Partial molar property

Partial molar property INTRODUCTION A partial molar property is the contribution (per mole) that a substance makes to an overall property of a mixture. The easiest partial molar property to visualize is the partial molar volume, vj of a substance j the contribution j makes to the total volume of a mixture. we can see that although 1 mol of a substance has a characteristics volume when it is pure,1 mol of that substance can make different contributions to the total volume of a mixture because molecules pack together in different ways in the pure substance and in mixture. the partial molar volume at an intermediate composition of the watterethanol mixture is an indication of the volume the H2o molecules occupy when they are surrounded by a mixture of molecules representative of the overall composition(half water, half ethanol) for instance. when the molar fraction are both 0s. The partial molar volume, VJ, of any substance J at a general composition, is defined as: where 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 constant: 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 from: The 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. PARTIAL MOLAR GIBBS ENERGY The most useful partial molar quantity is the partial molar free energy Gi,pm. It is so useful that it is given the name of chemical potential and a separate sumbol  µi . the chemical potential is just another name for the molar Gibbs energy. For a substance in a mixture, the chemical potential is defined as being the partial molar Gibbs energy: i.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 constant: In the above plot, the partial molar Gibbs energy is greater at I than at II. The total Gibbs energy of a binary mixture is given by: where 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, pressure 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 follows: The 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. it is possible to use the relationships between G and H, and G and U, to generate the following relations: Now H=U+PV To measure partial molar volumes There are several ways that partial molar volumes can be measured. One way is to begin with one mole of a compound, call it component 1, add a small amount of component 2 and measure the volume, add a little more of component 2 and measure the volume again. Keep doing this until the desired concentration range has been covered. Then fit the volume data to a curve, for example, of the form, The constants, a, b, c, etc are obtained from the curve fitting and the first term is the molar volume of pure component 1. Then the partial molar volume of component 2 can be obtained by direct differentiation, Ideal Solutions We will define an ideal solution as a solution for which the chemical potential of each component is given by, whereis the chemical potential of pure component i, and Xi is the mole fraction of component i in the solution. whereis the vapor pressure of pure component i.) We have to prove that an ideal solution obeys Raoults law (using definition). Consider a solution of two components where the mole fraction of component 1 is X1. We know that the chemical potential of component 1 must be the same in the solution as in the vapor in equilibrium with the solution. That is, Equation 10 doesnt help us very much all by itself. However we have some more information. We know that for the pure component 1 we have X1 = 1, and we know that the pressure of component 1 vapor in equilibrium with the liquid is just the vapor pressure of the pure liquid, p1*, so that, which is Raoults law. [5]Chemical potential of an ideal gas the chemical potential  µ of an ideal gas at a given temperature is related to its pressure p through eq.  µ= µ + RT ln(p/p0) (15) where  µo is the standard chemical potential when the when the pressure of the gas is po, equation 15 suggest that at a given temperature, the pressure of the gas is a measure of its chemical potential. if inequalities in pressure exist in a gas container, the gas flows spontaneously from the high pressure region to the lower pressure region until the pressure is equalized throughout the vessel. In the later stage, the gas has the same value of chemical potential throughout the container. IMPORTANCE OF CHEMICAL POTENTIAL The chemical potentials are the key properties in chemical thermodynamics. the  µi determine reaction equilibrium and phase equilibrium. Moreover, all other partial molar properties and all thermodynamics properties of the solution can be found from the  µi ‘s APPLICATIONS Partial molar properties are useful because chemical mixtures are often maintained at constant temperature and pressure and under these conditions, the value of any extensive property can be obtained from its partial molar property. They are especially useful when considering specific properties of pure substances (that is, properties of one mole of pure substance) and properties of mixing. Δmix H ≠¡ H H*, Δ mixS≠¡ S S*, ΔmixG≠¡G G* Where H,S and G are properties of the solutions and H*,S*, And G* are properties of the pure unmixed components at the same T and P as the solution. the key mixing quantity is ΔmixG =G G*. The Gibbs energy G of the solution is G=iGi(where Gi is a partial molar quantity). The gibbs energy G* of the unmixed components is G*=iG*m,i(where G*m,i is the molar Gibbs energy of pure substance i). Therefore ΔmixG≠¡ G G* = i(Gi G*m,i) const T,P (1) which is similar for ΔmixV. we have ΔmixG = ΔmixH TΔmixS const T,P (2) which is a special case of ΔG =ΔH TΔS at constant T. ΔmixS and ΔmixV can be found as partial derivatives of ΔmixG. Taking (T,nj of eq(1), we have = i G*m,i) = i T,nj = i(Vi V*m,i) T,nj =ΔmixV (3) The changes ΔmixV, ΔmixU, ΔmixH, ΔmixCp that accompany solution formation are due entirely to changes in intermolecular interactions( both energetic and structural). However, changes in S,A and G result not only from changes in intermolecular