Partial Molar Properties And Their Application

Partial Molar Properties And Their ApplicationThermodynamics deals with animation changes and its relationship with work. It is based on three laws of thermodynamics which be apply as axioms just as Newtons laws motion from the basis of classical mechanics. The first two laws are based on facts find in every day life. The predictions based on these laws have been verified in most cases and so far no case has been reported where the laws improve down. The laws can be stated in mathematical variety. Hence, thermodynamics is an exact science. The thermodynamic theory can be developed without gaps in the argument using yet moderate knowledge of mathematics.B.ABOUT PARTIAL MOLAR PROPERTYThermodynamic relations derived earlier are applicable to closed formations. In a system where non only the work and wake but also several kinds of matter are being exchanged, a multi serving open system has to be considered. Here, the counts of the various substances are treated as variables l ike either different thermodynamic variables. For example, the gibbs free vigour of a system is a go not only of temperature and ram , but also of the amount of each substance in the system,such thatG=f(T,p,n1,n2.nk)Where n1,n2,.,nk represent the amounts of each of the K components in the system . for simplicity, let a system contain only two components. The total differential of G isdG=(?G/?T)P,n1,n2 dT+(?G/?p)T,n1,n2 dp+(?G/?n1)T,p,n2 dn+(?G/?n2)T,p,n1 dn2In this eq., the partial derivatives (?G/?n1)T,P,n2 and (?G/?n2)T,P,n1 are known as partial hoagie free energies of components one and two , complaisanceively. In genral, the partial derivative of a thermodynamic pop off Y with respect to the amount of component i of a alloy when T,p and amounts of other constituents are kept unceasing , is known as the partial molar station of the ith component and is represented as Yi,pm. ThusYi,pm=(?Y/?ni)T,p,njs i=jC.DEFINITION OF PARTIAL MOLAR PROPERTYThe partial molar plaza ma y be defined in either of the following two ways1. it is the change in Y when 1 bulwark of component i is added to a system which is so large that this addition has a negligible effect on the account of the system.2. Let dY be the change in comfort of Y when an infinitesimal amount dni of component i is added to a sysem of definite composition. By an infinitesimal amount dni we mean that its addition does not cause both appreciable change in the composition of the system. If we divide dY by dni , we get the partial molar prop (?Y/?ni). thusly, the partial molar property of the component i may be defined as the change in Y per mole of component i when an infinitesimal amount of this component is added to a system of definite composition.D.TYPES OF MOLAR PROPERTIES(a.) Partial molar muckleThe partial molar garishness is broadly understood as the contribution that a component of a mixture makes to the overall saturation of the re resolution. However, there is rather more to i t than thisWhen one mole of piss is added to a large volume of body of water at 25C, the volume increases by 18cm3. The molar volume of axenic water would thus be reported as 18cm3 mol-1. However, addition of one mole of water to a large volume of pure ethanol results in an increase in volume of only 14cm3. The reason that the increase is different is that the volume occupied by a addicted number of water molecules depends upon the identity of the surrounding molecules. The value 14cm3 is said to be the partial molar volume of water in ethanol.In familiar, the partial molar volume of a substance X in a mixture is the change in volume per mole of X added to the mixture.The partial molar volumes of the components of a mixture vary with the composition of the mixture, because the environment of the molecules in the mixture changes with the composition. It is the changing molecular environment (and the consequent readjustment of the interactions between molecules) that results in the thermodynamic properties of a mixture changing as its composition is altered.The partial molar volume, VJ, of any substance J at a general composition, is defined asFig the partial molar volumes of water and ethanol at 25degree Cwhere the subscript n indicates that the amount of all the other substances is held constant.The partial molar is the heel over of the plot of the total volume as the amount of J is changed with all other variables held constant advert that it is quite strength for the partial molar volume to be negative, as it would be at II in the above diagram. For example, the partial molar volume of magnesium sulphate in water is -1.4cm3 mol-1.i.e. addition of 1 mol MgSO4 to a large volume of water results in a decrease in volume of 1.4 cm3. (The compaction occurs because the salt breaks up the open structure of water as the ions become hydrated.) in one case the partial molar volumes of the two components of a mixture at the composition and temperature of inter est are known, the total volume of the mixture can be calculated fromThe expression may be extended in an analogous modality to mixtures with any number of components.The most common method of measuring partial molar volumes is to measure the dependence of the volume of a solution upon its composition. The observed volume can then be fitted to a function of the composition (usually using a computer), and the slope of this function can be set(p) at any composition of interest by specialty.