1.4.3.1 Laws of Thermodynamics

Unit 1  Vaporising Rubbing Alcohol  Thermal decomposition reactions  Forming a cation from an atom in the gas phase  Dissolving ammonium chloride in water

1.4.3.1 Laws of Thermodynamics First law of thermodynamics: Energy of the Universe is always constant.

First law of thermodynamics is a mathematical statement of the law of conservation of energy: Energy can be neither created nor destroyed.

SECOND LAW OF THERMODYNAMICS:

The Universe Tends Toward Maximum Disorder

When a swimmer falls into the water (a spontaneous process), the energy of the coherent motion of his body is converted to that of the chaotic thermal motion of the surrounding water molecules. The reverse process, the swimmer being ejected from still water by the sudden coherent motion of the surrounding water molecules, has never been witnessed even though such a phenomenon violates neither the first law of thermodynamics nor Newton’s laws of motion. This is because spontaneous processes are characterized by the conversion of order (in this case the coherent motion of the swimmer’s body) to chaos (here the random thermal motion of the water molecules). The second law of thermodynamics, which expresses this phenomenon, therefore provides a criterion for determining whether a process is spontaneous. Note that thermodynamics says nothing about the rate of a process; that is the purview of chemical Spontaneity and Disorder

Spontaneous processes

occur in directions that increase the overall disorder of the universe, that is, of the system and its surroundings. Disorder  Defined as the number of equivalent ways, W, of arranging the components of the universe

Figure 1.34 In the above picture, one boy goes up gaining energy but the other one looses same amount of energy. Thus Total energy of 2 boys is constant.

Entropy

 It is a thermodynamic Figure 1.35 As you can see here, if you throw the bricks in random, most property which probable is that it will fall randomly as shown right diagram… it will never provides a quantitative fall as perfect wall structure. Hence what we can say about it? measure of the disorder of a given thermodynamic state,  Entropy of the system  is proportional to the number of gas molecules it contains.

Unit 1  Entropy is a state function because it depends only on the parameters that describe a state.  The entropy (disorder) of a substance increases with its volume.  Thus entropy depends on concentration.

In some cases we find order is increasing, as in

living cell.  Living cell tries to attain more and more stability and thus becoming ordered.  But it is creating disturbance in outer environment, by releasing some chemicals or by using some energy from the surrounding.  ∆S = -∆H / T

Measurement of Entropy

 In chemical and biological systems, it is impossible, to determine the entropy of a system by counting the number of ways it can assume its most probable state.  For spontaneous processes where T is the absolute temperature at which the change in heat occurs.  It is evident, however, that any system becomes progressively disordered (its entropy increases) as its temperature rises  Thus the entropy change of a reversible process at constant temperature can be determined from measurements of the heat transferred and the temperature at which this occurs.  The entropy of the universe must increase even though the entropy of the system does not change.

Third law of thermodynamics Entropy of a system becomes 0 as temperature approaches 0 K

The third law of thermodynamics is essentially a statement about the ability to create an absolute temperature scale, for which absolute zero is the point at which the internal energy of a solid is precisely 0. Various sources show the following three potential formulations of the third law of thermodynamics: It is impossible to reduce any system to absolute zero in a finite series of operations. The entropy of a perfect crystal of an element in its most stable form tends to zero as the temperature approaches absolute zero. As temperature approaches absolute zero, the entropy of a system approaches a constant. The third law means a few things, and again all of these formulations result in the same outcome depending upon how much you take into account: However, due to quantum constraints on any physical system, it will collapse into its lowest quantum state but never be able to perfectly reduce to 0 entropy, therefore it is impossible to reduce a physical system to absolute zero in a finite number of steps Gibbs free energy, G, expresses the amount of energy capable of doing work during a reaction at constant temperature and pressure. When a reaction proceeds with the release of free energy (that is, when the system changes so as to possess less free energy), the free-energy change, ∆G, has a negative value and the reaction is said to be exergonic. In endergonic reactions, the system gains free energy and ∆G is positive.

Figure 1.35 In the above fig, the molecules in solids are compact…so less freedom , Entropy is less In the liquid …little more freedom , Entropy is higher. In the gases …more freedom , Entropy is higher. In other words, entropy of the system is always is increasing.

