Thermodynamics Practice

Introduction

Thermodynamics practice requires disciplined signs and reference states. Reversing a reaction reverses its enthalpy change; doubling every coefficient doubles the per-equation change; mixing joules and kilojoules can overturn a Gibbs calculation. A negative ΔG describes a favored direction under stated conditions, not an assured fast reaction. This set asks the solver to make those conditions explicit before interpreting a number.

Core explanation

Enthalpy is a state function. Hess's law follows: adding reaction equations adds their enthalpy changes when all states, temperatures and stoichiometric conventions match. Reverse an equation and change the sign of ΔH; multiply it by a factor and multiply ΔH by the same factor. Standard enthalpy of formation refers to forming one mole of a substance from elements in their specified standard reference states. A tabulated ΔH° value is not a universal heat measurement for any apparatus; heat flow matches enthalpy change under constant pressure with only pressure–volume work and appropriate boundaries.

Entropy relates to the spread of matter and energy among accessible microscopic states. System entropy can decrease while the total system-plus-surroundings entropy increases. For constant temperature and pressure, Gibbs energy change can be calculated from ΔG = ΔH − TΔS when the terms describe the same process and assumptions are valid. A negative ΔG favors the forward change from the specified state, a positive value favors the reverse, and zero corresponds to equilibrium for the reaction coordinate. The “standard” superscript means each substance is in a defined standard state; it does not mean the actual vessel is at those compositions.

For a reaction with current quotient Q , ΔG = ΔG° + RT ln Q . At equilibrium, Q = K and ΔG = 0, giving ΔG° = −RT ln K for dimensionless activities. Thus even if ΔG° is negative, an unusual product-rich mixture may have positive actual ΔG and move backward. Neither ΔG nor K specifies a reaction rate. A kinetic barrier may keep a thermodynamically favored process unobservably slow without catalysis or initiation.

Step-by-step reasoning

1. Write the exact reaction with coefficients and physical states. 2. Align thermodynamic data to that reaction by reversing or scaling with corresponding sign changes. 3. Convert ΔS to units consistent with ΔH before calculating TΔS . 4. Decide whether a standard-state or actual-composition result is requested. 5. Interpret the sign for direction under the stated constraints, then discuss kinetics separately.

Visual explanation

Draw two paths connecting the same initial and final thermodynamic states. Their intermediate steps differ, but the summed ΔH is the same, illustrating Hess's law. A second curve of Gibbs energy against reaction progress has a minimum at equilibrium; an activation barrier is drawn over a pathway without moving the initial and final levels. The diagrams separate state-function difference from route and rate.

Real-world analogy

Elevation difference between two towns does not depend on the road taken, resembling a state-function change. A steep pass or long detour can change travel time, resembling a kinetic barrier. The analogy is imperfect because enthalpy and Gibbs energy are thermodynamic quantities with chemical reference states, not literal heights.

Real-world example

An instant cold pack can absorb heat while dissolving a salt. The process may still occur spontaneously under initial conditions if entropy and mixing contributions outweigh the endothermic enthalpy. Calling it “endothermic” tells the direction of heat transfer under specified conditions, not the sign of ΔG by itself. A practical formulation also depends on how much salt can dissolve and how quickly the pack mixes.

Why?

Why must reaction coefficients accompany an enthalpy value? A reported ΔH of −100 kJ “for the reaction” scales with how many moles of the balanced equation occur. If the equation is doubled, the same chemistry represented at twice the amount has ΔH = −200 kJ. Without the equation, the energy number lacks a quantitative basis.

Common misconception

“Exothermic means spontaneous.” Entropy can outweigh enthalpy. “Spontaneous means fast.” It is a direction statement, not a rate statement. “ΔG° and ΔG are identical.” Composition contributes through Q . “Entropy is just disorder.” Microscopic accessibility is a more reliable concept. “Hess's law works even when phases are silently changed.” Phase changes carry their own energy terms.

Worked example

A reaction has ΔH° = +25.0 kJ mol⁻¹ and ΔS° = +100 J mol⁻¹ K⁻¹ over a modest range. Convert ΔS° to +0.100 kJ mol⁻¹ K⁻¹. At 298 K, ΔG° = 25.0 − 298(0.100) = −4.8 kJ mol⁻¹ . The forward standard-state direction is favored despite heat absorption. At 200 K, the same approximation gives +5.0 kJ mol⁻¹, so the standard-state direction reverses. The crossover estimate is 25.0/0.100 = 250 K. This assumes ΔH° and ΔS° do not change materially with temperature; heat capacities could alter a precise result.

Quick check

1. What happens to ΔH when the written reaction is reversed? Answer: Its sign reverses, with the same magnitude under matched conditions. 2. Does ΔG° < 0 guarantee a fast observed reaction? Answer: No. Kinetic barriers can make it slow.

Exam focus

Show equation scaling and phases in Hess-law work. Convert entropy units before multiplying by temperature. Distinguish ΔG° from ΔG and state whether the conclusion is about standard states or an actual mixture. Explain equilibrium with Q and K , then avoid converting a thermodynamic conclusion into an unsupported rate claim.

Advanced insight

Standard reaction Gibbs energy can be inferred from measured equilibrium constants, but the constant must be dimensionless with a consistent activity convention. Coupled reactions can make an unfavorable step occur as part of an overall favorable process; the relevant ΔG is for the complete coupled reaction. Enthalpy and entropy often vary with temperature through heat capacities, so linear extrapolation from one temperature is a limited approximation.

Summary

Hess's law uses state-function additivity with matching states and coefficients. Gibbs energy combines enthalpy and entropy for common direction questions, while actual composition modifies the standard result. Equilibrium position and reaction speed remain distinct.

Practice questions

1. If A → B has ΔH = −40 kJ per equation, what is ΔH for 2B → 2A? Answer: +80 kJ, because the reaction is reversed and doubled. 2. Find ΔG at 300 K for ΔH = −10 kJ mol⁻¹ and ΔS = −20 J mol⁻¹ K⁻¹. Answer: −10 − 300(−0.020) = −4 kJ mol⁻¹. 3. At equilibrium, what is actual reaction ΔG? Answer: Zero for the defined reaction coordinate and constraints. 4. Can a product-rich mixture move in reverse despite ΔG° < 0? Answer: Yes. A sufficiently large Q can make actual ΔG positive.