THERMODYNAMICS
Thermodynamics is used to answer the question “why does a change occur in the first place.” In other words, we can predict if a reaction will occur without prodding when reactants are combined under certain conditions.
A spontaneous process is one that occurs by itself under certain conditions, whereas a non-spontaneous process is one that must be forced to occur.
Spontaneous has nothing to do with being fast though, since metal rusting is technically spontaneous but can take a very long time to occur.
If a change is spontaneous in one direction, it is not spontaneous in the other. For example, water falls downhill, but never flows up.
The First law of thermodynamics states that energy can be changed in form but cannot be created or destroyed, or,that the internal energy (E) of a system changes through the addition or removal of heat and/or work:
E = q + w
This change is measure in enthalpy (H). But the first law just accounts for the energy involved and doesn’t really say anything about whether or not the process will occur on its own, and says nothing at all about the direction of the change.
You cannot tell whether a change will be spontaneous or not based simply on whether its exothermic or endothermic (based on the change in energy), like scientists once believed. Exothermicity favors the spontaneity of a reaction, but it doesn’t guarantee it.
Since we can’t use enthalpy changes alone to predict spontaneity, we turn to the second law of thermodynamics and entropy. Entropy is the measure of randomness or disorder in a system, and is denoted by the letter S.
Entopy describes the extent to which particles are distributed in a given space. The greater the disorder, the greater the entropy.
Entropy is a state function (depends only on the present state of the system and not how the system actually got there).
Ssys = Sinitial – Sfinal
Order and disorder are directly related to probablitity. Take for example a new deck of cards that you have just opened. All the cards are arranged in order. There is only one way to do this. However, once you shuffle the deck, the chances of getting all the cards back in order has become very slim. This is because there are more ways for the cards to be out of order than there are for the cards to be in order.
Another example is the presence of gas in a sectioned reaction vessel. It is possible to evacuate the vessel in such a way that all the moles of gas will be present in one section. However, if you don’t seal the section off, the gas will ease its way back into the section you have evacuated. This is because increased volume gives each particle an increased number of places that it can be, this then increases the number of ways the particles may be arranged.
As the number of molecules increases, the odds of all the gas being in the same flask becomes lower and lower, so your system becomes more and more disordered. Thus, entropy is increasing.
The number of ways of arranging the components of a system, whether they be the cards in our deck or the particles of gas, is directly related to its entropy. We call each individual possible arrangement a microstate, which isrepresented by W. The Boltzmann equation relates the entropy to the number of microstates in a system.
Boltzmann’s Equation:
S = klnW
k= Boltzmann’s constant (R/NA) =1.38x10-23 J/K
Keep in mind that the changes in the deck and flask occurred with no change in the internal energy of the system. In these cases, enthalpy would not have helped in determining the spontaneity.
-A system with relatively few ways to arrange its components (smaller W), such as solids or stacked cards, has a relatively low disorder and lowentropy.
-A system with many ways to arrange its componenets (larger W), such as a gas or scattered cards, has a relatively high disorder and high entropy.
All processes occur spontaneously in the direction that increases the entropy of the universe (system plus surroundings). This is known as the second law of thermodynamics.
Suniv = Ssys + Ssurr > 0
The sign on the entire process must be greater than 0, but there is no restriction as to whether or not the surroundings should gain or lose heat. A process can be endothermic or exothermic, but as long as the overall exchange between the system and the surroundings is greater than 0, the entropy of the universe has increased.
Third law of thermodynamics: a perfect crystal has zero entropy at a temperature of absolute zero (at 0 K, there is no chance of any movement). There is only 1 microstate here, so W=1, and S = kln(1) = 0.
Basically, the third law just says that everything will have some entropy as long as the temperature is above o Kelvin (and it will be).
Ways to predict relative entropy values for a system:
1. Temperature changes: entropy increases with increasing temperature. A rise in temperature will increase the random motion of the molecules.
2. Phase changes: solids have less entropy than liquids, which have less entropy than gases. Molecules are more ordered in the liquid state than the gaseous state because there are fewer positions for them to occupy (less microstates).
3. Dissolution of a solid or liquid: generally if a solid or liquid is dissolved in a solvent, the entropy increases. If you are going from a highly ordered crystal to an ion or even individual molecules dissolved in aliquid, you have increased the entropy. The same is true for a liquid.
4. Dissolution of a gas: generally if a gas is dissolved in a solvent, the entropy of the system decreases. Basically, you are restricting the number of places a gas can go, so you are increasing order and decreasing entropy.
5. Atomic size or molecular complexity: generally more complex compounds have a higher disorder, and larger atoms have a higher disorder.
6. If a reaction produces more gas molecules than it consumes, the entropy will increase.
Entropy values that are found in tables are referred to as Standard Molar Entropies and are in terms of J/mol*K. They are found at 1 atm and 25oC (298 K).
To calculate the change in entropy of a reaction:
Standard reaction entropy:
aA + bB cC + dD
Sorxn = (c)(SoC) + (d)(SoD)] – (a)(SoA) + (b)(SoB)]
Sorxn = mSoproducts – mSoreactants
Or, the overall entropy of a reaction will be equal to the sum of the entropy of the products multiplied by their stoichiometric coefficients minus the sum of the entropy of the reactants multiplied by their stoichiometric coefficients.
Decreases in the entropy of the system can occur only if increases in the entropy of the surroundings outweigh them. The role of the surroundings is either to add heat to the system or remove heat from it.
