Chem 204 MT2

What does per mole of reaction physically signify in a thermochemical equation?

It denotes one mole of stoichiometric reaction cycles as written in the balanced equation rather than one mole of a specific substance

For compression, why does a reversible process represent the minimum work required from the surroundings (w_rev = w_min.)

For reversible compression, the external pressure is kept infinitesimally higher than the gas pressure; the surroundings therefore perform the minimum force necessary to compress the gas.

True or false; all irreversible processes, and thus thinking, increase the entropy of the universe according to the second law of thermodynamics, ∆S_irrev > 0.

True

How does reversible expansion differ from reversible compression?

In reversible expansion the external pressure is kept infinitesimally lower than internal pressure and represents the maximum amount of work that can be extracted from the system; In reversible compression the external pressure is infinitesimally higher than the gas pressure and represents the minimum work required from the surroundings to achieve the compression.

Why is ∆U = q + w only true for a closed system?

Relation ∆U = q + w is the First Law of Thermodynamics for a closed system (where energy can cross the system boundary as heat or work, but mass cannot). For an open system, mass flows across boundaries, bringing additional energy transport terms into the internal energy balance.

Why does internal energy depend only on temperature for an ideal gas but not for a real gas?

For a real gas, intermolecular attractions and repulsions exist, making internal energy depend on both temperature and volume/pressure

Why is the heat capacity of a gas (Cp) temperature dependant?

Cp depends on temperature because molecular vibrational modes become progressively un-frozen and thermally accessible as temperature rises.

How does a chemical reaction affect the number of thermodynamic components?

Each independent reaction reduces the number of components by 1; to determine the number of independent components, count chemically distinguishable species and subtract independent reaction relationships and additional composition constraints: 𝐶 = 𝑆 − 𝑅 − 𝑅′.

eg. 2NH₃(g) ⇌ N₂(g)+3H₂(g); 3 species: NH₃, N₂, H₂ and 1 independent reaction; c = 3-1 = 2

What can be concluded about the sign of entropy change ∆S for a spontaneous dissolution process that causes the solution to become colder?

The solution (surroundings) lost heat, meaning the system gained it; q_sys > 0 and ∆H > 0 for endothermic processes. Because dissolution proceeds spontaneously, 𝛥𝐺 < 0 → ∆G = ∆H - T∆S < 0 ; since both ∆H and T are positive quantities, entropy contribution must overcome the positive enthalpy

(Dispersing ions into solution increases the overall number of accessible configurations/micro-states)

Why can’t a temperature change alone determine the sign of ∆H or ∆G?

Temperature changes alone do not directly measure 𝛥𝐻 or establish the sign of 𝛥𝐺 because these state functions depend on the specific thermodynamic constraints and energy transfers

What is the value of ∆G when, for processes where ∆H and ∆S share the same sign, the temperature is that at which the preferred direction flips?

∆G = 0 (equilibrium); ∆G = ∆H - T∆S → T∆S = ∆H → T_flip = ∆H/∆S

What are possible explanations for the observation that no chemical change occurs after mixing three miscible liquids (A, B, and C) over the course of a week?

1. system is at chemical equilibrium (∆rG = 0)

2. non-spontaneous process: all potential chemical reactions between A, B, and C have a positive Gibbs energy change (∆rG > 0)

3. high activation energy barrier (∆Ga or Ea): ambient thermal energy is insufficient to overcome this barrier

4. absence of necessary catalyst

Why does a negative Gibbs energy change (∆G < 0) indicate that a reaction is thermodynamically favorable, but it does not guarantee that the reaction will occur rapidly or detectably?

If the chemical pathway requires breaking strong covalent bonds, the reaction will possess a high activation energy barrier (∆Ga or Ea). When ambient thermal energy is insufficient to overcome this barrier, the reaction rate will be imperceptibly slow.

An increase in Gibbs energy (∆rG > 0) corresponds to what change in total entropy (∆S_total)?

An increase in Gibbs energy tends to lower total entropy; Holding enthalpy change (∆H) and absolute temperature (T) constant, ∆G is a linear function of ∆S with a slope equal to -T;

∆G = -T(∆S) + ∆H

As ∆S increases, the subtractive term -T∆S becomes larger in magnitude, pulling ∆G down. This represents an inverse linear (opposite) relationship, rather than a reciprocal inverse proportion.

