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Questions and Answers
For a reaction to be spontaneous, what must be true of the Gibbs free energy change ($\Delta G$)?
For a reaction to be spontaneous, what must be true of the Gibbs free energy change ($\Delta G$)?
- $\Delta G > 0$
- $\Delta G$ must be equal to $\Delta H$
- $\Delta G = 0$
- $\Delta G < 0$ (correct)
The entropy of a gas is generally lower than that of a liquid.
The entropy of a gas is generally lower than that of a liquid.
False (B)
Which of the following statements best describes the relationship between enthalpy ($\Delta H$), entropy ($\Delta S$), and Gibbs free energy ($\Delta G$)?
Which of the following statements best describes the relationship between enthalpy ($\Delta H$), entropy ($\Delta S$), and Gibbs free energy ($\Delta G$)?
- $\Delta G = \Delta H + T\Delta S$
- $\Delta G = T\Delta H - \Delta S$
- $\Delta G = \Delta H - T\Delta S$ (correct)
- $\Delta G = -\Delta H + T\Delta S$
What condition is met when a system is at equilibrium in terms of Gibbs Free Energy?
What condition is met when a system is at equilibrium in terms of Gibbs Free Energy?
For the reaction $N_2(g) + 3H_2(g) \rightarrow 2NH_3(g)$, under what conditions is the reaction spontaneous at all temperatures?
For the reaction $N_2(g) + 3H_2(g) \rightarrow 2NH_3(g)$, under what conditions is the reaction spontaneous at all temperatures?
The Gibbs free energy change ($\Delta G$) can be directly measured using a calorimeter.
The Gibbs free energy change ($\Delta G$) can be directly measured using a calorimeter.
According to the equation $\Delta G = \Delta H - T\Delta S$, spontaneity is favored by ______ enthalpy and ______ entropy.
According to the equation $\Delta G = \Delta H - T\Delta S$, spontaneity is favored by ______ enthalpy and ______ entropy.
Which of the following factors affects the change in spontaneity with temperature?
Which of the following factors affects the change in spontaneity with temperature?
How is the entropy change of the surroundings ($\Delta S_{surr}$) related to the heat transferred to the surroundings ($q_{surr}$) and the temperature ($T$)?
How is the entropy change of the surroundings ($\Delta S_{surr}$) related to the heat transferred to the surroundings ($q_{surr}$) and the temperature ($T$)?
What thermodynamic property do reactions maximize as they approach equilibrium?
What thermodynamic property do reactions maximize as they approach equilibrium?
The standard Gibbs free energy of formation ($\Delta G_f^\circ$) of an element in its standard state is always positive.
The standard Gibbs free energy of formation ($\Delta G_f^\circ$) of an element in its standard state is always positive.
The change in Gibbs Free energy is ______ for a system at equilibrium.
The change in Gibbs Free energy is ______ for a system at equilibrium.
Which of the following is true regarding the Standard Gibbs Free Energy of Formation?
Which of the following is true regarding the Standard Gibbs Free Energy of Formation?
Consider a reaction with $\Delta H = -100 \text{ kJ}$ and $\Delta S = -50 \text{ J/K}$. Below what temperature (in Kelvin) will the reaction be spontaneous?
Consider a reaction with $\Delta H = -100 \text{ kJ}$ and $\Delta S = -50 \text{ J/K}$. Below what temperature (in Kelvin) will the reaction be spontaneous?
For elements, $S^\circ$ is equal to zero.
For elements, $S^\circ$ is equal to zero.
Reactions that consume or generate gases can have ______ entropy changes.
Reactions that consume or generate gases can have ______ entropy changes.
In an endothermic reaction, is entropy increased or decreased?
In an endothermic reaction, is entropy increased or decreased?
In the Gibbs Free Energy equation, what is $G$ equal to?
In the Gibbs Free Energy equation, what is $G$ equal to?
When ice melts, is entropy increased or decreased?
When ice melts, is entropy increased or decreased?
At equilibrium, systems are static.
