Chem I Lesson 12 - Thermodynamics, Entropy, Gibbs Free Energy, and Le Chatlier's Principle
If Keq < 1 then ΔG°...?
If Keq < 1 then ΔG°> 0
If Keq = 1 then ΔG° ..... ?
If Keq = 1 then ΔG° = 0
ΔG = 0
System is in equilibrium ΔH = TΔS
True or False: ΔG for phase change equilibria is zero
True
What are two notable exceptions to Le Chatelier's Principle?
*Le Chatelier's Principle does not always predict the correct shift! Notable exceptions are: 1) solvation reactions. Ex: solubility of a salt generally increases with increasing temperature, even when a reaction is exothermic, largely due to the significant increase in entropy that occurs with dissolution 2) increased pressure due to the addition of a nonreactive gas
What are the two natural tendencies behind spontaneity?
1. Tendency for a system to achieve a lower energy state (Enthalpy ΔH <0) 2. Tendency for a system's energy to become dispersed among a larger number of energy levels (Entropy ΔS >0)
If equilibrium constant for a reaction written in one direction is Keq, the equilibrium constant for the reverse reaction is _________ ?
1/Keq
Common Bond Dissociation Energies: C-C: 348 kJ/mol C-H: 415 kJ/mol C=O: 805 kJ/mol O-H: 463 kJ/mol C-O: 360 kJ/mol Methanol reacts with acetic acid to form methyl acetate and water. Based on the values, what is the heat of reaction in kJ/mol? A) 0 B) 464 C) 824 D) 1288
A) 0
Nitric acid is produced commercially by oxidation in the Oswald Process. The first step is: 4NH3(g) + 5O2(g) ⇌ 4NO(g) + 6H202(g) A container holds 4 moles of gaseous ammonia, 5 moles of gaseous oxygen, 4 moles of gaseous nitric oxide, and 6 moles of water vapor at equilibrium. Which of the following would be true if the container were allowed to expand at constant temperature? A) Initially during the expansion the forward reaction rate would be greater than the reverse reaction rate B) The equilibrium would shift to the left C) The partial pressure of oxygen would increase D) The pressure inside the container would increase
A) Initially during the expansion the forward reaction rate would be greater than the reverse reaction rate Expansion of the container increases the volume and decreases the pressure - eliminate D. By Le Chatelier's principle, a decrease in pressure shifts the reaction to the side with more moles of gas. Here, the equilibrium will shift to the right (more moles on right side) by increasing the forward reaction rate.
Sulfur dioxide reacts with oxygen in a reversible reaction to form sulfur trioxide as shown: 2SO2(g) + O2(g) ⇌ 2SO3(g) ΔH°= -200 kJ/mole If the temperature at which the reaction takes place is increased, which of the following will take place? A) The rates of both the forward and reverse reactions will increase B) Only the rate of the forward reaction will increase C) Only the rate of the reverse reaction will increase D) The rates of neither the forward nor reverse reaction will increase
A) The rates of both the forward and reverse reactions will increase Increasing temperature increases the energy available to both forward and reverse reactions, enabling both to more easily overcome activation energy. CAVEAT: The rate of the reverse reaction will increase more than the rate of the forward reaction because the reaction is exothermic, making heat a product. Based on Le Chatelier's law, an increase in temperature (heat) will cause a leftward shift by increasing the reverse rate of reaction more than the forward rate
What is the third law of thermodynamics?