interactions but also from the unavoidable increase in entropy that accompanies the constant T and P mixing of substance and the simultaneous increase in volume each component occupies. Even if the intermolecular interactions in the solution are the same as in the pure substances, ΔmixS and ΔmixG will still be no zero. GIBBS- DUHEM EQUATION A relation that imposes a condition on the composition variation of the set of chemical potentials of a system of two or more components, where Sis entropy, Tabsolute temperature ,Ppressure, nithe number of moles of the ith component, and ÃŽ ¼iis the chemical potential of the ith component. Also known as Duhems equation. Deriving the Gibbs-Duhem equation for volume. The total differential of the Gibbs free energy in terms of its natural variables is With the substitution of two of the Maxwell relations and the definition of chemical potential, this is transformed into: the chemical potential is just another name for the partial molar (or just partial, depending on the units of N) Gibbs free energy, thus The total differential of this expression is Subtracting the two expressions for the total differential of the Gibbs free energy gives the Gibbs-Duhem relation: FUGACITY The presences of molecular interactions distinguish the real gases from ideal gases where the molecular interactions are completely absent. For a real gas Vm ≠  RT/P and hence d µÃ¢â€°  RT d ln P. Since the ideal gas equations are not directly applicable to real gases, we are faced with a problem. We can either sacrifice the equations or the variable. If we abandon the general equation of chemical potential then we have to use various equation of state fitting with P-V-T data. The use of such equations of state will make the treatment more complicated. So we find it easier to retain the general form of the chemical potential and to define a new variable which has the dimensions and general properties of pressure. The new variable is called the fugacity, which is derived from the Latin fugere, to flee, and means literally ‘escaping tendency. It is denoted by f. it is a corrected pressure which applies to real gases. all the effects arising due to interactions are containe d in f. the chemical potential of a pure real gas can be expressed in a form  µ= µo + RT ln(f/atm)  µo is the standard chemical potential at unit fugacity. at very low pressure . the ratio (f/p) = ÃŽ ³ is called the fugacity coefficient. for an ideal gas f=p and the fugacity coefficient is unity. with this definition of the fugacity we may now express the chemical potential as:  µ= µo + RT ln(ÃŽ ³P/atm) =  µo + RT ln(P/atm) + RT ln ÃŽ ³ on compairing this expression with that for an ideal gas[ µideal =  µo + RT ln(P/atm) Condition of fugacity of a gas Let us consider the relation d µ= VmdP d µ = Vm(ideal)dP and d µ(real) = Vm(real) dP Let us consider a change in the state of the system from an initial pressure P ´ to a final pressure P, and let f ´ be the fugacity of the real gas at pressure P ´ and f the fugacity at pressure P. Integration of the expression for chemical potential yields (ideal) = m(ideal)dP or  µ(ideal)  µÃ‚ ´(ideal) = m(ideal)dP and  µ(real)  µÃ‚ ´(real) = m(real)dP but for an ideal gas the chemical potential is given by  µ(ideal) =  µo(ideal) + RT ln(P/atm)  µÃ‚ ´(ideal) =  µo(ideal) + RT ln(P ´/atm)  µo is the standard chemical potential.  µ(ideal)-  µÃ‚ ´(ideal) = RT ln(P/P ´) = m(ideal)dP (1) For the real gas  µ(real) =  µo(real) + RT ln(f/atm) and  µÃ‚ ´(real) =  µo(real) + RTln(f/atm)  µ(real)  µÃ‚ ´(real) = RT ln(f/atm) RT ln(f ´/atm) = RT ln(f/f ´) = m(ideal)dP (2) Taking the difference of equation (2) and (1), we get RT ln(f/f ´) RT ln(P/P ´) = m(real) Vm(ideal)]dP or RT ln(f/P) RT ln(f ´/P ´) = m(real) Vm(ideal)]dP (3) where = Vm(ideal) Vm(real) now, = + RT ln(f/p) RT ln(f ´/P ´) = + (4) If the pressure P ´ is very low then the gas will behave ideally and for this condition Vm(ideal) ≈ Vm(real) and = 1, The second term or left side and right side of equation (4) will be equated to zero, therefore RT ln(f/P) = or ln(f/P) = -1/RT Antilograthim gives (f/P) = exp or f= P exp( = P exp[Vm(real) Vm(ideal) )]dP (5) SUMMARY we had covered in this term paper about partial molar properties one important thing is The properties of a solution are not additive properties, it means volume of solution is not the sum of pure components volume. When a substance becomes a part of a solution it looses its identity but it still contributes to the property of the solution. The term partial molar property is used to designate the component property when it is a mixture with one or more component solution. the most important partial molar quantity is the partial molar free energy it is an intensive property because it is a molar quantity.it is denoted by  µi.now we also know that how to measure the partial volume. and then the ideal solution is the solution in which the components in pure form here we take the pure components of chemical potential . then the applications of partial molar property is the property of mixing which is very useful. it is defined in term paper and the important concept Gibbs duhem equation A relation that imposes a condition on the composition variation of the set of chemical potentials of a system of two or more components physical significance is that if the composition varies,the chemical potentials do not change independently but in a related way.and then included fugacity another important part of partial molar properties. The fugacity f plays the role of pressure and need not be equal to the actual pressure of the real gas. RESULT The overall result is the partial molar property is not of all about pure components. The term partial molar property is used to designate the component property when it is a mixture with one or more component solution. and also find out the chemical potential other name of gibbs energy and about ideal gases, fugacity.

