Question

Determine whether the system \(\Delta H_{\mathrm{system}}=-20.5 \mathrm{k}, T=298 \mathrm{K}, \mathrm{and}\) \(\Delta S_{\text { system }}=-35.0 \mathrm{J} / \mathrm{K}\) is spontaneous or nonspontaneous.

Short answer

The system with ∆H = -20.5 kJ, T = 298 K, and ∆S = -35.0 J/K is spontaneous, as the Gibbs free energy change (∆G) is calculated to be -10,070 J, which is negative.

Step-by-step solution

1. Identify given values

We are given: ∆H = -20.5 kJ T = 298 K ∆S = -35.0 J/K Note that the units of ∆H and ∆S are different (kJ for ∆H and J for ∆S). Make sure to convert them to the same unit before substitution into the equation.

2. Convert the units of ∆H and ∆S

To convert the units of ∆H to J (joules), multiply by 1000: ∆H = -20.5 kJ × 1000 = -20,500 J The units of ∆S are already in J/K, so no conversion is needed.

3. Calculate ∆G using the Gibbs free energy equation

Now calculate ∆G using the equation ∆G = ∆H - T∆S: ∆G = (-20,500 J) - (298 K × -35.0 J/K)

4. Simplify and solve for ∆G

Multiply and simplify the equation: ∆G = -20,500 J + (10,430 J) = -10,070 J

5. Determine spontaneity

Since ∆G is negative (-10,070 J), the reaction is spontaneous. In conclusion, the system with ∆H = -20.5 kJ, T = 298 K, and ∆S = -35.0 J/K is spontaneous.

Key concepts

Thermodynamics

Thermodynamics is the branch of physics that deals with heat, work, and temperature, and their relation to energy, radiation, and physical properties of matter.
The field divides energy into two main categories: internal energy, which is contained within a system, and external work and heat.
One of the key concepts in thermodynamics that relates to this problem is the Gibbs Free Energy equation, represented by \( \Delta G = \Delta H - T\Delta S \).
This equation links enthalpy \( (\Delta H) \), entropy \((\Delta S)\), and temperature \((T)\) to determine whether a process is spontaneous.

• Entails Energy Transactions: Thermodynamics explains how energy moves and transforms within systems.
• Defines System Behavior: Understanding the thermodynamic principles helps predict the feasibility of chemical reactions.
• Laws of Thermodynamics: There are three laws which define how energy is conserved, how entropy increases, and how absolute zero is unattainable.

Understanding these core principles helps you appreciate how reactions are controlled and predicted in chemistry.

Enthalpy

Enthalpy, denoted by \((\Delta H)\), is a thermodynamic quantity equivalent to the total heat content of a system. It reflects the energy required to create the system, accounting for internal energy minus the work done by the system.
It is an important factor in the Gibbs Free Energy equation for understanding the energy changes in chemical reactions:

• Exothermic vs Endothermic: A negative \((\Delta H)\) indicates an exothermic reaction, where heat is released.
• Calculating Changes: Enthalpy changes are critical for calculating \( \Delta G \), and so affect spontaneity.
• Tied To Bonds: Changes in \( \Delta H \) often relate to breaking and forming of bonds in chemical reactions.

Recognizing enthalpy helps predict whether a reaction will liberate or absorb energy.

Entropy

Entropy, represented by \((\Delta S)\), is a measure of the disorder or randomness in a system. It describes the number of ways a system can be arranged, where higher entropy means more randomness.
In thermodynamics, it helps predict the direction of spontaneous processes.

• Order to Disorder: Systems naturally move towards greater entropy.
• Role in Spontaneity: A positive \( \Delta S \) suggests a move toward increased disorder and potential spontaneity.
• Temperature Dependence: Entropy is directly multiplied by temperature in the \( \Delta G \) equation, aligning it with heat energy.

Understanding entropy is crucial to predict the likelihood and direction of reactions.

Spontaneity

Spontaneity in chemistry refers to whether a chemical reaction will occur naturally without continuous energy input.
This concept is critical when guessing whether a reaction needs external energy to proceed. It hinges on the sign of Gibbs Free Energy change \( (\Delta G) \).

• Negative \( \Delta G \): Indicates a spontaneous reaction. The reaction will proceed on its own.
• Positive \( \Delta G \): Signifies a non-spontaneous reaction. Energy input is needed to drive the reaction.
• Zero \( \Delta G \): Means the system is at equilibrium, and no net change will occur.

Understanding this concept allows chemists to rationalize the conditions under which reactions occur naturally.

Chemistry Education

Chemistry education covers a broad spectrum of principles and reactions, equipping learners with essential skills for scientific inquiry and experimentation.
Key topics like Gibbs Free Energy help students understand how chemical reactions proceed, including factors of energy changes and molecular disorder.

• Critical Thinking: Students learn to analyze when and why reactions occur.
• Practical Applications: Knowledge of thermodynamics and related concepts is vital for real-world applications.
• Conceptual Understanding: Equips students with tools to predict the behavior of chemical systems.

Comprehending these foundational subjects empowers students to pursue advanced studies and foster innovations in chemistry.