At equilibrium, systems are static.
The same equilibrium position will be reached by starting with either $N_2O_4$ or with ______.
The same equilibrium position will be reached by starting with either $N_2O_4$ or with ______.
In terms of an equilibrium, what can be said about homogenous equilibrium?
In terms of an equilibrium, what can be said about homogenous equilibrium?
Why is equilibrium is a dynamic process?
Why is equilibrium is a dynamic process?
What happens to concentration of reactant and product as a chemical system approaches equilibrium?
What happens to concentration of reactant and product as a chemical system approaches equilibrium?
When concentrations concentration remains constant over time, a chemical system is in equilibrium.
When concentrations concentration remains constant over time, a chemical system is in equilibrium.
To determine the direction a reaction goes to reach equilibrium, the system will shift to ______ to reach equilibrium.
To determine the direction a reaction goes to reach equilibrium, the system will shift to ______ to reach equilibrium.
If Q > K, what occurs?
If Q > K, what occurs?
If a system is at equilibrium, what is $Q$ equal to?
If a system is at equilibrium, what is $Q$ equal to?
Which equation do you use to determine $K$ from $\Delta_rG^\Theta$?
Which equation do you use to determine $K$ from $\Delta_rG^\Theta$?
Since $G$ is a State Function so we can manipulate any number of reactions (like the First Law of Thermodynamics).
Since $G$ is a State Function so we can manipulate any number of reactions (like the First Law of Thermodynamics).
For a reaction to be spontaneous, the Gibbs "free energy" ($G$) is ______.
For a reaction to be spontaneous, the Gibbs "free energy" ($G$) is ______.
If $\Delta_rG^\Theta > 0$, what occurs?
If $\Delta_rG^\Theta > 0$, what occurs?
What is the name of the process extraction of copper from ores is?
What is the name of the process extraction of copper from ores is?
Is converting copper ore to its elements favored?
Is converting copper ore to its elements favored?
At any phase boundary, an ______ exists between two phases in the system: $\Delta G=0$.
At any phase boundary, an ______ exists between two phases in the system: $\Delta G=0$.
What is the equation to calculate the entropic change($\Delta S_{surr}$)?
What is the equation to calculate the entropic change($\Delta S_{surr}$)?
Flashcards
Gibbs Energy (G)
Gibbs Energy (G)
A thermodynamic function that determines the spontaneity of a reaction involving both entropy and enthalpy.
Endothermic Reaction
Endothermic Reaction
A reaction that absorbs heat from its surroundings; positive ΔH.
Entropy (S)
Entropy (S)
A measure of the number of possible arrangements of energy in a system; reactions happen spontaneously with an increase in this.
Spontaneous Process
Spontaneous Process
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Entropy and Phase
Entropy and Phase
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Spontaneity & Gibbs
Spontaneity & Gibbs
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Gases in Reactions
Gases in Reactions
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Gibbs at Minimum
Gibbs at Minimum
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Phase Equilibrium
Phase Equilibrium
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Standard Gibbs Energy
Standard Gibbs Energy