1. Exothermic change: heat lost by the system is gained by the surroundings.
qsys < 0, qsurr > 0 and Ssurr > 0
2. Endothermic change: heat gained by the system is lost by the surroundings.
qsys 0, qsurr 0 and Ssurr 0
The change in entropy of the surroundings is directly related to an opposite change in the heat of the system and inversely related to the temperature of the surroundings before the heat is transferred.
Ssurr = -qsys/T
OR
Ssurr = -Hsys/T
Basically, whatever heat is gained or lost from the system either comes from or goes to the surroundings, so the surroundings should have the opposite enthalpy change that the system had. The temperature is necessary, because it is nice to know what effect the temperature will have on the surroundings. If you’re adding heat to surroundings that are already hot, it probably won’t make much difference, but if you’re adding heat to surroundings that were initially cold, you’ll probably notice something there.
The entropy change of the forward reaction is equal in magnitude but opposite in sign to the entropy change of the reverse reaction. Thus, when a system reaches equilibrium, neither the forward nor the reverse reaction is spontaneous, and so neither process proceeds any further.
Suniv = Ssys + Ssurr = 0 at equilibrium
Ssys=-Ssurr
For an exothermic reaction, there are two possible ways to increase the entropy of the universe.
1.Hsys < 0, Ssys > 0
The system becomes more disordered, increasing the entropy of the universe.
2.Hsys < 0, Ssys < 0
The surroundings become more disordered, increasing the entropy of the universe.
For an endothermic reaction, there is one possible way to increase the entropy of the universe.
1.Hsys > 0, Ssys > 0
The entropy of the system must outweigh the fact that the surrounding are becoming more ordered as a result of losing heat.
To determine if a system is spontaneous using just Entropy, you need to determine both Ssys and Ssurr, but Ssurr is hard to find, so generally we turn to another term to determine spontaneity.
Gibbs Free energy (or free energy) – a function that combines the system’s enthalpy and entropy. The free energy change is a measure of the spontaneity of a process and of the useful energy available from it. Free energy is also a state function, and is denoted G.
Gibbs Equation:
Gsys = Hsys – TSsys
The sign of G tells us if a reaction is spontaneous:
G < 0 for a spontaneous process (proceeds in forward direction)
G > 0 for a nonspontaneous process (may proceed in the reverse direction)
G = 0 if a process is at equilibrium
If G in nonspontaneous in one direction (G is +), then it will be spontaneous in the opposite direction (G is -).
If you are not given the enthalpy and entropy changes for a system, you can determine Gorxn based on standard free energy values:
Gorxn = mGoproducts – mGoreactants
Gof refers to the standard free energy of formation, and is in terms of 1 mole of a compounds that has been synthesized from it’s elements. Again, we are at 1 atm and 25oC.
It is useful to remember that Go for an element is 0, and that the Go for the reverse process is just –Gofor the forward reaction.
For a spontaneous process, G is the maximum work obtainable from the system as the process takes place:
G = wmax
For a nonspontaneous process, G is the minimum work that must be done to the system to make the process take place.
A spontaneous reaction will occur and can do work on the surroundings.
A nonspontaneous reaction will not occur unless the surroundings do work on it.
A reaction at equilibrium cannot do work.
Effect of Temperature on Spontaneity:
The values for H and S will be set for a given reaction, so at 298, there is only the one possible G value. However, the temperature term in the Gibbs equation is not set. So, if we were to find that a reaction is nonspontaneous as written, we could always work to see if there is a temperature at which our reaction might become spontaneous.
Temperature independent cases:
1. Reaction is spontaneous at all temps
2. Reaction is non spontaneous at all temps.
Temperature dependent cases:
3.Reaction is spontaneous at higher temperatures.
4. Reaction is spontaneous at lower temperatures.
These are just wordy ways of expressing what is in the following chart.
To predict the sign of G without doing any math, you need to know both the sign of H and S. If you know these two things, you can follow the chart below.
Relationship of Reaction Spontaneity and Sign
Ho / So / -TSo / Go / Description- / + / - / - / Spontaneous at all T
+ / - / + / + / Nonspontaneous at all T
+ / + / - / + or - / Spont, at high T; non spont at low T
- / - / + / + or - / Spont at low T, non spont at high T
Basically, either both terms have to be negative or the negative term must be larger than the positive term for G to be less than zero. That is why there are two instances that are temperature dependent. Therefore, the temperature will determine the relative size of the TS term.
You can determine the temperature at which a process becomes spontaneous by setting G equal to o in the Gibbs equation. Anything above that temperature will make G negative, and will make the reaction spontaneous.
Ho = TSo and T = Ho/So
Coupling of reactions: breaking down a spontaneous multi-step reaction to it’s individual steps.
In a multi-step process, it is possible that not all the reactions will be spontaneous. However, they all occur because the one spontaneous reaction provides enough every to the others to make them occur.
G versus Concentration:
If the reactions are not at 1 atm and 25oC (as they often won’t be), we should use the following equation, which relates the standard free energy change to the actual free energy change.
G = Go + RTlnQ
Since the relationship between Go and Q is logarithmic, small changes in free energy values produce very large changes in Q. As Go becomes more positive, Q becomes much smaller.
Q is a measure of the concentration of the products to the concentration of the reactants. If we know all of these concentrations, we can find out what G is at concentrations other than 1 M.
Remember, partial pressures and concentrations are interchangeable in Q.