How does increasing pressure change chemical potential (µ) at constant temperature?

Increasing pressure raises the chemical potential ($\mu$) of every phase in direct proportion to its molar volume (Vm)

For water, how does increasing pressure change melting and boiling points (T_fus and Tb)?

Increasing pressure for water;

• lowers melting point; 𝜇𝑠 increases more than 𝜇𝑙 —> $T_{m}^{\prime}(P_2)<T_{m}(P_1)$

• raises boiling point; 𝜇𝑔 increases more than 𝜇𝑙 —> 𝑇𝑏′ (𝑃2) > 𝑇𝑏(𝑃2); retains normal behaviour

(Spontaneous processes proceed toward states of lower chemical potential µ)

What does Chemical Potential µ measure?

µ measures the thermodynamic tendency of a substance to undergo physical change or chemical reaction

For a pure substance, µ is defined as the molar Gibbs energy: Gm = µ

Why does water spontaneously freeze?

Spontaneous processes proceed toward states of lower chemical potential; ∆µ < 0

µ (s) < µ (l)

How does the slope of the solid–liquid phase boundary on a $P$-$T$ phase diagram for water differ from that of typical substances?

Water has an anomalous negative slope because solid ice occupies a larger molar volume than liquid water ($V_m(\text{liquid}) < V_m(\text{solid})$), resulting in $\Delta_{\text{fus}}V_m < 0$. In contrast, typical substances expand upon melting and have a positive slope because $\Delta_{\text{fus}}V_m = V_m(\text{liquid}) - V_m(\text{solid}) > 0$, as governed by the Clapeyron equation: $\frac{dP}{dT} = \frac{\Delta_{\text{fus}}H_m}{T_{\text{fus}} \Delta_{\text{fus}}V_m}$.

At equilibrium, CaCO₃(s) ⇌ CaO(s) + CO₂(g), how many phases are present, and why?

3 phases: CaCO₃(s), CaO(s), and CO₂(g). Each distinct solid is a separate phase; all gases mixed together count as one gas phase

What to evaluate when comparing the relative densities of phases on a $P$-$T$ phase diagram?

1. Slope of the Solid–Liquid Coexistence Line: Governed by the Clapeyron equation, the sign of the slope ($\frac{dP}{dT}$) is determined solely by $\Delta_{\text{fus}}V_m = V_m(\text{liquid}) - V_m(\text{solid})$.

2. Vertical Cuts (Increasing Pressure at Constant Temperature): If you draw a vertical line straight up (increasing pressure at constant $T$) across a phase boundary, the system transitions to the phase occupying the smaller molar volume (the denser phase) to minimize chemical potential.

Why is there no four-phase coexistence point in a pressure–temperature phase diagram for a one-component system?

Gibb’s Phase Rule; Four phases cannot mutually coexist in equilibrium for a single component, because setting p = 4 with c = 1 yields f = -1, violating the physical constraint f ≥ 0

Why is reaction enthalpy an extensive property?

Enthalpy depends directly on the quantity of matter reacting so scaling stoichiometric coefficients multiplies reaction enthalpy by the same factor

Under what specific conditions does measured heat transfer equal reaction enthalpy change?

When the process occurs at constant external pressure with expansion work as the only allowable work

Why do enthalpy change and internal energy change differ for gas-phase reactions?

Gas production or consumption performs expansion work against external pressure represented by the difference term ∆n_gasRT

Why is constant pressure heat capacity greater than constant volume heat capacity for ideal gases?

Heating at constant pressure requires additional energy to perform work expanding against surroundings whereas constant volume heating performs no work

Why are constant pressure and constant volume heat capacities nearly identical for liquids and solids?

Condensed phases undergo negligible volume changes upon heating so expansion work against surroundings is virtually zero;

• Cv: heat added goes mainly into increasing the internal energy of the substance.

• Cp: heat added can also do expansion work (P∆V) but ∆V is minimal

Why is Hess Law valid for calculating unknown reaction enthalpies?

Enthalpy is a state function dependent only on initial and final states so the net enthalpy change is independent of the reaction path

Why is the standard enthalpy of formation of pure elements in reference states set to zero?

It establishes an arbitrary baseline reference scale to measure relative formation energies of chemical compounds consistently

Why does liquid water have a more negative standard enthalpy of formation than water vapor?

