exothermic Processes:

  • The enthalpy of the system decreases.

  • Heat flows from the system into the surroundings.

  • The surroundings observe a temperature increase.

  • Reactants have a higher level of potential energy than the products (E_{p, reactants} > E_{p, products}).

• Endothermic Processes:

  • Heat flows from the surroundings into the chemical system.

  • The surroundings observe a temperature decrease.

  • Reactants absorb energy to produce products.

  • Reactants have a lower level of potential energy than the products (E_{p, reactants} < E_{p, products}).

• Diagram Requirements: A complete diagram must include the reactants, products, and the enthalpy change value.

Practical Examples and Communication Conventions

• Example: Burning of Magnesium: Used to produce bright emergency flares. (Exothermic reaction; would be drawn with reactants higher than products).

• Example: Decomposition of Water: Driven by electrical energy from a solar cell. (Endothermic reaction; would be drawn with reactants lower than products).

• Molar Enthalpy of Methanol Combustion: A value of $-725.9\,kJ/mol$ means the complete combustion of $1\,mol$ of methanol releases $725.9\,kJ$ of energy.

• Identification of Communication Errors: Communication conventions are vital for international scientific collaboration. Variations in presenting the same result must be mathematically and chemically consistent:

  • A reaction involving $1\,mol$ of reactant with $\Delta H_m = -241.8\,kJ/mol$ is equivalent to an equation with $+\,241.8\,kJ$ on the product side.

  • If the reaction coefficients are doubled (e.g., from $1\,H_2$ to $2\,H_2$), the energy value must also be doubled (e.g., from $241.8\,kJ$ to $483.6\,kJ$).

  • Error catch: In the provided Practice #3, option C states $\Delta_c H = 241.8\,kJ$ without the negative sign for an exothermic reaction, failing to communicate the same result as the others.