Affinity 101 - Are energy and/or entropy with us?
CC Attribution 3.0 Germany:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
Lauth, Jakob Günter (SciFox)
PhysChemBasics#4: Affinity 101 The 1st and 2nd law are statements about energy and entropy in the universe. We can measure the change in energy and entropy during a process and are also able to calculate these quantities using thermodynamic tables. We may combine energy and entropy using the Gibbs Helmholtz equation and arrive at Gibbs Free Energy which is a measure of instability. It tells us whether or not a process will run spontaneously.
 Some processes do run spontaneously. So they have an affinity, a driving thermodynamic force. Others don't. Today we will see how we can use the first and the second law to calculate the affinity of a process in advance. Hello and welcome to Fiskem Basics, our topic today. The driving force of a process or the affinity. We will see that affinity has two components, energy and entropy. So in a way we may ask, are energy and or entropy with us? Let's take the oxyhydrogen reaction and the auto-protolysis of water as examples. The formation and the self ionization of water into H plus and OH minus ions. Do these processes have a driving force? What about energy and entropy? An important quantity in thermodynamics is internal energy, which comprises all energy in a system. Where is, for example, the internal energy of water located? Well, the water molecules are not at rest. They have kinetic energy, rotational energy, vibrational energy. There are also energies between different molecules and very importantly chemical binding energies between the atoms. All of these energies are part of the internal energy. Although we can't measure absolute values of internal energy, it only because there is no natural zero, but we can measure its change. Whenever we add or remove energy from a system, the internal energy changes. These inputs and outputs of energy to or from a system can take place as heat, q, or as work, w. So if we are to calculate delta u for, say, the oxy hydrogen reaction, we simply have to add up all the heat and work values of this reaction. As you may remember, heat and work are path-fansitive. So you have to select one path to calculate your change in internal energy. We go for the reversible path, so we have to sum up the three numbers and the result is negative 564 GJ for delta u. Calculating delta u is particularly easy if the work is zero. And this is the case if the volume remains constant in a spontaneous process. Constant volume means no pressure volume work. The heat, q sub v, released in an isochoric spontaneous process, is identical to the change in internal energy delta u. However, we don't deal very often with isochoric processes. Isobaric processes are much more common. In these processes, we have to take into account pressure volume work. Negative p times delta v. This means that the isobaric heat, q sub p, plus pressure volume work is equal to delta u. We can solve this equation for q sub p and then get delta u plus p times delta v. Because we very often measure isobaric heat, the combination u plus p times v was simply renamed enthalpy. Thus, enthalpy is an artificial quantity and has no clear meaning. But the change in enthalpy is always the same as a spontaneous isobaric heat. We measure the isobaric heat of negative 572 KJ in the oxyhydrogen gas reaction. This also corresponds to the enthalpy of this reaction. With this in mind, you may create the thermodynamic profile of enthalpy. Enthalpy H is the measure of the energy content of a system. It's useful with application of the first law. The change in enthalpy can simply be measured using an isobaric heat, q sub p. Whenever isobaric heat occurs, we change enthalpy. So enthalpy clearly depends on temperature, on the phase and on chemical structure. There is no natural zero of enthalpy, but all elements at 25 degrees Celsius were arbitrarily defined to have zero enthalpy. If you look up enthalpies in thermodynamic tables, we'll find negative values for most of the chemical compounds. That means these compounds are lower in energy, or rather in enthalpy than the elements. The entropy changes whenever isobaric heat is added or removed. For example, when there is a change in temperature, a phase change or a chemical reaction. If on the other hand we mix just two ideal systems like hydrogen and oxygen gas, no heat is released or absorbed with ideal systems, there is no enthalpy of mixing. If we melt one mole of solid ice at 0 degrees centigrade to one mole of liquid water at 0 degrees centigrade, we need 6 kilojoules. If we evaporate the liquid water at 0 degrees centigrade, we need another 45 kilojoules. So if we were to evaporate the solid ice right away, there would be some of these two heat amounts, that is 51 kilojoules. This is a statement of Hess's law. The reaction enthalpies are path-independent. In mathematicians