Converting water vapor to liquid releases additional energy equal to the enthalpy of condensation due to strong hydrogen bonding

Why does reversing a chemical equation reverse the algebraic sign of its enthalpy change?

Enthalpy is a state function so the energy absorbed in the forward direction must equal the energy released in the reverse direction

Why does reaction enthalpy estimated from average bond enthalpies differ from exact formation enthalpies?

Average bond enthalpies are mean values calculated across diverse molecular environments whereas formation enthalpies use exact standard states

What is the distinction between bond dissociation enthalpy and average bond enthalpy?

Bond dissociation enthalpy is the exact energy to break a specific bond in a specific gas molecule while average bond enthalpy is averaged across various molecules

Why does standard reaction enthalpy vary with temperature according to Kirchhoff Law?

Kirchhoff's law exists because changing temperature changes the enthalpies of reactants and products according to their heat capacities, and if those heat capacities differ, their enthalpy difference (∆rH) changes.

What key assumption is required when applying the integrated Kirchhoff equation over a temperature interval?

The difference in molar heat capacities (∆Cp) between products and reactants is assumed constant over the temperature range

Why is biological glucose respiration energetically equivalent to direct combustion in air?

Enthalpy is a state function so the total heat change depends strictly on initial reactants and final products regardless of metabolic steps

Why is an exothermic reaction enthalpy change insufficient to guarantee spontaneity?

Spontaneity requires an increase in total universal entropy which depends on both system heat release and spatial energy dispersal

How does the Boltzmann equation relate thermodynamic entropy to microstates?

Entropy equals Boltzmann constant times the natural logarithm of the number of accessible spatial and energetic microstates ∆S = K_BlnW

Why does a reversible expansion perform more work than an irreversible expansion between identical states?

Reversible expansion maintains external pressure infinitesimally close to internal gas pressure maximizing work output at every stage

Why is system entropy change identical for reversible and irreversible expansions between same initial and final states?

Entropy is a state function dependent strictly on initial and final thermodynamic states regardless of the path taken

Why does surroundings entropy change differ between reversible and irreversible isothermal expansions?

Surroundings entropy depends on actual heat transferred across the boundary which varies because work output depends on the expansion path

How does the Second Law of Thermodynamics define spontaneity for an isolated system?

An isolated system undergoes spontaneous change if and only if its internal entropy increases until reaching maximum at equilibrium

Why does a perfect crystal at absolute zero temperature have an absolute entropy of zero according to the Third Law?

A perfect crystal at zero Kelvin possesses only one accessible ground state microstate making entropy equal to Boltzmann constant times ln 1

What physical factor causes residual entropy in solid substances at absolute zero?

Random molecular orientations or structural defects frozen into the crystal lattice preventing complete structural order

Why does standard molar entropy increase when a substance transitions from liquid to gas?

Vaporization dramatically increases molar volume and spatial microstate availability allowing vastly greater energy dispersal

How is Gibbs energy derived from the Second Law criterion for spontaneity?

Multiplying total universal entropy change by negative temperature under constant T and P yields delta G as a system-only criterion

What is the conceptual difference between thermodynamic driving force ∆G and kinetic rate?

∆G determines thermodynamic feasibility and equilibrium position while activation energy (Ea) barrier determines the reaction rate

Under what thermal conditions is an endothermic reaction with positive entropy change spontaneous?

At high temperatures where the negative T delta S term exceeds the positive enthalpy term making delta G negative

How is the reversal temperature calculated for a reaction where enthalpy and entropy changes share the same sign?

Reversal temperature equals enthalpy change divided by entropy change representing the point where delta G equals zero

∆G = 0; T∆S = ∆H → T_equ = ∆H/∆S

What does Gibbs energy change physically measure for a process at constant temperature and pressure?

The maximum theoretical amount of useful non-expansion work that can be extracted from the system

∆G_P,T = w_non-exp,max

How does ATP hydrolysis drive endergonic metabolic pathways in living cells?

Enzymatic coupling links favorable ATP hydrolysis to an unfavorable reaction yielding a net negative coupled Gibbs energy change

∆rG_coupled = ∆rG_{x(unfavourable)} + ∆rG_hydrolysis

What does the partial derivative of molar Gibbs energy with respect to temperature at constant pressure represent?

It equals negative molar entropy indicating molar Gibbs energy decreases with increasing temperature

What does the partial derivative of molar Gibbs energy with respect to pressure at constant temperature represent?