Any pure element/compound in its solid form at absolute zero and in internal equilibrium has an entropy of ZERO
At equilibrium the rate of the forward reaction ________ the rate of the reverse reaction, entropy is at is __________, and Gibbs Free Energy is at its _________
At equilibrium the rate of the forward reaction EQUALS the rate of the reverse reaction, entropy is at is MAXIMUM, and Gibbs Free Energy is at its MINIMUM
Which of the following statements is true of a process that is spontaneous in the forward direction: A) ΔG > 0 and Keq > Q B) ΔG > 0 and Keq < Q C) ΔG < 0 and Keq > Q D) ΔG < 0 and Keq < Q
C) ΔG < 0 and Keq > Q
The standard enthalpy formation for liquid water is: H2(g) +1/2O2(g) --> H20(l) ΔH°f = -285.8 kJ/mole Which of the following could be the standard enthalpy of formation for water vapor? A) -480.7 kJ/mole B) -285.8 kJ/mole C) -241.8 kJ/mole D) +224.6 kJ/mole
C)-241.8 kJ/mole The standard enthalpy of formation for water vapor is H2(g) +1/2O2(g) --> H20(g) The formation of a gas requires MORE HEAT than the formation of a liquid, therefore ΔH must be greater than -285.9 kJ/mole, eliminating choice A and B. -285.9 kJ/mole represents the energy released from the formation of covalent bonds, which are intramolecular forces. The difference between liquid water and water vapor is a phase change, which is achieved by breaking intermolecular forces. Intermolecular forces are weaker than intramolecular forces - therefore the amount of additional energy added to -285.9 kJ/mole would no exceed 285.9 kJ/mole, eliminating choice D (?) Eliminate A, B, and D to get C
What is change in Gibbs Free Energy? Give Equation
Change in Gibbs Free Energy is a measure of the change in the enthalpy and the change in entropy as a system undergoes a process, and it indicates whether a reaction is spontaneous or not ΔG = maximum amount of energy released by a process - occurring at constant temperature and pressure - that is available to perform useful non-PV work ΔG = ΔH + TΔS *ΔS = Entropy change of SYSTEM *ΔH= Measure of heat flow into or out of system *TΔS = total amount of energy that's absorbed by a system when its entropy increases reversibly
Pure sodium metal spontaneously combusts upon contact with room temperature water. What is true about the equilibrium constant of this combustion reaction at 25°C? A) Keq < 0 B) 0 < Keq < 1 C) Keq = 1 D) Keq > 1
D) Keq > 1
The condensation of water: H20(g) ---> H20(l) Which of the following will be positive for the condensation of water at 25°C and 1 atm? A) ΔH B) ΔS C) ΔG D) None of the above
D) None of the above Bonds are formed when water condenses, so energy is released and ΔH is negative The water molecules become less random going from gas to liquid phase, so ΔS is negative Condensation occurs spontaneously at 25°C (room temperature), so ΔG is spontaneous
For a particular reversible reaction, the forward process is exothermic and the reverse process is endothermic. Which of the following statements must be true about this reaction? A) The forward reaction will be spontaneous under standard conditions B) The reverse reaction will be spontaneous under standard conditions C) The activation energy will be greater for the forward reaction than for the reverse D) The activation energy will be greater for the reverse reaction than for the forward reaction
D) The activation energy will be greater for the reverse reaction than for the forward reaction Activation energy is greater for an endothermic reaction than for an exothermic reaction
What is the second law of Thermodynamics?
Energy spontaneously disperses from being localized to becoming spread out if it is not hindered from doing so. The entropy of an isolated system will never decrease Simply: entropy always increases
Which determines spontaneity - Enthalpy or Entropy?
Entropy
Describe entropy in terms of disorder and dispersal
Entropy increases as a system has more disorder or freedom of movement, and energy is dispersed in a spontaneous system. Entropy of the universe can never be decreased spontaneously
Define entropy conceptually
Entropy is a measure of how energy is spread out among the atoms and molecules of a system. *Energy spread out over a greater number of available energy levels means an increase in entropy Ex: boiling is associated with an increase in entropy because liquid becomes disordered gas Ex: freezing is associated with a decrease in entropy because liquid becomes well ordered solid
Is entropy an extensive or intensive property?
Extensive. As the amount of substance increases, entropy increases
True or False: Among molecules in the same phase, the larger molecule (with more bonds) has a lower entropy at a given temperature
False Among molecules in the same phase, the larger molecule (with more bonds) has a HIGHER entropy at a given temperature
True or False: Exothermic reactions (ΔH<0) are always spontaneous and endothermic reactions (ΔH>0) are always nonspontaneous
False. Exothermic reactions are not necessarily spontaneous and endothermic reactions are not necessarily nonspontaneous. Enthalpy is not a sufficient criteria for predicting spontaneous change
True or False: Rate of reaction depends on ΔG
False. Rate of reaction depends on Ea, activation energy
True of False: A spontaneous process is one that occurs in a system left to itself and happens quickly
False. Spontaneity signifies nothing about how fast a process occurs Thermodynamics can tell us if a process is spontaneous but only CHEMICAL KINETICS can tel us how fast the process will occur
True or False: The entropy of a system will always increase in a spontaneous reaction
False. The entropy of the UNIVERSE will always increase in a spontaneous reaction
What is Gibbs Free Energy, conceptually
Gibbs Free Energy is a thermodynamic state function/different criterion for spontaneous change that is based only on the system, without regard to surroundings! (Unlike entropy)
ΔG°rxn = -RTln(Keq) Explain what happens in this equation when Keq is large, aka the equilibrium position is farther to the right
Greater Keq = more positive value of its natural logarithm = more negative the ΔG°rxn = the more spontaneous the reaction
Q < Keq What is happening with the reaction? What is ΔG?
