In this article we will discuss about Thermodynamics. After reading this article you will learn about: 1. Study of Thermodynamics 2. The Laws of Thermodynamics.
Study of Thermodynamics:
The study of thermodynamics is assemblage of matter and energy that are called systems. Classical thermodynamics enquires into the alterations in the content of energy and its distribution that take place when a system passes from an initial state into a terminal state at equilibrium.
The state of a system can be defined in terms of its temperature, pressure and composition, and when both temperature and pressure of a system are kept constant, energetic changes are directly related to changes in composition.
Two most important systems of classical thermodynamics are:
(i) The isolated system, and
(ii) The closed system.
An isolated system is completely insulated from its surroundings and is both materially and energetically self-contained. A closed system though materially self-contained, is freely able to exchange energy with its surroundings. In closed system temperature and pressure (T and P) are constant.
In biology classical thermodynamics is concerned with the reaction taking place at constant temperature and pressure. The systems plus the surroundings constitute the universe.
Units of Measuring Energy:
The most common unit of energy used in thermodynamics is the calorie (1 cal = 4.184 J). The SI unit employed in thermodynamics is the Joules (J) or kilo-joules (1 kJ = 1000J).
The energy content of a system is related to the standard quantity of the compound, i.e., 1 mol., as both are directly proportional. Values of energy terms expressed in cal/mole are converted to values in J mol-1 by multiplying by 4.184. Conversely, to convert) mol-1 to cal/mole it is divided by 4.184.
The Laws of Thermodynamics (Conservation of Energy):
(i) First Law of Thermodynamics:
It states that the total energy of an isolated system is constant though within the system it may change its form. Or, in all chemical and physical changes, energy is neither created nor destroyed but is only transformed from one form to another. Or, in any process the total energy of the system and its surroundings remains constant. Or, nobody can get something for nothing.
Thus change in an isolated system can neither lead to an increase nor a decrease in the intrinsic energy of the system, but it can only redistribute the intrinsic energy in different forms.
A closed system involves both re-distribution of energy within the system and transfer of energy between the system and its surroundings. Thus whatever reaction takes place in a closed system, the total internal energy content of that system and its surroundings must be constant.
If a closed system (T and P constant) having initially a total internal energy content E1, undergoes some change resulting in a different intrinsic energy E2 the change in energy ΔE = (E2 – E1), is an equal but opposite change in the intrinsic energy content of its surroundings.
The energetic interactions between the system and its surroundings is achieved by (i) thermal transfer, and (ii) performance of work. If the reaction in a closed system brings a change in its volume, then by its volume change (ΔV m-3), the system obligatorily performs work on the surroundings equal to – wobligatory = – PΔVJ mol-1.
The minus sign is introduced as it conventionally considers that energy is released from the system to its surroundings, that is utilized for the work done. Various other types of work may optionally be performed by the reaction, so that the total energy lost by the system in the performance of all types of work (both obligatory and optional) may be summed in one term as – w J mol-1.
The thermal transfer between the system and its surroundings is designated as q J mol-1. Thus in a closed system (T and P constant), any change in intrinsic energy (ΔEsystem J mol-1) is the outcome of heat exchanged and work performed; i.e.
ΔEsystem = E2 – E1 = (q – w) J mol-1.
Heat is a reflection of random molecular motion, whereas work is defined as the distance moved under the influence of force associated with organised motion.
Force may be of different forms like the gravitational force exerted by one mass on another, the expansional force exerted by a gas, the fissional force exerted by a spring or muscle fibre, the electrical force of one charge on another, and the dissipative forces of friction and viscosity.
The intrinsic energy (E) of a system is the characteristic of the system that depends on the present state and is independent of its previous history. So the intrinsic energy is the so-called function of state. There are three further energetic functions of state of the system and its surroundings namely, enthalpy, entropy and free energy.
Enthalpy:
Enthalpy is a new thermodynamic quantity (Greek: enthalpein, to warm in) and is abbreviated H. It is the heat content of the reacting system. It reflects the number and kinds of chemical bonds in the reactants and products. For a reaction in closed system (T and P constant) it has been established that,
which is defined as the quantity of heat absorbed by a closed, isothermal system when at constant pressure it undergoes a change of state without performing any work associated with its change in volume. Thus enthalpy of a system consists of the internal energy (E), plus the absolute pressure (P) multiplied by the volume (V).
When a chemical reaction releases heat into the surroundings, it is said to be exothermic. The heat content of the products is less than that of the reactants and ΔH has a negative value.
Reacting systems that take up heat from their surroundings are endothermic and have positive values of ΔH. For a chemical reaction, the sign and magnitude of ΔH is largely attributable to the energy changes associated with the making and breaking of chemical bonds.
