Work Equilibrium And Free Energy Pogil Answer Key

Work, Equilibrium, and Free Energy: A Deep Dive with Answers

Understanding work, equilibrium, and free energy is crucial for grasping fundamental concepts in chemistry and physics. This comprehensive guide delves into these interconnected ideas, providing explanations and solutions to common problems often found in POGIL (Process Oriented Guided Inquiry Learning) activities. We’ll explore the relationships between these concepts, clarifying how they dictate the spontaneity and direction of processes. This detailed exploration will equip you with a robust understanding of these principles and their practical applications.

What is Work?

In thermodynamics, work (W) refers to energy transfer that occurs when a force causes displacement. In chemical systems, work often manifests as:

• Expansion/Compression Work: Changes in volume against an external pressure (like gas expansion in a piston).
• Electrical Work: Movement of charges across a potential difference (like in electrochemical cells).

It's important to note the sign convention: work done by the system is negative (W < 0), and work done on the system is positive (W > 0). This is because the system loses energy when it does work.

Calculating Work

The calculation of work depends on the type of process. For a reversible, isothermal expansion or compression of an ideal gas:

W = -nRT ln(V_f/V_i)

Where:

• n = number of moles of gas
• R = ideal gas constant
• T = temperature in Kelvin
• V_f = final volume
• V_i = initial volume

What is Equilibrium?

Equilibrium describes a state where opposing forces or influences are balanced. In a chemical system, it means the rates of the forward and reverse reactions are equal, resulting in no net change in the concentrations of reactants and products. This doesn't mean the reactions stop; rather, they proceed at the same rate in both directions.

There are different types of equilibrium:

• Chemical Equilibrium: The dynamic balance between reactants and products in a reversible chemical reaction.
• Thermal Equilibrium: When two objects in contact reach the same temperature.
• Mechanical Equilibrium: When there's no net force acting on a system.

What is Free Energy?

Gibbs Free Energy (G) is a thermodynamic potential that measures the maximum reversible work that may be performed by a thermodynamic system at a constant temperature and pressure. It combines enthalpy (H) and entropy (S) to predict the spontaneity of a process:

ΔG = ΔH - TΔS

Where:

• ΔG = change in Gibbs Free Energy
• ΔH = change in enthalpy (heat content)
• T = temperature in Kelvin
• ΔS = change in entropy (disorder)

Interpreting Free Energy Changes

• ΔG < 0 (negative): The process is spontaneous (exergonic) under the given conditions. It will proceed in the forward direction without external input.
• ΔG > 0 (positive): The process is non-spontaneous (endergonic) under the given conditions. It requires energy input to occur.
• ΔG = 0 (zero): The system is at equilibrium. There is no net change in the forward or reverse direction.

The Relationship Between Work, Equilibrium, and Free Energy

These three concepts are intricately linked. The maximum work a system can perform at constant temperature and pressure is equal to the change in Gibbs Free Energy:

W_max = -ΔG

At equilibrium, ΔG = 0, meaning no more work can be done by the system. The direction of spontaneous change is always towards minimizing free energy. A system will naturally proceed towards equilibrium, where its free energy is at a minimum.

POGIL Activities and Example Problems: Work, Equilibrium, and Free Energy

Let's tackle some typical problems encountered in POGIL exercises:

Problem 1: Gas Expansion

One mole of an ideal gas expands isothermally and reversibly from 10 L to 20 L at 298 K. Calculate the work done by the gas.

Solution:

Use the formula for reversible isothermal expansion work:

W = -nRT ln(V_f/V_i)

W = -(1 mol)(8.314 J/mol·K)(298 K) ln(20 L/10 L)

W = -1717.4 J (The negative sign indicates work is done by the system)

Problem 2: Spontaneity and Free Energy

A reaction has ΔH = +50 kJ/mol and ΔS = +150 J/mol·K. Is the reaction spontaneous at 298 K?

Solution:

Calculate ΔG:

ΔG = ΔH - TΔS

ΔG = (50,000 J/mol) - (298 K)(150 J/mol·K)

ΔG = +5000 J/mol (positive)

Since ΔG is positive, the reaction is not spontaneous at 298 K.

Problem 3: Equilibrium Constant and Free Energy

The equilibrium constant (K) for a reaction is 10⁵ at 298 K. Calculate the standard free energy change (ΔG°) for the reaction.

Solution:

Use the relationship between ΔG° and K:

ΔG° = -RT ln K

ΔG° = -(8.314 J/mol·K)(298 K) ln(10⁵)

ΔG° = -28,500 J/mol (approximately -28.5 kJ/mol) (The negative ΔG° indicates the reaction is spontaneous under standard conditions.)

Problem 4: Effect of Temperature on Spontaneity

A reaction has a positive ΔH and a positive ΔS. Under what temperature conditions will the reaction become spontaneous?

Solution:

For ΔG to be negative (spontaneous), the term -TΔS must be more negative than ΔH. Since both ΔH and ΔS are positive, the reaction will only be spontaneous at high temperatures, where the -TΔS term dominates.

Advanced Concepts and Applications

This section briefly touches upon more advanced topics related to work, equilibrium, and free energy:

• Non-reversible Processes: Work calculations become more complex for non-reversible processes. The work done is always less than the maximum reversible work (-ΔG).
• Standard Free Energy Change (ΔG°): This refers to the free energy change under standard conditions (typically 298 K and 1 atm pressure).
• Free Energy and Chemical Potential: Free energy is closely related to chemical potential, which describes the tendency of a substance to undergo chemical change.
• Coupled Reactions: Non-spontaneous reactions (ΔG > 0) can be driven by coupling them to spontaneous reactions (ΔG < 0) with a large negative ΔG.
• Free Energy and Biological Systems: Free energy changes are crucial in understanding metabolic processes in living organisms. ATP hydrolysis, for instance, is a highly exergonic reaction that fuels many cellular processes.

Conclusion

Understanding the interplay between work, equilibrium, and free energy is fundamental to comprehending chemical and physical processes. This guide provides a solid foundation, offering explanations and solved examples to help you navigate POGIL activities and grasp these essential concepts. By mastering these principles, you'll be better equipped to tackle more complex thermodynamic problems and gain a deeper appreciation for the driving forces behind chemical reactions and physical transformations. Remember to practice consistently and explore further resources to solidify your understanding.