Greater conc. of reactants/smaller conc. of products than at equilibrium Reaction will be forward/go right to increase products to get to equilibrium ΔG < 0
Q > Keq What is happening with the reaction? What is ΔG?
Greater concentration of products/smaller concentration of reactants than at equilibrium. Reaction will shift left/go reverse to increase reactants and restore equilibrium ΔG > 0
What are the only two ways to change the energy of a system?
Heat and Work
Explain how heat is connected to disorder
Heat is the transfer of random kinetic energy and this random kinetic energy increases the disorder of an environment Heat transferred from system to surroundings via an exothermic reaction increases entropy of surroundings Heat transferred from surroundings to system via an endothermic reaction decreases entropy of surroundings
If Keq > 1 then ΔG°...? What other variable does spontaneity depend on?
If Keq > 1 then ΔG° < 0 *This relationship does NOT say that a reaction is always spontaneous if it has an equilibrium constant > 1. K and ΔG° depend on TEMPERATURE. This relationship says that if a reaction has Keq > 1, the reaction is spontaneous at the temperature used to derive that particular equilibrium constant and standard state
If ΔH <0, the products are more _________ than the reactants
If ΔH <0, the products are more STABLE than the reactants
What is the expression for equilibrium constant for: 3H2(g) + N2(g) ⇌ 2NH3(g)
Keq = [NH3]^2 / [N2][H2]^3
-ΔS and +ΔH
Non spontaneous
Practice Question: ΔG Predict ΔG sign: Cl2(g) --> 2Cl(g)
One mole produces two moles so ΔS > 0. Bonds are broken, which requires energy be absorbed, but no bonds are formed, so reaction is endothermic and ΔH > 0. This reaction will only be spontaneous at high temperatures!
When does Keq change for a given reaction?
Only when temperature changes
How can entropy help explain Rauolt's Law?
Raoult's law is a law of thermodynamics that states that the partial pressure of each component of an ideal mixture of liquids is equal to the vapor pressure of the pure component multiplied by its mole fraction in the mixture Psolv = Xsolv⋅P°solv Psolv = vapor pressure of solvent Xsolv = mole fraction of solvent in solution P°solv = vapor pressure of pure solvent A solution has a higher entropy than the pure solvent, so the vapor from the solution must have a high entropy than the vapor from the pure solvent. Entropy of a vapor pressure increases as its molecules expand into a larger volume, aka they're at lower pressure. Thus, solutes in a solution reduce the vapor pressure of the solvent
Q = Keq What is happening with the reaction? What is ΔG?
Reactants and products are present in equilibrium proportions Reaction rates of forward and reverse reaction are equal. Reaction is in dynamic equilibrium ΔG = 0
Keq is for when a reaction is in equilibrium. What equation can we use for when a reaction is not at equilibrium to assess where the reaction currently is in relation to equilibrium? Name the variable
Reaction Quotient, Q Q = [C]^c[D]^d / [B]^b[A]^a
+ΔS and -ΔH
Spontaneous
+ΔS and +ΔH
Spontaneous at high temperatures
-ΔS and -ΔH
Spontaneous at low temperatures
What are standard state conditions? What is STP?
Standard state conditions (thermodynamics): 298K (25°C), 1 atom, 1M conc. of all compounds STP (ideal gas law): 273 K (0°C), 1atm, and 1 mol of ideal gas occupies 22.4 L
Le Chatlier's Principle What are the three different types of stress that usually obey this principle?
States that if a stress is applied to a system at equilibrium, the system shifts in the direction that relieves the stress. Three types of stress that usually obey Le Chatlier's Principle: 1. addition or removal of a product or reactant 2. changing the pressure or volume of system 3. heating or cooling the system
Practice: Find Keq and ΔG°rxn Determine Keq at 25°C for: 2NO2(g) ⇌ N2O4(g) ΔG°f for N2O4(g) = 97.82 kJ/mole ΔG°f for NO2(g) = 51.30 kJ/mole
Step 1: Find ΔG°rxn ΔG°rxn = (1 mole N2O4 x 97.82 kJ/mole) - (2 mole NO2 x 51.30 kJ/mole) = -4.78 kJ Step 2: Find Keq ln(Keq) = -ΔG°rxn / RT ln(keq) = -(-4780 J /mole) / (8.3145 J/mol⋅K)(298K) = 1.93 *note units of ΔG°rxn change from kJ to J/mole Keq = e^1.93 = 6.9 *makes sense because since ΔG°rxn was negative, Keq must be > 1.
The __________ the Keq value, the farther to the __________ the equilibrium position
The LARGER the Keq value, the farther to the RIGHT the equilibrium position
What is the standard entropy of reaction (ΔS° or ΔS°rxn). Give equation
The entropy change for a reaction in which the reactants in their standard state yields products in their standard states.