terms, enthalpy is a quantity whose values are independent of path, and it was called a state function, and its differential is exact. Work on heat are quantities that depend on the path followed between states. They are called path functions, and their differentials are inexact. Let's draw an enthalpy diagram of water and the elements it is composed of. The elements H2 and O2 mark the Vero level. The atoms H and O mark a significantly higher energy level, and water is relatively low in energy. The blue arrows are so-called enthalpies of formation. The blue arrow down is the enthalpy of formation of water. The arrow up symbolizes the enthalpy of formation of the atoms. According to Hess's law, we can handle these arrows like we can add or subtract vectors. The red arrow here is the atomization enthalpy of water, the heat that we need to completely split water molecules into atoms. This heat corresponds to 1850 kilojoules. Conversely, 1850 kilojoules would be released if two water molecules were formed from the atoms. This means the green arrow corresponds to 4 times the OH bond enthalpy. Bond enthalpies are usually average values. Therefore, the statement that the sum of the bond enthalpies corresponds to the enthalpy of atomization is only approximate. With enthalpies of formation, which are tabulated in many chemistry textbooks, we can do a lot of useful thermochemical calculations. For example, if you want to know how much heat is released or consumed when water is split into H plus and OH minus, we draw an enthalpy diagram. The standard enthalpy of formation of any element in its most stable form is zero. At lower enthalpies, we find the reactant water and the enthalpy of the products H plus and OH minus is located between the aforementioned levels. The two blue arrows represent the enthalpy of formation. These arrows always start at zero level. The red arrow is the enthalpy of reaction. It starts at the reactant and ends at the product. We have to treat this diagram like a vector diagram. The enthalpy of reaction, the red arrow, is equal to the enthalpy of formation of the products, the short blue arrow, minus the enthalpy of the formation of the reactant, the long blue arrow. We end up with an enthalpy of reaction of plus 56 kJ. This means that the auto-protolysis of water is endothermic. We would have to invest 56 kJ of heat to dissociate one mole of water completely into one mole of H plus and one mole of OH minus. So energy is obviously not with us. Now let's look at entropy. Remember the thermodynamic profile of this quantity. Anthropy is a measure of disorder. It makes sense to introduce this quantity because the second log can easily be formulated with it. We can measure the entropy changes according to cloud use as reduced heat, corrosion of reversible heat and temperature. That's what our masquot QT stands for, Q of it. Like enthalpy, entropy depends on temperature, phase and chemical structure, but also on delusion. Even in ideal systems, the entropy increases with delusion. The entropy has an absolute zero point. That is what the third law states, pure crystals at zero Kelvin. As a result, only positive entropy values can be found in thermodynamic tables in textbooks. The entropy according to cloud use is measured using the reduced reversible heat. The index reversible is sometimes very important. If we carry out the oxyhydrogen gas reaction spontaneously, we have a lot of heat that is released. But that is not the reversible heat that we need. We have to run the oxyhydrogen gas reaction reversibly over a fuel cell, then we get negative 98 kJ as reversible heat. We have to use this heat in Clausius formula. By the way, the entropy can also be measured in statistical thermodynamics using Ludwig Boltzmann's definition, S equals k times log of W with k being the Boltzmann constant and W being the thermodynamic probability. But we do not want to take this route here. The entropy always changes when we do add or remove heat, or more specifically, reversible heat, to or from a system. With temperature changes, with phase changes and with chemical reactions. In addition, entropy increases with mixing. The corresponding equations are given here. We calculate entropy of reaction just like enthalpy of reaction, starting with standard values from thermodynamic tables and applying Hess's law. We look at the standard entropies of the products and the reactants and calculate the difference between these two levels. With auto-protolysis, entropy decreases sharply, which means that the process is not favored entropically. Entropy is not with us. First law and second law in the general wording always consider the whole universe. The energy of the universe is constant. The entropy of the universe drives for a maximum. If we want to calculate the affinity of a process, it is easier to focus on the system, more specifically on the stability of the system. Mr. Gaines has derived