Joules /mole. Kelvin (J/mol- K) (Table 1.6). Under the conditions existing in biological systems (including constant temperature and pressure), changes in free energy, enthalpy, and entropy are related to each other quantitatively by the equation. ∆G=∆H - T∆S.

In which ∆G is the change in Gibbs free energy of the reacting system, ∆H is the change in enthalpy of the system, T is the absolute temperature, and ∆S is the change in entropy of the system. By convention, ∆S has a positive sign when entropy increases and ∆H, as noted above, has a negative sign when heat is released by the system to its surroundings. Either of these conditions, which are typical of favorable processes, tend to make ∆G negative. In fact, ∆G of a spontaneously reacting system is always negative. The second law of thermodynamics states that the entropy of the universe increases during all chemical and physical processes, but it does not require that the entropy increase take place in the reacting system itself. The order produced within cells as they grow and divide is more than compensated for by the disorder they create in their surroundings in the course of growth and division. In short, living organisms preserve their internal order by taking from the surroundings free energy in the form of nutrients or sunlight, and returning to their surroundings an equal amount of energy as heat and entropy. The composition of a reacting system (a mixture of chemical reactants and products) tends to continue changing until equilibrium is reached. At the equilibrium concentration of reactants and products, the rates of the forward and reverse reactions are exactly equal and no further net change occurs in the system. The concentrations of reactants and products at equilibrium define the equilibrium constant, Keq. In the general reaction aA + bB cC + dD, where a, b, c, and d are the number of molecules of A, B, C, and D participating, the equilibrium constant is given by

Where [A], [B], [C], and [D] are the molar concentrations of the reaction components at the point of equilibrium. Under standard conditions (298 K = 250 C), when reactants and products are initially present at 1 M concentrations or, for gases, at partial pressures of 101.3 kilopascals (kPa), or 1 atm, the force driving the system toward equilibrium is defined as the standard free-energy change, ∆G By this definition, the standard state for reactions that involve hydrogen ions is [H+] = 1 M, or pH 0. Most biochemical reactions, however, occur in well-buffered aqueous solutions near pH 7; both the pH and the concentration of water (55.5 M) are essentially constant. For convenience of calculations, biochemists therefore define a different standard state, in which the concentration of H+ is 10-7 M (pH 7) and that of water is 55.5 M; for reactions that involve Mg2+ (including most in which ATP is a reactant), its concentration in solution is commonly taken to be constant at 1 mM. Physical constants based on this biochemical standard state are called standard transformed constants and are written with a prime (such as ∆G’0 and K’eq) to distinguish them from the untransformed constants used by chemists and physicists. By convention, when H2O, H+, and/or Mg2+ are reactants or products, their concentrations are incorporated into the constants K’eq and ∆G’0 . Just as K eq is a physical constant characteristic for each reaction, so too is ∆G a constant. There is a simple relationship between K eq and ∆G’o: ∆G’o= -RT ln K’eq.

The standard free-energy change of a chemical reaction is simply an alternative Table 1.6 Relationships among Keq, G, and the Direction of Chemical Reactions under Standard Conditions mathematical way of expressing its equilibrium constant. If the equilibrium constant for a given chemical reaction is 1.0, the standard free-energy change of that reaction is 0.0 (the natural logarithm of 1.0 is zero). If K’eq of a reaction is greater than 1.0, its ∆G is negative. If K’eq is less than 1.0, ∆G is positive. Because the relationship between ∆G and K’eq is exponential, relatively small changes in ∆G correspond to large changes in K’eq.

Sample problem

Calculate the the standard free-energy change of the reaction catalysed by the enzyme

phosphoglucomutase: Glucose 1-phosphate  glucose 6-phosphate

Solution : Chemical analysis shows that whether we start with, say, 20 mM glucose 1-phosphate (but no glucose 6-phosphate) or with 20 mM glucose 6-phosphate (but no glucose 1-phosphate), the final equilibrium mixture at 25oC and pH 7.0 will be the same: 1 mM glucose 1-phosphate and 19 mM glucose 6-phosphate. (Remember that enzymes do not affect the point of equilibrium of a reaction; they merely hasten its attainment.) From these data we can calculate the equilibrium constant:

Because the standard free-energy change is negative, when the reaction starts with 1.0 M glucose 1phosphate and 1.0 M glucose 6-phosphate, the conversion of glucose 1-phosphate to glucose 6phosphate proceeds with a loss (release) of free energy