Give equation for Keq, equilibrium constant
The law of mass action for aA + bB ---> cC + dD states that if the system is at equilibrium, then there is the following constant ration: Keq = [C]^c[D]^d / [B]^b[A]^a *Keq is unitless *Pure liquids/pure solids are given a coefficient of 1 for the equilibriums expression and don't not contribute to Keq *Solvents are considered ideally dilute for MCAT
Bioenergetics
The study of how energy flows through living organisms. Used to describe energy state in biological systems
What is the utility of the Reaction Quotient, Q
The utility of Q is not the value itself, but the COMPARISON that can be made at any given moment in the reaction to the known Keq for the reaction at a particular temperature We can use Q to predict the direction in which reaction will proceed
Compare thermodynamics vs. chemical kinetics
Thermodynamics determines the equilibrium state of a system, can predict proportions of products/reactants present at equilibrium/determine spontaneity and if a forward reaction will go to completion Chemical kinetics determines the pathway by which equilibrium will be reached,
What does Trouton's rule say? Give equation
Trouton's rule says that the entropy of vaporization is almost the same value, between 85-88 J/mol⋅K, for various kinds of liquids. ΔS°vapn = ΔHvapn/Tbp ≈ 85-88 J/mol⋅K Trouton's rule implies that the evaporation of one mole of liquid at the normal bp is accompanied by about the same increase in the number of accessible energy levels (a marker of entropy) from one liquid to another.
When does Trouton's rule work best and when does it not?
Trouton's rule works best for non polar/organic substances and generally fails for liquids with excessive hydrogen bonding, which leads to lower entropy than would otherwise be expected in the liquid state and a greater than expected entropy of vaporization, ΔS°vapn > 87 J/mol⋅K Ex: For vaporization of H2O at 100°C, ΔS°vapn = 109 J/mol⋅K
True or False: A reaction can proceed even if it is unfavorable in terms of enthalpy or energy, but a reaction must increase the entropy of the universe (but not necessarily the system) in order to proceed
True
True or False: Equilibrium is the point of maximum universal entropy for that reaction
True
True or False: If a process is spontaneous, the reverse process is non sponstaneous and vice versa
True
True or False: You need to take both ΔG and activation energy into account to determine whether a reaction will proceed
True
True or False: For any substance, sublimation will be the phase transition with greatest entropy What will be the phase change with least entropy?
True Deposition
True or False: The more atoms in its molecules, the greater the entropy of the substance
True. More atoms = more vibrational modes of moving with respect to one another = more ways the molecule can absorb energy = more energy levels available to disperse energy = GREATER ENTROPY
Why can heat be used as a measure of internal energy in living systems?
Volume and Pressure are constant in cellular environments, which eliminates work from our calculations of internal energy, and the only quantity of interest in determining internal energy, ΔU, is heat, Q If ΔU=Q-W and W=0, then ΔU=Q
When, and only when, can entropy be used as the sole criterion for spontaneous change?
We can use entropy as the sole criterion of spontaneous change only if we consider entropy change of a system AND its surroundings. This is total entropy change of universe: ΔStotal = ΔSuniverse = ΔSsystem +ΔSsurroundings For any spontaneous process, ΔSuniverse > 0
Why is there an entropy increases associated with a substance being heated when the spatial distribution of the gas molecules is no more random than at a lower temperature?
When a fixed quantity of gas is heated in a closed volume, the spatial distribution of the gas molecules is no more random than at a lower temperature. BUT - along with the increased energy in the heated gas comes a very large increase in the NUMBER OF ENERGY LEVELS among which the energy is dispersed - this increases entropy! This is why the idea of entropy as increased disorder/randomness is not sufficient!
When energy is distributed into a system at a given temperature, its entropy ____________. When energy is distributed out of a system at a given temperature, its entropy______________.
When energy is distributed into a system at a given temperature, its entropy INCREASES. When energy is distributed out of a system at a given temperature, its entropy DECREASES.
When is enthalpy equal to heat?
When pressure is constant. (So any reaction going on under atmospheric pressure). This is why heat and enthalpy are often thought of as interchangeable
Why does water boil at 100°C and not 20°C?