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Standard Gibbs Energy Change
Standard Gibbs Energy Change
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Equilibrium Constant Expression
Equilibrium Constant Expression
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Chemical Equillibrium
Chemical Equillibrium
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Homogenous Equilibrium
Homogenous Equilibrium
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Reaction Quotient (Q)
Reaction Quotient (Q)
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A,G, AG and Q
A,G, AG and Q
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Systems not at equilibrium
Systems not at equilibrium
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K=Q
K=Q
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Gibbs energy change for mixing
Gibbs energy change for mixing
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Study Notes
L18: Spontaneity & Gibbs Energy
- Gibbs energy, enthalpy, spontaneity, and temperature are key concepts to understand
- Gibbs energy changes are also important to calculate
- Spontaneity changes with temperature should be understood
Summary of Entropy Changes
- The entropy for an element standard state is not equal to zero
- The entropy of a gas > liquid > solid
- Entropy increases with molecular complexity
- Reactions involving gases allow predictable entropy changes, such as in the Haber reaction: N₂(g) + 3H₂(g) → 2NH₃(g), where ΔᵣS° < 0
- Forming a solution from a molecular solid result in an entropy increase, as ΔSsurr = qsurr/T = -ΔᵣH°/T
Spontaneity and Enthalpy
- Spontaneity isn't solely determined by enthalpy
- An endothermic reaction can be spontaneous
- Barium hydroxide reacts spontaneously: Ba(OH)₂·8H₂O(s) + 2 NH₄SCN(s) → Ba²⁺(aq) + 10 H₂O(l) + 2 SCN⁻(aq) + 2 NH₃(g)
- Entropy increases with spontaneity due to more ways to arrange products
Determining Spontaneity
- Spontaneity is determined by: ΔSuniverse = ΔSsys + ΔSsurr and ΔSsurr = qsurr/T = -ΔᵣH°/T
- Evaluating spontaneity requires system knowledge
- Gibbs energy (G) calculation provides a simple method
- Entropy and enthalpy effects are included in Gibbs Energy
Entropy and Enthalpy Relationship
- ΔSuniv = ΔSsys + ΔSsurr = ΔᵣS + qsurr/T = ΔᵣS - ΔᵣH/T
- Multiplying by -T: -TΔSuniv = ΔᵣH - TΔᵣS
- Gibbs energy (G) is defined as: -TΔSuniv = ΔᵣG, leading to: ΔᵣG = ΔᵣH - TΔᵣS
Gibbs Energy
- Gibbs "free energy" equation: G = H - TS
- Spontaneous reaction maximizes Suniverse and minimizes G in a system
- For a spontaneous reaction: ΔG < 0
Gibbs Energy as the Driving Force
- Gibbs energy drives chemical reactions as a combination of enthalpy and entropy
- For a spontaneous process: ΔG = ΔH - TΔS < 0
- Free energy is minimized
- ΔG < 0: The forward process is spontaneous
- ΔG > 0: The reverse process is spontaneous
- ΔG = 0: The system is at equilibrium
Minimizing Gibbs Energy
- Spontaneous exothermic reactions are dominated by enthalpy lowering, such as burning H₂ in the air
- Endothermic reaction with Ba(OH)₂ spontaneously proceed because reactants have low entropy(solids) and products have high entropy(liquids, dissolved ions, NH₃(g))
- Raising the entropy dominates ΔG, driving an enathalpically unfavored state to minimize overall ΔG
Gibbs Energy and Ice Melting
- Ice melts at 10°C but not at -10°C due to Gibbs energy