1.4.5 Colligative properties

Solutions have different properties than either the solutes or the solvent used to make the solution. Those properties can be divided into two main groups--colligative and non-colligative properties. Colligative properties depend only on the number of dissolved particles in solution and not on their identity. Noncolligative properties depend on the identity of the dissolved species and the solvent.  To explain the difference between the two sets of solution properties, we will compare the properties of a 1.0M aqueous sugar solution to a 0.5 M solution of table salt (NaCl) in water.  Despite the concentration of sodium chloride being half of the sucrose concentration, both solutions have precisely the same number of dissolved particles because each sodium chloride unit creates two particles upon dissolution--a sodium ion, Na+, and a chloride ion, Cl.  Therefore, any difference in the properties of those two solutions is due to a non-colligative property.  Both solutions have the same freezing point, boiling point, vapour pressure, and osmotic pressure because those colligative properties of a solution only depend on the number of dissolved particles. The taste of the two solutions, however, is markedly different.  The sugar solution is sweet and the salt solution tastes salty. Therefore, the taste of the solution is not a colligative property. Another non-colligative property is the color of a solution. A 0.5 M solution of CuSO4 is bright blue in contrast to the colourless salt and sugar solutions. Other non-colligative properties include viscosity, surface tension, and solubility.

Raoult's Law and Vapour Pressure Lowering

When a non-volatile solute is added to a liquid to form a solution, the vapour pressure above that solution decreases. To understand why that might occur, let's analyse the vaporization process of the pure solvent then do the same for a solution. Liquid molecules at the surface of a liquid can escape to the gas phase when they have a sufficient amount of energy to break free of the liquid's intermolecular forces. That vaporization process is reversible. Gaseous molecules coming into contact with the surface of a liquid can be trapped by intermolecular forces in the liquid. Eventually the rate of escape will equal the rate of capture to establish a constant, equilibrium vapour pressure above the pure liquid.  If we add a non-volatile solute to that liquid, the amount of surface area available for the escaping solvent molecules is reduced because some of that area is occupied by solute particles.

Unit 1  Therefore, the solvent molecules will have a lower probability to escape the solution than the pure solvent.  That fact is reflected in the lower vapour pressure for a solution relative to the pure solvent. That statement is only true if the solvent is non-volatile. If the solute has its own vapour pressure, then the vapour pressure of the solution may be greater than the vapour pressure of the solvent.  Note that we did not need to identify the nature of the solvent or the solute (except for its lack of volatility) to derive that the vapour pressure should be lower for a solution relative to the pure solvent. That is what makes vapour pressure lowering a colligative property--it only depends on the number of dissolved solute particles. The French chemist Francois Raoult discovered the law that mathematically describes the vapour pressure lowering phenomenon. Raoult's law is given in: Raoult's law states that the vapour pressure of a solution, P, equals the mole fraction of the solvent, c solvent, multiplied by the vapour pressure of the pure solvent, Po . While that "law" is approximately obeyed by most solutions, some show deviations from the expected behaviour. Deviations from Raoult's law can either be positive or negative. Figure 1.36 The Vapour Pressure of a A positive deviation means that there is a higher than expected Solution is Lower than that of the Pure vapour pressure above the solution. A negative deviation, Solvent. On the surface of the pure conversely, means that we find a lower than expected pressure for the solution. vapour solvent (shown on the left) there are more solvent molecules at the surface than in the right-hand solution flask.The reason for the deviation stems from a flaw in our Therefore, it is more likely that solvent consideration of the vapour pressure lowering event--we assumed molecules escape into the gas phase that the solute did not interact with the solvent at all. That, of on the left than on the right. course, is not true most of the time. If the solute is strongly held Therefore, the solution should have a by the solvent, then the solution will show a negative deviation lower vapor pressure than the pure from Raoult's law because the solvent will find it more difficult to solvent. escape from solution. If the solute and solvent are not as tightly bound to each other as they are to themselves, then the solution will show a positive deviation from Raoult's law because the solvent molecules will find it easier to escape from solution into the gas phase. Solutions that obey Raoult's law are called ideal solutions because they behave exactly as we would predict. Solutions that show a deviation from Raoult's law are called non-ideal solutions because they deviate from the expected behaviour. Very few solutions actually approach ideality, but Raoult's law for the ideal solution is a good enough approximation for the non- ideal solutions that we will continue to use Raoult's law. Raoult's law is the starting point for most of our discussions about the rest of the colligative properties, as we shall see in the