The value of ΔH depends only on the initial and final states of the system and is totally independent of the mechanism of the reaction. This is the basis of Hess’s Law of Constant Heat Summation, which states that the thermal transfer in a particular reaction is the same whether it is accomplished in one or several stages.
For example, the value of ΔH for the reaction P → S is – 4.5 kJ mol-1 when this is taking place at certain fixed temperature and pressure. If the same reaction takes place in a stepwise manner, the total magnitude of ΔH for the contributory reactions will equal the value of ΔH for the overall reaction. Thus if,
since ΔH = – 4.5 kJ mol-1 for the overall reaction P → S, then (a) + (b) + (c) = – 4.5 kJ mol-1.
(ii) Second Law of Thermodynamics:
It states that any system, and its surroundings, tend spontaneously toward increasing disorder. Or, heat cannot be completely converted into work without changing some part of the system. Or, no real process can be 100 per cent efficient. Or, in any energy conversion some energy is transferred to the surroundings as heat.
Entropy:
The measure of randomness or disorder is termed entropy (S) coined first by Rudolf Clausius in 1851. The term literally means “a change within”. It is the outcome of the second law. It is a function of state, and any change in state of a system is associated with a change of entropy AS = (Sfinal – Sinitial). Entropy is essentially a mathematical function with no physical analogue involving statistical and probability considerations.
It can be defined as S = k In w, where k is a proportionality constant (Boltzmann’s constant), and In w is the natural logarithm of w, the thermodynamic probability.
It is the number of ways in which the system can be microscopically arranged without changing its macroscopic features. The S value of an isolated system is an index of its intrinsic stability. The greater the entropy of the system the more stable is this and the smaller is its capacity for spontaneous change.
Entropy is state or condition not only of energy status but also of matter. For example, an aerobic organism extracts free energy from glucose, taken from its environment. The energy is released from the glucose molecule through oxidation with molecular oxygen, also obtained from the surroundings.
The oxidized products, CO2 and H2O, are returned to the surroundings leading to an increase in entropy, whereas the organism itself remains in a steady state without changing its internal order. The entropy arises from heat dissipation as well as from molecular disorder.
C6H12O6 + 6O2 → 6CO2 + 6H2O
One molecule of glucose and 6 molecules of oxygen are more randomly dispersed into 12 molecules (6CO2 + 6H2O) through oxidation. Thus through chemical reactions number of molecules increases. When a solid substance is converted into liquid or gas, they have more freedom to move or fill space than a solid.
(iii) Third Law of Thermodynamics:
It assumes that perfect crystals of all compounds possess zero entropy at the absolute zero (OK). The entropy of each compound increases with the increase in temperature. The quantity is measured in JK-1 mol-1. If the entropy of a system and its surroundings increases during a process, then it is a spontaneous process.
The criterion for spontaneous process in a closed system can be revealed as
ΔSsystem + ΔSsurroundings = a positive value.
If the value is zero (0) the total (isolated) system remains throughout at equilibrium, i.e., when the entropy reaches its maximum level for a system and its surroundings, the system is said to be at equilibrium.
The spontaneous processes are irreversible without an input of energy into the system that increases entropy in the surroundings. For example, perfume molecules do not spontaneously condense back into an open bottle. All natural processes that take place at a significant rate are thermodynamically irreversible.
Free Energy:
The entropy changes are of limited usefulness in predicting the direction and the equilibrium position of chemical reactions.
The 2nd Law’s criterion of spontaneity, i.e., feasibility of independent occurrence of reaction in a closed system (T and P constant) is inconvenient as it compels us to measure the entropy changes in both the system itself and its surroundings. But entropy cannot always be directly measured or calculated in chemical processes.
A more useful criterion than the entropy change has been derived for predicting the direction and the equilibrium position of chemical reactions, namely, the change in free energy, that form of energy capable of doing work under constant temperature and pressure.
The thermodynamic measure of the maximum energy available for conversion to work (at constant temperature and pressure) is called the Gibbs free energy symbolized as G, after John Willard Gibbs who drew attention to its significance in systems maintained at constant pressure.
The free-energy change of a reacting system related the entropy (at constant temperature and pressure), through the following equation:
ΔH – TΔS = ΔG
where ΔG is the free energy change of the system, ΔH is the change in enthalpy, T is the absolute temperature, and AS is the change in entropy.
