Question

(a) What is meant by the term state function? (b) Give an example of a quantity that is a state function and one that is not. (c) Is the volume of the system a state function? Why or why not?

Short answer

(a) A state function is a property of a system that depends only on its current state and is independent of the path taken to reach that state. (b) Internal energy (U) is an example of a state function, while work (W) is not a state function. (c) Yes, the volume of the system (V) is a state function because it depends only on the current conditions of the system, such as pressure, temperature, and composition, and does not depend on the process or the path taken to reach the current state.

Step-by-step solution

(a) Definition of State Function

A state function is a property of a system that depends only on its current state and is independent of the path taken to reach that state. In other words, state functions are determined by the system's current conditions, and their values do not depend on the system's history or how the system reached its current state.

(b) Example of State Function and Non-State Function

One example of a state function is internal energy (U). Internal energy is a property of the system that depends only on the current temperature, pressure, and composition of the system, but not on the history or the process by which the system reached its current state. An example of a quantity that is not a state function is work (W). Work depends on the path taken to reach the current state of the system, i.e., the specific processes that occurred or the way the energy was transferred as the system reached its current state.

(c) Is Volume a State Function?

Yes, the volume of the system (V) is a state function. Similar to internal energy, the volume of a system depends only on the current conditions of the system, such as pressure, temperature, and composition, and it does not depend on the process or the path taken to reach the current state. As long as the system's pressure, temperature, and composition are fixed, the volume will also remain constant, regardless of how the system reached that state.

Key concepts

Internal Energy

Internal energy, often denoted by the symbol \( U \), is a fundamental concept in chemistry that represents the total energy contained within a chemical system. This energy manifests as the sum of potential energy, which is the energy due to the positions of the particles, and kinetic energy, the energy of motion of the particles. An easy way to understand internal energy is by picturing a balloon: the energy that the gas molecules possess inside the balloon, due to their motion and interactions, comprises the balloon's internal energy.

What's crucial about internal energy is that it's a state function, which means its value doesn't depend on how the system arrived at its current state. Whether the molecules gained energy through heating or were compressed, the final amount of internal energy is the same if the end conditions are identical.

The change in internal energy (\( \Delta U \)) is what chemists often focus on, especially in reactions and processes. It can be calculated using the first law of thermodynamics, which relates the change in internal energy to the heat added to the system (\( Q \)) and the work done by the system (\( W \)): \[ \Delta U = Q - W \]

• \( Q \) is positive if heat is added to the system, increasing its internal energy.
• \( W \) is positive if work is done by the system, which decreases its internal energy.

Understanding internal energy helps students predict how energy transfers will affect chemical reactions and the physical states of substances.

Thermodynamic Properties

Thermodynamic properties are characteristics that describe the physical and energetic state of a thermodynamic system. These properties fall into two categories: intensive and extensive. Intensive properties, such as temperature and pressure, are independent of the mass of the substance. In contrast, extensive properties, such as volume and internal energy, depend on the amount of substance present.

State functions are a fundamental group of thermodynamic properties used to determine the condition of a system. Examples of state functions include internal energy (\( U \)), pressure (\( P \)), volume (\( V \)), and enthalpy (\( H \)). These are all intrinsic to the system and are not concerned with how the system arrived at its current state.

Importance of Thermodynamic Properties

Thermodynamic properties are essential for understanding the balance of energy within a chemical system, which is vital for numerous applications, including the design of engines, refrigerators, and even predicting the feasibility of chemical reactions. Scientists and engineers often use these properties to analyze energy changes and to determine the work potential of a system. By studying thermodynamic properties, students gain insight into fundamental concepts like the conservation of energy and the directionality of spontaneous processes.

Path Dependence in Chemistry

Path dependence in chemistry refers to the concept that certain thermodynamic quantities depend on the specific way a system transitions from one state to another. Unlike state functions, which are path-independent, path-dependent quantities, such as work (\( W \)) and heat (\( Q \)), are determined by the particular route taken during a process.

For example, when compressing a gas in a cylinder, if done slowly (isothermally), the work done by the gas differs from that when compressed rapidly (adiabatically). Despite ending at the same volume and pressure, the paths are different, and so is the work involved. These quantities are essential in understanding how energy is transferred and the efficiency of transformations in chemical processes.

Implications of Path Dependence

The implications of path dependence are significant in real-world applications where energy efficiency is key. For instance, in industrial chemical processes, path-dependent quantities are meticulously controlled to optimize energy use. Moreover, when studying chemical reactions, knowing the path dependence helps chemists understand how changing reaction conditions might influence the overall energy balance of a reaction. Students must grasp this concept to accurately predict the outcome of thermodynamic processes and to solve real problems they may encounter in practical applications.