Boiling Point Elevation

One consequence of Raoult's law is that the boiling point of a solution made of a liquid solvent with a nonvolatile solute is greater than the boiling point of the pure solvent. The boiling point of a liquid or is defined as the temperature at which the vapour pressure of that liquid equals the atmospheric pressure. For a solution, the vapour pressure of the solvent is lower at any given temperature. Therefore, a higher temperature is required to boil the solution than the pure solvent.. As you can see in the figure 1.37 the vapour pressure of the solution is lower than that of the pure solvent. Because both pure solvent and solution need to reach the same pressure to boil, the solution requires a higher temperature to boil. If we represent the difference in boiling point between the pure solvent and a solution as ΔTb, we can calculate that change in boiling point from the: In this we use the units molality, m, for the concentration, m, because molality is temperature independent. The term Kb is a boiling point elevation constant that depends on the particular solvent being used. The term i in the above equation is called the van't Hoff factor and represents the number of dissociated moles of particles per mole of solute. The van't Hoff factor is 1 for all non-electrolyte solutes and equals the total

Unit 1 number of ions released for electrolytes. Therefore, the value of i for Na2SO4 is 3 because that salt releases three moles of ions per mole of the salt.

Freezing Point Depression

As you may have noticed when we looked at the , the freezing point is depressed due to the vapour pressure lowering phenomenon. The points out that fact: In analogy to the boiling point elevation, we can calculate the amount of the freezing point

depression with the :

Note that the sign of the change in freezing point is negative because the freezing point of the solution is less than that of the pure solvent. Just as we did for boiling point elevation, we use molality to measure the concentration of the solute because it is temperature independent. Do not forget about the van't Hoff factor, I, in your freezing point calculations. One way to rationalize the freezing point depression phenomenon without talking about Raoult's law is to consider the freezing process. In order for a liquid to freeze it must achieve a very ordered state that results in the formation of a crystal. If there are impurities in the liquid, i.e. solutes, the liquid is inherently less ordered. Therefore, a solution is more difficult to freeze than the pure solvent so a lower temperature is required to freeze the liquid.

Osmotic Pressure

Osmosis refers to the flow of solvent molecules past a semipermeable membrane that stops the flow of solute molecules only. When a solution and the pure solvent used in making that solution are placed on either side of a semipermeable membrane, it is found that more solvent molecules flow out of the pure solvent side of the membrane than solvent flows into the pure solvent from the solution side of the membrane. That flow of solvent from the pure solvent side makes the volume of the solution rise. When the height difference between the two sides becomes large enough, the net flow through the membrane ceases due to the extra pressure exerted by the excess height of the solution chamber. Converting that height of solvent into units of pressure gives a measure of the osmotic pressure exerted on the solution by the pure solvent. P stands for pressure, r is the density of the solution, and h is the height of the solution.

Figure 1.37 Phase Diagram for a Solvent and its Solution with a Nonvolatile Solute

Figure 1.38 Phase Diagram for a Solution and the Pure Solvent Indicating the Freezing Point Depression

Unit 1 You can understand why more molecules flow from the solvent chamber to the solution chamber in analogy to our discussion of Raoult's law. More solvent molecules are at the membrane interface on the solvent side of the membrane than on the solution side. Therefore, it is more likely that a solvent molecule will pass from the solvent side to the solution side than vice versa. That difference in flow rate causes the solution volume to rise. As the solution rises, by the pressure depth equation, it exerts a larger pressure on the membrane's surface. As that pressure rises, it forces more solvent molecules to flow from the solution side to the solvent side. When the flow from both sides of the membrane are equal, the solution height stops rising and remains at a height reflecting the osmotic pressure of the solution.

The equation relating the osmotic pressure of a solution to its concentration has a form quite similar to the ideal gas law:

Although the above equation may be more simple to remember, and is more useful. This form of the equation has been derived by realizing that n / V gives the concentration of the solute in units of molarity, M.

Figure 1.39 shows a typical setup for measuring the osmotic pressure of a solution.

Critical thinking Questions 1. What is the 'pH' of pure water and that of rain water? Explain the difference. 2. What is the pH of solution 'A' which liberates CO2 gas with a carbonate salt? Give the reason? 3. What is a universal indicator? What is its advantage?