The criteria of spontaneity of reaction in a closed system can briefly be expressed as follows:
(a) When the reaction proceeding at measurable rates under conditions of thermodynamic irreversibility, i.e., the system is not already at equilibrium
ΔG < 0 (i.e., negative)
(b) In the conditions of thermodynamic reversibility, i.e., at equilibrium
ΔG = 0
So, in any closed system (T and P constant) which is not at equilibrium, only exergonic reactions (-ΔG) can occur spontaneously. If under given conditions a reaction A + B → C + D is endergonic (+ ΔG), then the reverse reaction C + D → A + B will be exergonic (- ΔG) and could proceed spontaneously.
Standard free energy change can be determined by the following equation:
ΔG° = – RT In Keq = – 2.3 RT log Keq
where, ΔGo = standard free energy change in joules (J) or calories (cal)
R = the ideal gas constant (8.304 J mol-1 K-1)
T = absolute temperature (K)
In = natural logarithm
Keq = equilibrium constant; the subscript “eq” denotes reactant and product concentration at equilibrium:
= concentration of products multiplied together/concentration of reactants multiplied together
When one mole of each reactant is converted to one mole of each product, maximum standard free energy change occurs. In other words, the standard free energy change, ΔG°, is the change in free energy when the concentration of reactants and products is 1M.
The above equation is one of the most useful links between thermodynamics and biochemistry and has a host of application. The equation is easily modified to allow computation of the change in free energy for concentrations. In the reaction A + B ↔ C + D, the actual change in free energy, ΔG, is given by the equation
where the brackets refer to the concentrations at the time of the reaction. The value of ΔG is a function of the displacement of the reaction from equilibrium. It is central to an understanding of bioenergetics.
The equilibrium constant depends on temperature, that can be sure by rearranging the equation:
where, H° and S° represent enthalpy and entropy in standard state. The above equation has the form y = mn + 6, the equation for a straight line. A plot of In Keq versus 1 /T is known as Van’t Hoff plot. From the measurements of Keq at different temperatures the values of ΔH°, ΔS° and ΔG° can be determined more easily than measuring by calorimetry.
In biochemistry the standard free energy changes of reactions are conventionally symbolized by ΔG°’ instead of ΔG° used in physical chemistry. If a reaction includes neither H2O, H+, nor an ionizable species, then ΔG°’ = G°.
Living organisms are open systems and can never be at equilibrium. They take up nutrients from the environment and release waste products and generate work and heat. They continuously ingest high enthalpy and low entropy nutrients which they convert to low enthalpy, high entropy waste products.
The free energy released in this conversion powers the cellular activities that produce the high degree of organizational characteristics of life. If the flow of conversion processes is interrupted anyhow, the system ultimately reaches equilibrium causing death.
So, the living organisms maintain a steady state meaning that all the flows in the system are constant so that the system does not change with time. Similarly energy flow in the biosphere is an example of a system in a steady state. In all living systems the flow of energy is always downhill (ΔG < 0).
Example 1:
The hydrolysis of ATP liberates its terminal phosphate group. At 309K and pH 7 in the presence of Mg+2 ions, it was calculated that ΔH was – 20.08 kJ mol-1, ΔS was + 35.21 JK-1 mol-1. Calculate the corresponding value of ΔG of the reaction.
For an isothermal reaction at constant pressure in a closed system,
ΔG = ΔH – TΔS
For the given reaction,
ΔG =?
ΔH = – 20080 J mol-1
T = 309K
ΔS = + 35.21 J K-1 mol-1
Substituting these values in the above equation,
ΔG = – 20080 – (309 x 35.21) J mol-1
or, ΔG = – 20080 – 10880 J mol-1
= – 30.95 k J mol-1
Example 2:
ΔGo of glucose and ethanol in aqueous solution equals to – 917.0 and – 181.6 k J mol-1 respectively, and ΔGf° of carbon dioxide as a gas is – 394.5 k J mol-1. Deduce ΔG° for the net reaction of alcoholic fermentation.
Glucose → 2 Ethanol + 2 CO2
In aqueous solution (at 298K) with the evolution of gaseous CO2.
Since the value of ΔG° are additive,
ΔGo = (sum of values of ΔG f° of products) – (sum of values of ΔGf° of reactants).
Example 3:
During glycolysis, fructose 1, 6-bisphosphate is broken down to yield glyceraldehyde 3-phosphate and dihydroxyacetone phosphate. During gluconeogenesis, fructose bisphosphate is synthesized from these triose phosphates. The reaction is reversible and the same enzyme catalyses both the reactions.
If the thermodynamic equilibrium constant for the reaction from left to right equals to 8.91 x 10-5 mol dm-3, calculate the value of ΔGo for the cleavage of FBP (R = 8.314 J K-1 mol-1).
As temperature is not mentioned here, it may be assumed that the reaction performed isothermally at 298 K (25°C).
We may apply the following equation:
