First Law of Thermodynamics Notes

5.4 The First Law of Thermodynamics

Goals for Section 5.4

• Recognize how energy transferred as heat and work done on or by a system contributes to changes in the internal energy of a system.
• Calculate the work done by a system by the expansion of a gas against a constant pressure.
• Calculate changes in enthalpy and internal energy.
• Recognize state functions whose values are determined only by the state of the system and not by the pathway by which the state was achieved.

Introduction to Thermodynamics

Thermodynamics is the science of heat and work. Previously, the focus was solely on energy transferred as heat; now, we expand the discussion to include work. Work done by or on a system influences the system's energy. When a system performs work on its surroundings, energy is expended, leading to a decrease in the system's energy. Conversely, when work is performed on the system by the surroundings, the energy of the system increases.

Example of Work Done by a System

A practical illustration includes a scenario with dry ice (solid CO₂) inside a sealed plastic bag with a weight (a book) placed on top. As energy is transferred as heat from the surroundings to the dry ice, sublimation occurs:
CO₂(s, -78 °C)
ightarrow CO₂(g, -78 °C)
This process results in the gaseous CO₂ expanding within the bag, which lifts the book against gravitational force. Although work is done on lifting the book, the expanding gas must also push against atmospheric pressure, which also entails work.

Analyzing the System and Surroundings

• System: The CO₂ transitioning from solid to gas.
• Surroundings: The plastic bag, the book, the table-top, and the surrounding air.

Sublimation requires energy, which is absorbed from the surroundings as heat. Concurrently, the system performs work on the surroundings by lifting the book. This energy exchange can be quantified through an energy balance that includes both heat and work:

Mathematical Expression of First Law of Thermodynamics

The energy change for a system can be expressed using the equation:
igtriangleup U = q + w
Where:

• igtriangleup U = Change in internal energy of the system.
• q = Energy transferred as heat between the system and its surroundings.
• w = Energy transferred as work between the system and its surroundings.

This equation outlines the first law of thermodynamics: the energy change for a system is equal to the sum of the energy transferred as heat and the energy transferred as work. This is a manifestation of the conservation of energy principle.

Understanding Internal Energy

The quantity U in the equation represents internal energy, defined as the total energy (both potential and kinetic) within the system, derived from the energies associated with particles (atoms, molecules, ions) in the system:

• Potential Energy: Includes energies associated with forces between particles, such as bonds in molecules and forces between ions or molecules.
• Kinetic Energy: The energy of motion of these particles.

In practical applications, we usually measure changes in internal energy rather than absolute values.

Sign Conventions for Energy Transfer

The following sign conventions apply:

P-V Work

The type of work discussed in the sublimation example is known as P-V (pressure-volume) work, articulated as follows:

• For a gas in a cylinder with a piston, if the gas expands, moving the piston upward, it does work against constant external pressure.

The work done can be calculated using the formula:
w = -P imes igtriangleup V
Where:

• P = external pressure,
• igtriangleup V = change in volume.

This formulation assumes ideal conditions where no work is lost due to friction.

Heat Transfer and Work in Constant-Volume Processes

In a constant-volume process, igtriangleup V = 0, hence:
igtriangleup U = q when w = 0. Therefore, the change in internal energy under these conditions equals only the heat transferred.

Introduction to Enthalpy

For processes conducted at constant pressure, we define a new thermodynamic function called enthalpy (H).

• Enthalpy is described as:
  H = U + PV
  In constant pressure processes, the change in enthalpy can be expressed as:
  igtriangleup H = igtriangleup U + Pigtriangleup V
  Thus:
  igtriangleup H = qp Where: qp is the heat exchanged at constant pressure.

Significance of Enthalpy Changes

1. Negative values of igtriangleup H: Indicate that energy has been transferred from the system to the surroundings (exothermic processes).
2. Positive values of igtriangleup H: Indicate energy transfer from surroundings to the system (endothermic processes).

