CHEM111 Module 8: Thermodynamics Part 2

what law of thermodynamics does TD2 focus on?

what is this law

• the second law

• the state of entropy of the universe (as an isolated system) will always increase over time

• changes in entropy of the universe can never be negative

• a system will become more disordered as time increases (spontaneously move to a state of more disorder)

• every energy transfer increases disorder of the universe

what is an iteration of the 2nd law referring to spontaneous processes vs processes at equilibrium

what criteria does this provide for spontaneity of a system

• total entropy of the universe increases in a spontaneous process, and remains unchanged in a process at equlibrium

  • ΔSuniverse > 0 (spontaneous process)

  • ΔSuniverse <0 (non spontaneous process)

  • ΔSuniverse = 0 (process at equilibrium)

• therefore, for a reaction to be spontaneous, it must increase entropy of the universe

what is the criteria for sponteneity of a reaction

• what function does it increase

• what function is not involved (but may seem like it is)

• for a reaction to be spontaneous, it must increase entropy (S) of the universe

  • ΔSsystem + ΔSsurroundings = ΔS universe > 0

• it is not involved with energy of a system, it does not require decreasing / releasing energy of the system (so no correlation for exothermic / endothermic reactions)

what makes up ΔSuniverse

• ΔSsystem + ΔSsurroundings

can a reaction be spontaneous if the system disorder decreases?

can a reaction be non spontaneous if the system disorder increases?

• yes and yes!

• sponteneity relates to ΔSuniverse, which is made up of ΔSsystem + ΔSsurroundings, so if the ΔSsurroundings outmatches it respecively, these scenarios can occur

what does entropy measure

how is entropy denoted

what do higher entropies mean, what do lower entropies mean

is it a state function

• entropy (S) measures the disorder of a system

• a higher entropy, means more disorder in the system

• an entropy above 0 denotes a spontaneous reaction, while below 0 denotes a non-spontaneous reaction

• yes it is a state function (ΔS only depends on final - initial)

how are standard entropies denoted

what does this mean

what units are they given in

• S^o₂₉₈

• molar entropy of a substance at 298K, and 1 bar (standard state)

• given in J K-1

how do standard entropies differ from standard ΔH values

• elements in stable forms =/= 0

• are absolute (provide a ‘zero’ value for the substance) rather than relative (ΔH relative to number of mols)

how are standard entropies found? (how are these absolute values found for substances?)

what law does this relate to

• this relates to the 3rd law, stating S=0 at 0K, for a perfect crystal (so at T approaching 0K absolute value, ΔS approaches absolute ‘zero’ value)

• a ‘perfect crystal’ refers to a solid with everything perfectly in position (no disorder), a perfect highly ordered 3D lattice, due to no movement at 0K

• this cannot be achieved realistically, but 0K can be approached, to find this absolute value

• from the absolute, we can relate standard conditions to it

  • entropy at 298K becomes the sum of 5 entropy changes (all the state changes from solid → gas)

  • solid heating → melting → liquid heating → boiling → heating to 298K (ΔS increasing all the way)

  • therefore providing the tabulated values for 298K

how do you find ΔS of phase changes?

• use tabulated data of standard S, and standard ΔH

• it becomes ΔS_{phase change} = ΔH_{phase change} / T_{phase change}

• holds for any phase change (vap, fusion, etc)

• use units of K and J (must convert ΔH to J, as S provided in J)

how do you find the ΔS of a system (of a reaction)?

• S is a state function, so only depends on final - initial

• therefore becomes, sum of (S products) - sum of (S reactants)

• use all products and reactants, ensure to multiply by stoichometry

• find S using the tabulated standard values

how were spontaneity and internal energy (U) for reactions, thought to have been related?

why is this not the case?

• they were thought to relate because many spontaneous processes were exothermic, and non-spontaneous endothermic, so it was thought that spontaneous = decrease U

• however, this isn’t true, as the 1st law states total energy of universe is conserved so any energy lost from a system must be gained by the surroundings

• but, the definitions of system / surroundings can be reversed, so a spontaneous proces that decreases U in one definition, would increase U with system/surrounding swapped, while still being spontaneous

provide examples of spontaneous processes where ΔU = 0

what does this tell us about spontaneous processes

• a gas in a sphere, expands into the empty sphere beside it

• a hot and cold block are put in contact, and the temperatures become equal

• ink is put into solution, and it diffuses (disperses) throughout it

these processes aren’t energy driven, as there is no energy change in the system, yet they are spontaneous

also, each process can occur in one direction only, towards disorder, therefore telling us the direction of spontaneous change is towards a more disordered state

how is spontenity linked to disorder

• the direction of spontaneous change, is towards a more disordered state

• this is an iteration of the 2nd law too, randomness is being moved towards in the universe

what are the qualitative aspects of a system that help to predict ΔS

state

• S(solid) < S(liquid) S(aqueous) < S(gas)

• S(solute) + S(solvent) < S(solution)

• therefore consider these when asked about phase change reactions

temperature

• S(cold object) < S(hot object)

amount

• S(fewer moles) < S(more moles)

what does the Boltzmann constant propose

• the more microstates (W) a system may have (number of different ways that molecules can arrange themselves in a system), the more disordered (higher S) the system is

• this makes sense, as the system will spontaneously arrange itself in all possible microstates, therefore having more disorder

what directly causes the S of the surroundings

what determines its magnitude

what equation does this provide

• the S_surroundings, is directly caused by the heat released / absorbed by a (closed) system

  • a system releasing heat, will increase disorder (S) in the surroundings, as molecules will move faster (more disorder)

  • a system absorbing heat, will decrease disorder (S) in the surroundings, as molecules will move slower (more order)

• the magnitude depends on the magnitude of the heat transfer, but also the T

  • at lower T, a given amount of heat results in a large ΔS, as this disrupts an ordered system

  • but at high T, this given heat would result in a lesser ΔS, as it is already disordered (less of a disruption)

• ΔS(surroundings) = -ΔH(system) / T

what is Gibbs energy

what is it denoted

what is its purpose

is it a state function

• Gibbs energy provides H and S, as a function of T

• this is useful, as it simplifies their relationship, and narrows the focus to spontaneity of a given process (a system) rather than having to look at H AND S AND Ssurroundings

• denoted G

• it is a state function (only determined by final - initial)

how does ΔG_system differ for

• spontaneous process

• non-spontaneous process

• process at equilibrium

is this the same or different as ΔS

• spontaneous process (ΔG < 0)

• non-spontaneous process (ΔG > 0)

• process at equilibrium (ΔG = 0)

NOTE - the opposite of ΔS!

what equation provides ΔG

what are the units of each component

what are the units for ΔG

• ΔG = ΔH - TΔS

• T (K), ΔH (kJ), ΔS (J)

• ΔG (J)

• therefore convert ΔH to J

how do you calculate ΔG of a system, when only given information about the products and reactants?

• use the tabulated standard ΔfG^o₂₉₈ (for formation at standard conditions), to find ΔG for each product & reactant

• this considers the formation of each product / reactant, simply their creation using its constituent elements, in most stable forms

• ΔfG for elements in their stable form already = 0

• also ensure to multiply by stoichometries

• then simply ΔG = sum of (ΔG products) - sum of (ΔG reactants)

therefore can simply show spontaneity of a reaction, only having to look at ΔG tabulated data, not both ΔS AND ΔH as before.

how is ΔG affected by temperature

• ΔG is made up of ΔH and ΔS, which both only minorly vary with temperature, so small ΔT can be ignored

• however, sufficiently changing T will change ΔG (and therefore change spontaneity), due to the sign contribution of T in the equation for ΔG

• however, certain combinations of signs for ΔH and ΔS for a reaction, mean that changing T will not change spontaneity

  • +ΔH & -ΔS → + at all T (never spontaneous)

  • +ΔH & +ΔS → + at low T, - at high T (changes)

  • -ΔH & +ΔS → - at all T (always spontaneous)

  • -ΔH & -ΔS → + at high T, - at low T (changes)

• so if both the system & surroundings are spontaneous, it stays spontaneous

• and if both are non spontaneous, it remains non spontaneous

how does G change for products & reactants throughout a chemical reaction

how does this relate to equilibrium

how does this relate to the 2nd law

• G changes for products/reactants throughout a reaction, as they move to more stable states

  • so G(Reactant) decreases as the forwards reaction proceeds (to G=0)

  • G will then rise to G(products) as the reaction proceeds further (to produce the product)

• this minima (G=0) point, is equilibrium

• the reaction will remain here (in a state of chemical equilibrium), as the second law forbids G increasing without input (this would increase order)

• no net production of product and reactants results in ΔG=0

what formula is used to find variation of G with reaction extent, or ΔG for any reaction at any tempearture

what information is required

ΔG = ΔG^o+RTlogeQ

• use standard G values for products and reactants, and sum and minus them to find ΔrG

• use gas constant (make sure units are consistent)

• use given T

• use Q (activities of products / reactants), all reactants = 0, all products = infinity, at equilibrium Q=K

  • this provides ΔG for any reaction at any temperature, at any extent

how can K (equilibrium constant) be used to find ΔG (and vice versa)

and why?

• ΔrG^o = -RTlogeK

• this is gained from the previous formula relating ΔG and Q

• ensure units are consistent (for both ΔG & R)

• can rearrange to find K from ΔrG

does catalyst change K or ΔG

No!

• K depends on ΔG

• ΔG is a state function so only depends on final-initial, not the pathway, therefore alternate pathway of catalyst does not change it!

does K (equilibrium constant) vary with T?

how does the relationship between ΔG and K, and the Vant Hoff equation, provide the answer?

what principle does this then lead to

• Yes! K does vary with T, because to find K from ΔG and vice versa, T must be input

• as T increases, 1/T gets smaller, so K is pushed to a higher value (more products, Q must increase)

• as T decreases, 1/T gets larger, so K is pushed to a lower value (more reactants, Q must decrease)

• this supports Le Chatilier’s principle! Equilibrium shifts with T to the endo/exo relationship, depending on direction of T change

how can ΔrS and ΔrH provide K (equilibrium constant)

what is the proper name for these equations

• ΔS & ΔH can be used to find ΔG, which can be used to find K, along with R and the given T

• this relationship can be substituted in to form a new equation

logeK = -ΔH / RT + ΔS / R

• this is due to ΔS and ΔH’s little variance with T

• these are known as the Vant Hoff equations

what is the Vant Hoff equation

what relationship does this describe

how is this described in terms of graphed data

logeK = -ΔH / RT + ΔS / T

• this shows that when we plot variation of K with T (lnK on Y, 1/T on X), a linear relationship will be obtained

  • the intercept will = ΔS / R

  • the slope will = -ΔH / R

  • the linear will be positive for exothermic reactions (ΔH<0)

  • and negative for endothermic reqactions (ΔH)

• this is because this equation has the form of the equation of a straight line (y = intercept+slope)