that the term H minus T times S can only decrease in isobaric isothermal processes. This term is abbreviated as Gibbs free energy G. The free energy, the combination of these three state variables, is in fact a measure for the instability of a system. Delta G can therefore be seen as a measure of affinity. The more negative delta G, the larger the chemical driving force, the affinity. Let's complete the thermodynamic profile of G. Delta G has two contributions, the energetic contribution delta H and the entropic contribution T times delta S. In spontaneous processes, the Gibbs free energy can only decrease. We can measure Gibbs free energy by measuring a reversible work. Ever much more frequently, we calculate delta G using the so-called Gibbs Helmholtz equation from delta H and delta S. Just like entropy, Gibbs free energy depends on temperature, phase, structure and dilution. The elements at 25 degrees have arbitrarily been chosen to be zero level. If you look up, standard Gibbs free energies in tables for some compounds, the so-called chemical potentials, we can immediately state liquid water has a lower chemical potential at 25 degrees than gaseous water. And thus is more stable than gaseous water at that temperature. We are now able to characterize each process thermodynamically in energy, entropy and free energy terms. With autoprotolysis, for example, the energy increases. That is, the process is endothermic. The energy is not with us. With autoprotolysis, the entropy decreases. That is, the process is exotropic. Entropy is not with us either. And if we combine energy and entropy using Gibbs Helmholtz equation, we come to the conclusion that instability during the process increases, which means the products are more unstable than the reactants. The process at the whole is endergenic. Water will never spontaneously decompose completely into H plus and OH minus. But that does not mean that the process does not run at all. In the next lecture, we will calculate the equilibrium constant for this process, which is very small, but it's not zero. Let's summarize. The first and second law are statements about energy and entropy in the universe. We can measure the change in energy and entropy during a process. And we are also able to calculate these quantities using thermodynamic tables. We may combine energy and entropy using Gibbs Helmholtz equation and arrive at Gibbs free energy, which is a measure of instability. It tells us whether or not a process will run spontaneously. More information about the topic will be found in the books and in the lecture. Thanks for watching.
 Some processes do run spontaneously.  So they have an affinity, a driving thermodynamic force.  Others don't.  Today we will see how we can use the first and the second law  to calculate the affinity of a process in advance.  Hello and welcome to Fiskem Basics, our topic today.  The driving force of a process or the affinity.  We will see that affinity has two components, energy and entropy.  So in a way we may ask, are energy and or entropy with us?  Let's take the oxyhydrogen reaction and the auto-protolysis of water as examples.  The formation and the self ionization of water into H plus and OH minus ions.  Do these processes have a driving force?  What about energy and entropy?  An important quantity in thermodynamics is internal energy,  which comprises all energy in a system.  Where is, for example, the internal energy of water located?  Well, the water molecules are not at rest.  They have kinetic energy, rotational energy, vibrational energy.  There are also energies between different molecules  and very importantly chemical binding energies between the atoms.  All of these energies are part of the internal energy.  Although we can't measure absolute values of internal energy,  it only because there is no natural zero, but we can measure its change.  Whenever we add or remove energy from a system, the internal energy changes.  These inputs and outputs of energy to or from a system can take place as heat, q, or as work, w.  So if we are to calculate delta u for, say, the oxy hydrogen reaction,  we simply have to add up all the heat and work values of this reaction.  As you may remember, heat and work are path-fansitive.  So you have to select one path to calculate your change in internal energy.  We go for the reversible path, so we have to sum up the three numbers  and the result is negative 564 GJ for delta u.  Calculating delta u is particularly easy if the work is zero.  And this is the case if the volume remains constant in a spontaneous process.  Constant volume means no pressure volume work.  The heat, q sub v, released in an isochoric spontaneous process, is identical to the change in internal energy delta u.  However, we don't deal very often with isochoric processes.  Isobaric processes are much more common.  In these processes, we have to take into account pressure volume work.  Negative p times delta v.  