(b.) Partial molar gibbs energiesThe concept of a partial molar quantity can be extended to any all-inclusive state function. For a substance in a mixture, the chemical substance potential is a defined as the partial molar gibbs qualificationi.e. the chemical potential is the slope of a plot of the Gibbs energy of the mixture against the amount of component J, with all other variables held constantIn the above plot, the partial molar Gibbs energy is greater at I than at II. The total Gibbs ener gy of a binary mixture is given byThe above expression may be generalised quite trivially to a mixture with an arbitrary number of componentswhere the sum is across all the different substances present in the mixture, and the chemical potentials are those at the composition of the mixture.This indicates that the chemical potential of a substance in a mixture is the contribution that substance makes to the total Gibbs energy of the mixture.In general, the Gibbs energy depends upon the composition, squelch and temperature. Thus G may change when any of these variables alter, so for a system that has components A, B, etc, it is possible to rewrite the equation dG = Vdp SdT (which is a general result that was derived here) as followswhich is called the fundamental equation of chemical thermodynamics.At constant temperature and pressure, the equation simplifies toUnder these conditions, dG = dwn,max (as was demonstrated here), where the n indicates that the work is non-expansion work. Therefore, at constant temperature and pressureThe idea that the changing composition of a system can do work should be familiar this is what happens in an electrochemical cell, where the two halves of the chemical reaction are separated in space (at the two electrodes) and the changing composition results in the motion of electrons through a circuit, which can be used to do electrical work.On a final note, it is possible to use the relationships between G and H, and G and U, to generate the following relationsNote oddly the conditions (the variables that must be held constant) under which each relation applies.Fig the partial molar volumes of water and ethanol at 25degree Cwhere the subscript n indicates that the amount of all the other substances is held constant.The partial molar is the slope of the plot of the total volume as the amount of J is changed with all other variables held constantNote that it is quite possible for the partial molar volume to be negative, as it would be at II in the above diagram. For example, the partial molar volume of magnesium sulphate in water is -1.4cm3 mol-1. i.e. addition of 1 mol MgSO4 to a large volume of water results in a decrease in volume of 1.4 cm3. (The contraction occurs because the salt breaks up the open structure of water as the ions become hydrated.) Once the partial molar volumes of the two components of a mixture at the composition and temperature of interest are known, the total volume of the mixture can be calculated fromThe expression may be extended in an analogous fashion to mixtures with any number of components.The most common method of measuring partial molar volumes is to measure the dependence of the volume of a solution upon its composition. The observed volume can then be fitted to a function of the composition (usually using a computer), and the slope of this function can be determined at any composition of interest by differentiation.(C.)PARTIAL MOLAR THERMAL PROPERTIES1. Partial molar heat c apacities the heat capacity at constant pressure Cp of a solution containing n1 moles of solvent and n2 moles of solute is given byCp=(?H/?T)P,N eq(1)The pressure and compostion being constant. Upon differentiation with respect to n1,maintaining n2 constant,it follows thatCP1=(?CP/?n1)T,P,n2=?H/?T?n1 .eq(2)Where Cp1 is the partial molar heat capacity,at constant pressure,of the constituent 1 of the given solution. The partial molar heat constant H1 of this constituent is defined byH1=(?H/?n1)T,P,n2And indeed differentiation with respect to temp. gives(?H1/?T)P,N=?H/?T?n1 =CP1 .eq(3)The result being identical with CP1 by eq.(3).The partial molar heat capacity of the solvent is any particular solution thus be defined by either eq(1) and eq(2).Similarly,i.e.,constituent 2,Cp2=(?CP/?n2)T,P,n1=(?H2/?T)P,N ..eq(4)We know,Li=H1-H10Is differentiated with respect to temp.,at constant pressure and composition,it follows that(?L1/?T)P,N=(?H1/?T)P,N-(?H10/?T)P,N= Cp1-Cp10 eq(5)Where Cp1,identi cal with Cp1 or Cp1o, is the molar heat capacity of the pure solvent or the partial molar heat capacity of the solvent in a solution at infinite dilution. Thus, Cp10 may be regardedas an observational quantity, and if the variation of the relative partial molar heat content of the solvent with temperature,i.e. (?L1/?T)P,N, is known , it is possible to determine Cp1 at the corresponding composition of the solution. The necessary entropy are rarely available from direct thermal measurements