- H₂O(s) → H₂O(l) has a ΔH° = 6.01 kJ
| T (°C) | T (K) | ΔH° (kJ mol⁻¹) | ΔS° (J K⁻¹) | ΔG° (J mol⁻¹) |
|---|---|---|---|---|
| -10 | 263 | 6.03 | 22.1 | +220 |
| 0 | 273 | 6.03 | 22.1 | 0 |
| +10 | 283 | 6.03 | 22.1 | -220 |
- ΔG° = ΔH° - TΔS°
- Ice melts spontaneously at +10°C, but water freezes spontaneously at -10°C
Signs of ΔH & ΔS
- ΔG = ΔH - TΔS
- ΔG is negative only when the negative value of ΔH is larger than the negative value of TΔS
- H₂O(l) → H₂O(s) is exothermic with decreasing entropy, so is spontaneous at low temperatures (below 0 °C)
Free Energy: Example
- Equilibrium occurs when ΔG = 0
- For processes, where ΔH = +10 kJ and ΔS = -220 J K-1, solve for T in ΔG = ΔH - TΔS = 0 which is ΔG = 10000 J + 220 J K-1 x T = 0
- It cannot be zero at any temperature and process has a positive value always
Standard Gibbs Energy Change
- Similar to ΔH°, ΔG° (standard Gibbs Energy change) is the change under standard state conditions
- Standard Gibbs energies of formation (ΔfG°) are used
- For aA + bB → cC + dD
- ΔrG° = [cΔfG°(C) + dΔfG°(D)] - [aΔfG°(A) + bΔfG°(B)]
- ΔrG° = ΣΔGf°(products) - ΣΔGf°(reactants)
- It is exactly analogous to ΔfH° usage
Calculating Standard Gibbs Energy
- ΔG° = ΔH° - TΔS°
- ΔG° is not directly measured
- Determined by calculation from other measured quantities
- ΔH° measured by heat flow in a calorimeter
- S° determined from temperature dependence of heat capacity
Calculating ΔG°
– The reaction 2SO₂(g) + O₂(g) → 2SO₃(g) at 25 °C (298K) and 1 atm:
| Substance | ΔfH° (kJ mol⁻¹) | S° (J K⁻¹ mol⁻¹) |
|---|---|---|
| SO₂(g) | -297 | 248 |
| SO₃(g) | -396 | 257 |
| O₂(g) | 0 | 205 |
- Calculating ΔG° = ΔH° - TΔS°
- ΔᵣH° = 2 ΔfH° (SO₃) - 2 ΔfH° (SO₂) - ΔfH° (O₂) = -198 kJ
- ΔᵣS° = 2S°(SO₃) - 2S°(SO₂) - S°(O₂) = -187 J K⁻¹
- ΔᵣG° = ΔᵣH° - TΔᵣS° = -198,000 J - (298 K) (-187 J K⁻¹) = -142 kJ
Standard Gibbs Energy of Formation
- ΔfG°: Gibbs energy change to create 1 mol of a substance from constituent elements in their standard states
- Standard Gibbs energy formation units: kJ/mol
| Substance | ΔfH° (kJ mol⁻¹) | S° (J mol⁻¹ K⁻¹) | ΔfG° (kJ mol⁻¹) |
|---|---|---|---|
| NH₃(g) | -46.0 | 192.5 | -16.7 |
| NO₂(g) | +33.8 | 240.5 | +51.84 |
| O₂(g) | 0 | 205.0 | 0 |
| H₂O(l) | -285.9 | 69.96 | -237.2 |
- For an element in its standard state, ΔfG° = 0 (like ΔfH°)
Calculating ΔG° from Standard Gibbs Energies
- Consider: 2CH₃OH(g) + 3O₂(g) → 2CO₂(g) + 4H₂O(g)
| Compound | ΔfG° (kJ mol⁻¹) |
|---|---|
| CH₃OH(g) | -163 |
| O₂(g) | 0 |
| CO₂(g) | -394 |
| H₂O(g) | -229 |
- ΔG° = 2ΔfG° (CO₂(g)) + 4ΔfG° (H₂O(g)) - (2ΔfG° (CH₃OH(g)) - 3ΔfG° (O₂(g)) = -1378 kJ
Manipulating Reactions
- G is state function that be manipulated like Hess’s Law
- Example: C(diamond) → C(graphite) | Reaction | ΔG° (kJ mol⁻¹) | | ----------------------------- | --------------- | | C(diamond) + O₂(g) → CO₂(g) | -397 | | CO₂(g) → C(graphite) + O₂(g) | 394 | | C(diamond) → C(graphite) | -3 |
- Reaction is spontaneous but very slow
Ammonia Fusion Example
- Ammonia (NH₃) has an enthalpy of fusion (or melting) of 5.65 kJ/mol and an entropy of fusion of 28.9 J/K·mol. Determine the approximate melting point of ammonia
- Solve ΔG = ΔH - TΔS for when ΔG =0
- The answer is (A) 196 K
L19: Chemical Equilibrium
- Key aspects of chemical equilibrium involve writing equilibrium expressions, comparing and contrasting equilibrium constant magnitudes, and calculating reactant and product equilibrium concentrations
