Thermochemistry and the First Law of Thermodynamics

Fundamental Definitions in Thermochemistry

• Thermochemistry: This is defined as the scientific study of the heat changes that occur during chemical reactions.

• Heat: This refers to the transfer of thermal energy between two distinct bodies that exist at different temperatures.

• System: The system is the specific part of the universe that is under study or of specific interest to us, including the substances and conditions involved.

• Surroundings: This encompasses the remainder of the universe that exists outside the boundaries of the defined system.

• State of a system: This is defined by the values of all relevant macroscopic properties. These properties include:

  • Composition

  • Energy

  • Temperature

  • Pressure

  • Volume

• State functions: These are properties that are determined solely by the current state of a system. They are independent of the path or the method by which that condition or state was achieved.

Classification of Thermodynamic Systems

Systems are classified based on their ability to exchange matter and energy with their surroundings:

• Open system: A system that is capable of exchanging both mass and energy with its surroundings.

• Closed system: A system that allows for the transfer of energy (in the form of heat) but does not allow for the transfer of mass.

• Isolated system: A system that does not allow for the transfer of either mass or energy to or from the surroundings.

Thermal Processes and Energy Exchanges

• Exothermic process: Any process that gives off heat or transfers thermal energy from the system to the surroundings.

• Endothermic process: Any reaction or process in which heat must be supplied to the system from the surroundings.

• Thermodynamics: The scientific study concerning the interconversion of heat and other forms of energy.

The First Law of Thermodynamics

• Definition: The First Law of Thermodynamics states that energy can be converted from one form to another, but it cannot be created or destroyed.

• Internal Energy ($U$): While it is impossible to validate the law by determining the total energy content of the entire universe, its validity is tested by measuring the change in internal energy ($\Delta U$) of a system between an initial and final state.

• Internal Energy Change Formula:     $\Delta U = U_f - U_i$

  • $U_f$: Internal energy of the system in the final state.

  • $U_i$: Internal energy of the system in the initial state.

• Conservation of Energy in Chemical Reactions: Consider the reaction where one mole of sulfur reacts with one mole of oxygen gas to produce one mole of sulfur dioxide:     $S_{(s)} + O_{2(g)} \rightarrow SO_{2(g)}$

  • The reactant molecules ($S$ and $O_2$) constitute the initial state.

  • The product molecule ($SO_2$) constitutes the final state.

  • Even if the absolute internal energy of the components is unknown, the change in energy content ($\Delta U$) can be accurately measured.

• Universal Energy Balance: The relationship between the system and its surroundings is expressed as:     $\Delta U_{\text{sys}} + \Delta U_{\text{surr}} = 0$     $\Delta U_{\text{sys}} = - \Delta U_{\text{surr}}$

  • Subscripts "sys" and "surr" denote the system and surroundings, respectively.

  • When a system undergoes an energy change, the rest of the universe must undergo an equal and opposite change in energy.

  • Metaphor/Example: Energy lost in one location is gained in another, often in a different form. For instance, energy lost by burning oil in a power plant may eventually appear in a home as electricity.

Mathematical Application of the First Law

In chemistry, focus is placed on the energy changes within the system. The useful equation for the first law is: $\Delta U = q + w$

• $\Delta U$ is the change in internal energy.

• $q$ is the heat exchange between the system and the surroundings.

• $w$ is the work done on or by the system.

Sign Conventions for $q$ and $w$

• Heat ($q$):

  • Positive ($+$): For an endothermic process (heat absorbed by the system).

  • Negative ($-$): For an exothermic process (heat released by the system).

• Work ($w$):

  • Positive ($+$): For work done on the system by the surroundings (e.g., compression).

  • Negative ($-$): For work done by the system on the surroundings (e.g., expansion).

Worked Examples

Example 1

Problem: A gas is compressed in a cylinder with work equal to $462\,J$. During this process, there is a heat transfer of $128\,J$ from the gas to the surroundings. Calculate the energy change for this process.

• Strategy:

  • Compression indicates work is done on the gas, so $w$ is positive ($+462\,J$).

  • Heat is released by the gas to the surroundings, indicating an exothermic process, so $q$ is negative ($-128\,J$).

• Solution:     $\Delta U = q + w$     $\Delta U = -128\,J + 462\,J$     $\Delta U = 334\,J$

Example 2

Problem: The work done to compress a gas is $74\,J$. As a result, $26\,J$ of heat is given off to the surroundings. Calculate the change in energy of the gas.

• Formula:     $\Delta U = q + w$

• Logic:

  • Work of compression is work done on the system: $w = +74\,J$.

  • Heat given off is heat lost by the system: $q = -26\,J$.

• Solution:     $\Delta U = -26\,J + 74\,J$     $\Delta U = 48\,J$