It equals molar volume indicating molar Gibbs energy (and therefore chemical potential µ) increases with increasing pressure

Why does increasing pressure elevate molar Gibbs energy of ideal gases much more than liquid water?

Ideal gases have vastly larger molar volumes than liquid water making the pressure derivative of Gibbs energy much larger

What is the definition of chemical potential for a pure substance?

Chemical potential is the molar Gibbs energy of a pure substance measuring its thermodynamic tendency to transform or react

What do degrees of freedom represent in Gibbs Phase Rule f = c - p + 2?

The number of intensive variables like temperature or pressure that can be varied independently without changing coexisting phases

Why cannot four phases coexist at thermodynamic equilibrium for a single component system?

Setting four phases and one component yields negative one degrees of freedom violating the physical requirement that f must be non-negative

Why is the slope of chemical potential (µ) versus temperature steeper for gas than liquid?

Molar entropy of gas is greater than liquid and the slope equals negative molar entropy

(dG/dT)_P = -Sm

Why does increasing pressure lower the melting point of ice but raise the melting point of most substances?

According to the Clapeyron equation; dP/dT = ∆S/∆V;

For melting, ∆S > 0 so the sign of slope dP/dT is determined by ∆Vm = V_m(liquid) - V_m(solid)

For most substances ∆Vm > 0 meaning dP/dT is positive, therefore pressure increase raises the melting Temperature;

For water, ∆Vm < 0 causing the slope to be negative and leading to a lower melting temperature with increasing pressure

How is supercooled liquid water kinetically stabilized in a metastable state?

Pure water lacks nucleation centers creating an activation energy barrier that prevents ice crystal formation below freezing

What physical approximations convert the Clapeyron equation into the Clausius-Clapeyron equation for vaporization?

Liquid molar volume is neglected relative to gas molar volume and the gas phase is assumed to behave ideally

What assumption is required when using the integrated Clausius-Clapeyron equation to calculate vapor pressure?

The molar enthalpy of vaporization (∆_vapH) is assumed constant over the specified temperature interval;

dP/dT = ∆_trsH/T_trs∆_trsVm

Why does chemical potential equality define phase equilibrium between two coexisting phases?

Because chemical potential tells us the tendency of a substance to move from one phase to another.

Equal chemical potential (µ1 = µ2) means no net thermodynamic driving force exists for matter transfer between the coexisting phases

What is the difference between a single phase solution and a dispersion?

A single phase solution is uniform at the molecular level (eg. sugar water; solute completely dissolved in a liquid solvent) while a dispersion contains microscopic regions of distinct phases (eg. emulsion of milk reveals 2 phases; oil-in-water)

Why does the triple point of a pure substance have zero degrees of freedom?

Three coexisting phases for one component fix temperature and pressure uniquely so neither variable can be changed without losing a phase

f = c - p + 2

How does temperature affect phase stability based on molar entropy differences?

Increasing temperature favors phases with higher molar entropy because higher entropy produces a steeper decrease in chemical potential

Why does active ion transport against a concentration gradient require coupling to ATP hydrolysis?

Transporting ions against a gradient has a positive Gibbs energy change so coupling to exergonic ATP hydrolysis makes net delta G negative

Why is maximum work obtained only when a process occurs reversibly?

Reversible processes avoid dissipation through finite gradients ensuring no potential work is lost to entropy generation

What is the physical meaning of standard state superscript circle on thermodynamic quantities?

It specifies that all species are present in pure stable phases at 1 bar pressure and defined temperature

How does enthalpy of vaporization relate to liquid molecular interactions?

Enthalpy of vaporization measures the energy required to completely overcome attractive intermolecular forces holding liquid molecules together

Why is the change in internal energy zero for any isothermal expansion of an ideal gas?

Ideal gas internal energy depends strictly on temperature so constant temperature dictates zero internal energy change

Why does constant volume heating of an ideal gas increase internal energy but perform zero work?

No volume change means expansion work is zero so all absorbed heat goes directly into increasing internal kinetic energy

In what case can ∆G not be used to predict whether the process is spontaneous?

When T or P vary; ∆G < 0 is a criterion of spontaneity only if both T and P are held constant.

What causes the sign flip of enthalpy of reaction when reversing a reaction step in Hess Law?

Reversing direction turns heat absorption into heat release or vice versa because enthalpy change is path-independent state function