When water boils, hydrogen bonds are broken and water molecules gain sufficient energy to escape into the gas phase. Thus, boiling is an endothermic process and ΔH is positive. As thermal energy is transferred to the water molecules, energy is distributed through the molecules entering the gas phase. Thus, entropy is positive and the term TΔS is positive If both ΔH and TΔS are positive, the reaction will only be spontaneous when TΔS > ΔH to give a negative ΔG. This can only occur when the temperature is high - in this case 100°C This is an example of spontaneity only occurring when temperature is high if ΔH and ΔS are both positive
Practice Question: Find Keq Find Keq for th vaporization of water at 25°C: H2O(l) ⇌ H20(g) ΔG°rxn = +8.590 kJ ΔG°rxn becomes J/mole!
ln(Keq) = -ΔG°rxn / RT ln(Keq) = -8590 kJ/mole / (8.3145 J/mol⋅K)(298K) ln(Keq) = -3.465 (units all cancel) Keq = e^-3.465 = 0.0313 *Keq = PH20(g) (pressure) = tells us that the equilibrium vapor pressure of water at 25°C is 0.313atm
+ΔG
non spontaneous / Exergonic *this is not the same as exothermic which is used when discussing ΔH
-ΔG
spontaneous / Endergonic *this is not the same as endothermic which is used when discussing ΔH
What equation can we use to determine Gibbs Free Energy when a reaction IS at equilibrium? ** One of the most important equations in chemical thermodynamics
ΔG = 0 at equilibrium Q = Keq at equilibrium 0 = ΔG°rxn + RTln(Keq) ** ΔG°rxn = -RTln(Keq) ** Can also be arranged to: ***ln(Keq) = -ΔG°rxn / RT*** This equation says that if we have for a reaction at a given temperature, ew can calculate the equilibrium constant at that temperature *Notice Keq must be unit-less to take the log
If a catalyst reduces Ea significantly, what happens to ΔG?
ΔG stays the same!
What is another way to write the equation: ΔGrxn = ΔG°rxn + RTln(Q) Explain
ΔGrxn = RTln(Q/Keq) *If ratio of Q/Keq < 1 (meaning Q<Keq), then natural log. will be negative = ΔGrxn will be negative = reaction will spontaneously move forward *If ratio of Q/Keq > 1 (meaning Q>Keq), then natural log. will be positive = ΔGrxn will be positive = reaction will be spontaneously move in reverse direction *If ratio of Q/Keq = 1, reaction is at equilibrium --> ln(1) = 0 so ΔGrxn = 0
What equation can we use for Gibbs Free Energy to make predictions about reactions that do NOT occur under standard state conditions? Hint: 2 different equations
ΔGrxn = ΔG°rxn + RTln(Q) ΔGrxn = change in Gibbs Free Energy ΔG°rxn = change in standard state Gibbs Free Energy R = ideal gas constant = 8.3145 J/mol⋅K T = temperature in K Q = reaction quotient *Use of Q indicates reaction is not at equilibrium because at equilibrium, ΔG = 0 ΔGrxn = ΔG°rxn+ 2303⋅RTlogQ
What does ΔG°' adjust for that is not considered with ΔG° ? What is modified standard state for biological system?
ΔG°' adjusts only for the pH of the environment by fixing it at 7. Temp and conc. of all other reagents are still fixed at their values from standard conditions and must be adjusted for if they are not 1 M. Modified standard state is [H+] = 10^-7M or pH = 7
Give equation for ΔG°rxn and explain
ΔG°rxn is the free energy change when reactants and products are in their standard state conditions
2O3 ---> 3O2 ΔH = -285kJ What can we say about enthalpy and entropy of this reaction?
ΔH is exothermic, favoring reaction to the right ΔS increases, favoring reaction to the right **ΔS increases because the system of 6 Oxygen atoms arranged as 3O2 a molecules has MORE available energy levels among which a system's energy can be dispersed than does the system of 6 Oxygen atoms arranged in 2 O3 molecules
Describe the relationship between ΔS and Kelvin temp, T, in the equation for entropy
ΔS =Qrev/T The inverse relationship between ΔS and T reflects the fact that the proportional increase with temperature in the number of energy levels in a system is greater at lower temps than at higher temps Aka, a given a quantity of heat absorbed by a solid initially at a low temperature increases the number of available energy levels proportionally more than does the same quantity of heat when absorbed by a gas initially at a high temperature.
Give entropy equation
ΔS =Qrev/T ΔS = entropy (J/mol⋅K) --> units of entropy imply a distribution of energy in a system Qrev = heat that is gained/lost in a reversible reaction. Must be a reversible reaction because q is different for an irreversible process because heat is pathway dependent T = temperature in K
Give formula definition of second law of thermodynamics. Explain what this means.
ΔSsystem + ΔSsurroundings = ΔSuniverse > 0 For any process, change in entropy of system + change in entropy of surroundings = change in entropy of universe, which must always be increasing (must always be positive/greater than zero) Entropy of universe is always increasing