of L1, such as thus described in 44f,at several temperatures, but the information can very much be obtained, although not very accurately from E.M.F measurements.By differentiating the expression for the relative partial molar heat content of the solute it is found, in an exactly similar fashion to that used above , that(?L2/?T)P,N=(?H2/?T)P,N-(?H02/?T)P,N=CP2-CP20 eq(6)In this expression,Cp20 is the partial molar heat capacity of the solute in the infinitely lose weight solution. Although the experimentel significance of the quantity is not immediately obvious.thus from a knowledge of the variation of L2, the partial molar heat content of the solute with temprature it should be possible to derive, with the aid of equation(6) , the partial molar heat capacity of the solute Cp2 at the given composition.E.Determination of partial molar properties1.Direct methodin view of the definition of the partial molar properties Gi asGi=(?G/?ni)T,P,n1,.. .eq(1)An obvious method ffor its aspiration is to plot the value of the extensive properties G,at constant temperature and pressure, for various mixtures of the two components against the number of moles,e.g.,n2,of the one of them,the value of n1 being kept constant. The slope of the curve at any particular composition,which maybe determined by drawing a tengent to the curve, gives the value of G2 at that comoposition. Since the molality of a solution represents the number of moles of solute associated with a constant mass,and hence a constant number of moles,the plot of the property G against the molality can be used for the evaluation of the partial molar property of the solute. Once G2 at any composition has been determined, the corresponding value of G1 is readily derived by means of the relationship,G=n1G1+n2G2In view of the difficulty of determining the exact slope of the curve at all points, it is preferable to use an analytical procedure instead of the graphical one just described. The property G is then denotative as a function of the number of moles of one component,e.g.,the molality, associated with a constant amount of the other component. Upon differentiation with respect to n,i.g.,the molality, an expression for the partial molar property is obtained.2.from apparent molar propertiesa method that is often more convenient and accuarate than that described above,makes use of the apparent molar property.We knowG-n1G1=n22If n1 is maintained constant,so that n1G1 is constant, differentiation with respe ct to n2 , constant temp. and pressure being understood,givesG2 =(?G/?n2)n1 = (?G/?n2)n1 + G eq(2)G2 = ((?G/? ln n2)n1+ G ..eq(3)Since the molality m is resembling to n2, with n1 constant, eq(2) and eq(3) may be scripted asG2= m (d G/dm)+ G eq(4)G2=( d G/d ln m)+ G ..eq(5)Respectively. If the apparent molar property G is determined for various set of n2 , with n1 constant , or at various molalities, the partial molar property G2 can be calculated from the slope, at any given composition, of the plot of G against n2 or against ln n2. The method based on the use of eqs(3)(5) is usally more accurate than that involving the logarithmic plot,since it does not give undue importance to result obtained in dilute solutions. An analytical method can, of course, be used in place of the graphical procedure if G can be expressed as a function of n2 or of the molality.For use in a later connection, an alternative form of eq(4) is required and it will be derived here. The right hand side of this equation is equivalent to d(m G)/dm, that is,m (d G/dm)= G2and upon integration, m varying between the limits of zero and m, and mdG between zero and mG, it is found thatmG=?0m G2 dmG=1/m?0m G2 dmfor dilute solutions,the molality is proportional to the molar concentration c, and hence it is permissible to put this result in the formG=1/c?0m G2 dmF. APPLICATION OF PARTIAL MOLAR PROPERTIESThese properties are very useful since each and every reaction in chemical science occurs at a constant temperature and pressure and under these conditions we can determine these with the help of partial molar properties. They are highly useful when specific properties of pure substances andproperties of mixing are considered. By definition, properties of mixing are related to those of the pure substance byHere * denotes the pure substanceM the mixing propertyz corresponds to the specific propertyFrom the definition of partial molar properties,substitution yieldsHence if we know the partial molar p roperties we can derive the properties of mixing.For the internal energy U, enthalpy H, Helmholtz free energy A, and Gibbs free energy G, the following holdwhereP is the pressureV is the volumeT is temperatureS is the entropyG. BIBLIOGRAPHY1. THERMODYNAMICS AND CHEMICAL residueAUTHOR K L KAPOOR2. THERMODYNAMICS FOR CHEMISTSAUTHOR SAMUEL GLASSTONE3. http//www.everyscience.com/Chemistry/Physical/Mixtures/a.1265.php4. http//www.everyscience.com/Chemistry/Physical/Mixtures/b.1266.php5. http//www.chem.ntnu.no/nonequilibrium-thermodynamics/pub/192-Inzoli-etal.pdf6. http//physics.about.com/od/thermodynamics/p/thermodynamics.htm7. http//www.chem.boun.edu.tr/webpages/courses/chem356/EXP5-Determination%20of%20Partial%20Molar%20Quantities.pdf