This means that the isobaric heat, q sub p, plus pressure volume work is equal to delta u.  We can solve this equation for q sub p and then get delta u plus p times delta v.  Because we very often measure isobaric heat, the combination u plus p times v was simply renamed enthalpy.  Thus, enthalpy is an artificial quantity and has no clear meaning.  But the change in enthalpy is always the same as a spontaneous isobaric heat.  We measure the isobaric heat of negative 572 KJ in the oxyhydrogen gas reaction.  This also corresponds to the enthalpy of this reaction.  With this in mind, you may create the thermodynamic profile of enthalpy.  Enthalpy H is the measure of the energy content of a system.  It's useful with application of the first law.  The change in enthalpy can simply be measured using an isobaric heat, q sub p.  Whenever isobaric heat occurs, we change enthalpy.  So enthalpy clearly depends on temperature, on the phase and on chemical structure.  There is no natural zero of enthalpy, but all elements at 25 degrees Celsius  were arbitrarily defined to have zero enthalpy.  If you look up enthalpies in thermodynamic tables, we'll find negative values for most of the chemical compounds.  That means these compounds are lower in energy, or rather in enthalpy than the elements.  The entropy changes whenever isobaric heat is added or removed.  For example, when there is a change in temperature, a phase change or a chemical reaction.  If on the other hand we mix just two ideal systems like hydrogen and oxygen gas,  no heat is released or absorbed with ideal systems, there is no enthalpy of mixing.  If we melt one mole of solid ice at 0 degrees centigrade to one mole of liquid water at 0 degrees centigrade,  we need 6 kilojoules.  If we evaporate the liquid water at 0 degrees centigrade, we need another 45 kilojoules.  So if we were to evaporate the solid ice right away, there would be some of these two heat amounts, that is 51 kilojoules.  This is a statement of Hess's law.  The reaction enthalpies are path-independent.  In mathematicians terms, enthalpy is a quantity whose values are independent of path,  and it was called a state function, and its differential is exact.  Work on heat are quantities that depend on the path followed between states.  They are called path functions, and their differentials are inexact.  Let's draw an enthalpy diagram of water and the elements it is composed of.  The elements H2 and O2 mark the Vero level.  The atoms H and O mark a significantly higher energy level, and water is relatively low in energy.  The blue arrows are so-called enthalpies of formation.  The blue arrow down is the enthalpy of formation of water.  The arrow up symbolizes the enthalpy of formation of the atoms.  According to Hess's law, we can handle these arrows like we can add or subtract vectors.  The red arrow here is the atomization enthalpy of water,  the heat that we need to completely split water molecules into atoms.  This heat corresponds to 1850 kilojoules.  Conversely, 1850 kilojoules would be released if two water molecules were formed from the atoms.  This means the green arrow corresponds to 4 times the OH bond enthalpy.  Bond enthalpies are usually average values.  Therefore, the statement that the sum of the bond enthalpies corresponds to the enthalpy of atomization is only approximate.  With enthalpies of formation, which are tabulated in many chemistry textbooks,  we can do a lot of useful thermochemical calculations.  For example, if you want to know how much heat is released or consumed when water is split into H plus and OH minus,  we draw an enthalpy diagram.  The standard enthalpy of formation of any element in its most stable form is zero.  At lower enthalpies, we find the reactant water and the enthalpy of the products H plus and OH minus  is located between the aforementioned levels.  The two blue arrows represent the enthalpy of formation.  These arrows always start at zero level.  The red arrow is the enthalpy of reaction.  It starts at the reactant and ends at the product.  We have to treat this diagram like a vector diagram.  The enthalpy of reaction, the red arrow, is equal to the enthalpy of formation of the products, the short blue arrow,  minus the enthalpy of the formation of the reactant, the long blue arrow.  We end up with an enthalpy of reaction of plus 56 kJ.  This means that the auto-protolysis of water is endothermic.  We would have to invest 56 kJ of heat to dissociate one mole of water completely into one mole of H plus and one mole of OH minus.  So energy is obviously not with us.  Now let's look at entropy.  Remember the thermodynamic profile of this quantity.  Anthropy is a measure of disorder. It makes sense to introduce this quantity because the second log can easily be formulated with it.  We can measure the entropy changes according to cloud use as reduced heat,  corrosion of reversible heat and temperature.  