Describing Equilibrium
- Begins by dissociating to form NO₂(g) from N₂O₄(g) in a closed system where N₂O₄(g) begins to recombine to form N₂O₄(g)
- It is a dynamic process
Monitoring Equilibrium
- Monitor the appearance of brown NO₂ gas to show the concentration by observing
- Start with an initial [N₂O₄], and that species will decrease with time as the [NO₂] increases with time
- Equilibrium is reached when there is no net change
Homogenous Equilibrium
- Same equilibrium can be reached by starting with either N₂O₄ or with NO₂
- Reached when all species are in the same state
Equilibrium Constant
- To determine the expression of the equilibrium constant, K
- aA + bB ⇌ cC + dD
- K = ([C]^c[D]^d)/([A]^a[B]^b)
- Apply above for given reactants
Magnitude of Kc
- 2H₂(g) + O₂(g) ⇌ 2H₂O(g): K = [H₂O]² / [H₂]²[O₂] = 9.1 × 10⁸⁰ at 298 K
- N₂(g) + O₂(g) ⇌ 2NO(g): K = [NO]² / [N₂][O₂] = 4.8 × 10⁻³¹ at 298 K
- K >> 1: Products are favored
- K << 1: Reactants are favored
- K = 1: Equilibrium concentrations are comparable
Key Aspects of Chemical Equilibrium
- Key aspects of writing a balanced equilibrium reaction
- Calculating the equilibrium composition from equilibrium or initial concentrations
- Develop a quadratic formula to solve with ICE tables
- Manipulate equilibrium constants to find reaction stoichiometry
Equilibrium Constant (p)
- Express constant in gas-phase reactions that uses partial pressures: pV = nRT, and concentration = n / V
- For N₂O₄ ⇌ 2NO₂: K = (PNO₂/pΘ)² / (PN₂O₄/pΘ)
- pΘ: pressure in standard state usually specified at 10⁵ Pa.
Determining Non-Equilibrium
- Calculate at equilibrium
- Reaction quotient, Q must be introduced
- For: aA + bB ⇌ cC + dD, a reaction quotient is Q = ([C]ᶜ[D]ᵈ)/([A]ᵃ[B]ᵇ)
- When system not at equilibrium it helps describe the mass balance Compare the reaction quotient to with K
- Reaction moves forward if Q < K
- Reaction moves backward if Q > K
- System is at equilibrium when Q = K
Equilibrium Equations
- Calculate the change in the standard Gibbs energy when 1 mol of ice melts at 0 °C and 1.013 × 105 Pa.
- ΔfusH° = +6.01 kJ mol⁻¹
- ΔfusS° = +22 J mol⁻¹ K⁻¹
- ΔfusG° = ΔfusH° – TΔfusS°
- ΔfusG° = 6.01 kJ mol⁻¹ – (273.15 K × 22 × 10⁻³ kJ mol⁻¹ K⁻¹) = 0 kJ mol⁻¹
- At any phase boundary, an equilibrium exists between two phases in the system: ΔG = 0
Gibbs Energy Diagrams
- A minimum is present due to Gibbs energy, that ensures equilibrium in the reaction involving N₂O₄ and NO₂ systems
- ΔG is the determining factor is the reaction is observeable occuring to equilibrium
Gibbs Energies of Reactions
- Spontaneous occurance decreases in Gibbs diagram for chemical reactions
- The equations are:
- The key component is ΔmixG that gives rise to the minimum in Gibbs energy diagrams for chemical reactions
- Quantitatively between:
- ΔrG (change in gibbs energy)
- ΔrGΘ (standard change in gibbs energy)
- Q (reaction quotient)
The equation to show these is:
- ΔrG= ΔrGΘ+ RTInQ
Predicting Reactions
- The direction a reaction proceeds spontaneously in forward direction if it lowers the Gibbs energy if its: AG<0
Direction of Reaction
- Determine, mixture, predict the system shift: N₂(g) + 3H₂(g) ⇌ 2NH₃(g)
- ΔᵣGΘ = -33 kJ for which direction
- Q = (PNH₃/pΘ)²/ ((PN₂/pΘ)(PH₂/pΘ)³ which means if DG-33 kj/mol
- The system is at equilibrium
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