Comparison of Internal Energy and Enthalpy

• Internal energy (U) changes and enthalpy (H) changes differ primarily when significant volume changes occur, such as gas formation in reactions.
• For processes with minimal volume change, igtriangleup H and igtriangleup U yield similar values.

Specific Case Study

Consider the sublimation of dry ice or phase transitions. The fact that they involve significant volume changes means that the internal energy and enthalpy will differ considerably, particularly during reactions involving gas formation.

5.5 Enthalpy Changes for Chemical Reactions

Goals for Section 5.5

• Understand and utilize the enthalpy changes for transitions from reactants to products in standard states, igtriangleup H_{rxn}.

Enthalpy Changes in Reactions

• Enthalpy changes accompany reactions. For example, the enthalpy of reaction for the decomposition of water vapor is:
  H2O(g) ightarrow H2(g) + rac{1}{2}O_2(g) ext{ where } igtriangleup H = +241.8 rac{kJ}{mol ext{-rxn}}
  This positive sign signifies an endothermic process.

Standard Reaction Enthalpies

1. Standard state definition: Standard enthalpy changes imply elements in their most stable forms at 1 bar pressure and specified temperatures, typically 25 °C (298 K).
2. Conventional Formulas: The coefficient in the standard enthalpy formula means that these values are for the amounts specified in balanced equations.
3. Reverse reactions: The magnitude of igtriangleup H^ heta changes sign in reverse reactions.

Example: Formation of Water from Hydrogen and Oxygen

Using the combustion of hydrogen to calculate the enthalpy for the formation of liquid water vs. water vapor outlines the importance of considering the states of reactants and products in enthalpy calculations, as they drastically alter the attributed value of igtriangleup H.

Summary of Key Points

• Enthalpy is specific to the identity and state of substances participating in reactions and changes as per the number of reaction moles.
• Use Hess’ Law when direct measurement through calorimetric methods is unfeasible.

Calculation Example

• Consider quantifying the combustion of propane;
  ext{C}3 ext{H}8(g) + 5 ext{O}2(g) ightarrow 3 ext{CO}2(g) + 4 ext{H}_2 ext{O}(l) ext{ with } igtriangleup H^ heta = -2220 rac{kJ}{mol ext{-rxn}}

1. Enthalpy for sample combustion: Using mass and the enthalpy of the reaction from tabulated values allows calculating energy changes for specific masses of the reactant.
2. Combustion and energy efficiency: Enthalpy changes allow predictions about energy efficiencies and conversions within combustion reactions.

Summary of Enthalpy Changes

• The enthalpy change equals the total formation and decomposition energies associated with the balanced equation.
• Hess's law provides a method for finding indirect reaction enthalpies based on established measured values from potential parameters.

Applications of Hess's Law and Energy Level Diagrams

Understanding Enthalpy with Hess’s Law

• Enthalpy changes from reactions can be measured using calorimetry and indirect methods like Hess's Law.
• For reactions impossible to execute due to practical constraints, previous research enables employing known reactions to provide insight into estimated enthalpies of reactions.

Energy Level Diagrams

Visual representations of the relative positions of reactants and products concerning their enthalpies enhance understanding of reaction energetics as it relates back to thermodynamics. These diagrams clarify the magnitudes and directional flows of energy changes occurring during reactions.

Practical Problem Solving with Hess’s Law

1. Adjusting known reactions: Identify the required equation involving the reactants/products of interest and manipulate current equations to reflect the desired result.
2. Utilizing known energies: Understand how to utilize tabulated enthalpy values to facilitate effective calculations of unknown reaction enthalpies.
3. Summative calculations: Develop skills to combine known enthalpy values efficiently, allowing for broader applications across the entire field of chemical reactivity.

Implications of Thermodynamics on Equilibrium

Through this study, the relationship between reaction enthalpies, energy exchanges (heat and work), and the tendencies of systems towards equilibrium becomes apparent. Whether reactions are product- or reactant-favored illustrates underlying trends and provides insights into reaction kinetics and thermodynamic stability.