That's what our masquot QT stands for, Q of it.  Like enthalpy, entropy depends on temperature, phase and chemical structure, but also on delusion.  Even in ideal systems, the entropy increases with delusion.  The entropy has an absolute zero point.  That is what the third law states, pure crystals at zero Kelvin.  As a result, only positive entropy values can be found in thermodynamic tables in textbooks.  The entropy according to cloud use is measured using the reduced reversible heat.  The index reversible is sometimes very important.  If we carry out the oxyhydrogen gas reaction spontaneously, we have a lot of heat that is released.  But that is not the reversible heat that we need.  We have to run the oxyhydrogen gas reaction reversibly over a fuel cell, then we get negative 98 kJ as reversible heat.  We have to use this heat in Clausius formula.  By the way, the entropy can also be measured in statistical thermodynamics using Ludwig Boltzmann's definition,  S equals k times log of W with k being the Boltzmann constant and W being the thermodynamic probability.  But we do not want to take this route here.  The entropy always changes when we do add or remove heat, or more specifically, reversible heat, to or from a system.  With temperature changes, with phase changes and with chemical reactions.  In addition, entropy increases with mixing.  The corresponding equations are given here.  We calculate entropy of reaction just like enthalpy of reaction, starting with standard values from thermodynamic tables and applying Hess's law.  We look at the standard entropies of the products and the reactants and calculate the difference between these two levels.  With auto-protolysis, entropy decreases sharply, which means that the process is not favored entropically.  Entropy is not with us.  First law and second law in the general wording always consider the whole universe.  The energy of the universe is constant.  The entropy of the universe drives for a maximum.  If we want to calculate the affinity of a process, it is easier to focus on the system, more specifically on the stability of the system.  Mr. Gaines has derived that the term H minus T times S can only decrease in isobaric isothermal processes.  This term is abbreviated as Gibbs free energy G.  The free energy, the combination of these three state variables, is in fact a measure for the instability of a system.  Delta G can therefore be seen as a measure of affinity.  The more negative delta G, the larger the chemical driving force, the affinity.  Let's complete the thermodynamic profile of G.  Delta G has two contributions, the energetic contribution delta H and the entropic contribution T times delta S.  In spontaneous processes, the Gibbs free energy can only decrease.  We can measure Gibbs free energy by measuring a reversible work.  Ever much more frequently, we calculate delta G using the so-called Gibbs Helmholtz equation from delta H and delta S.  Just like entropy, Gibbs free energy depends on temperature, phase, structure and dilution.  The elements at 25 degrees have arbitrarily been chosen to be zero level.  If you look up, standard Gibbs free energies in tables for some compounds, the so-called chemical potentials,  we can immediately state liquid water has a lower chemical potential at 25 degrees than gaseous water.  And thus is more stable than gaseous water at that temperature.  We are now able to characterize each process thermodynamically in energy, entropy and free energy terms.  With autoprotolysis, for example, the energy increases.  That is, the process is endothermic. The energy is not with us.  With autoprotolysis, the entropy decreases. That is, the process is exotropic.  Entropy is not with us either.  And if we combine energy and entropy using Gibbs Helmholtz equation,  we come to the conclusion that instability during the process increases, which means the products are more unstable than the reactants.  The process at the whole is endergenic. Water will never spontaneously decompose completely into H plus and OH minus.  But that does not mean that the process does not run at all.  In the next lecture, we will calculate the equilibrium constant for this process,  which is very small, but it's not zero.  Let's summarize. The first and second law are statements about energy and entropy in the universe.  We can measure the change in energy and entropy during a process.  And we are also able to calculate these quantities using thermodynamic tables.  We may combine energy and entropy using Gibbs Helmholtz equation and arrive at Gibbs free energy,  which is a measure of instability.  It tells us whether or not a process will run spontaneously.  More information about the topic will be found in the books and in the lecture.  Thanks for watching.
PCB4_0_251.png PCB4_252_563.png PCB4_564_4835.png PCB4_4836_10343.png PCB4_10344_10895.png PCB4_10896_12923.png PCB4_12924_24395.png PCB4_24396_24443.png PCB4_24444_24457.png