Truth About God :: essays research papers

Truth About God "You are just like your fathers: You always resist the Holy Spirit! Was there ever a prophet your fathers did not persecute? They even killed those who predicted the coming of the Righteous One." - Acts 7:51-52 The Jews have always been afraid of the radicals of God. They have always dwelled in the safety and understandings of the past and fear the effects of these radicals. But when these radicals like the prophets arrive, they persecute them because they are uncertain about the truth. An example is when the Jews didn't want to believe Stephen in Acts 7:56-58, " Look,' he said, I see heaven open and the Son of Man standing at the right hand of God.' At this they covered their ears and yelling at the top of their voices, they all rushed at him, dragged him out of the city and stoned him." A lot of potshots have been taken at the Church over the years. In spite of its obvious imperfections, the Church is the means that has been chosen to carry the message of the Gospel to the world. One wonders why a better system could not have been devised. Then one realizes that any system that has people in it is going to be imperfect. Alexander Solzhenitsyn wrote in the Gulag Archipelago that it was in prison where he learned that the line separating good and evil passes not through states, not through classes, not through political parties, either, but right through every human heart and through all human hearts. When we give ourselves serious evaluation, we find things hiding in our hearts that, if we could choose, we would remove. Our hearts have been described as "a zoo of lust, a bedlam of ambitions, a nursery of fears, a harem of fondled hatreds." Yet the Church, by its very nature, must be made up of the likes of us. "Imagine yourself as a living house," wrote C. S. Lewis. "God comes in to rebuild that house. At first, perhaps, you can understand what He is doing. He is getting the drains right and stopping the leaks in the roof and so on. But presently He starts knocking the house about in a way that hurts abominably and does not seem to make any sense. What on earth is He up to?

Human and Monster Help People

In the Frankenstein, there are six characters that die in the novel. What is the fundamental cause of their death? Who is the real killer? One may argue that this question is meaningless because it is obvious that the nameless monster kills almost every character except victor’s mother, who died naturally. However, the real killer should not be just the one who kills people by his hand, but the one who causes the death of so many innocent people, fundamentally. In the novel, initially, the nameless creature is a really benevolent creature, but, with time went by, people’s discrimination gradually changed him to devil, who determined to revenge his creator by killing his beloved. Therefore, discrimination is the real killer. First, examining how the six characters died may lead to insight for the questions on hand. Caroline Beaufort, Victor’s mother, dies of scarlet fever. William Frankenstein, Victor’s youngest brother, is strangled by monster in the woods outside Geneva. Justine Moritz, a young girl adopted into the Frankenstein household, is executed for William’s murder. Henry Clerval, victor’s boyhood friend and Elizabeth Lavenza, victor’s the wife, are strangled by the monster too. Alphonse Frankenstein, Victor’s father, is overcome with grief over the deaths of his close family members. The monster is, directly or indirectly, involved every time character dies except victor’s mother’s death. But why does he do this? Is that because of his nature? No. The monster is virtuous at the beginning. The whole village was roused; some fled, some attacked me, until, grievously bruised by stones and many other kinds of missile weapons, I escaped to the open village, and fearfully took refuge in a low hovel, quiet bare, and making a wretched appearance. † (73) I found the monster’s reaction to people’s sudden attack is not him fighting back or an act of revenge, which is the normal response of ki ller or any other evil creature, but escape. â€Å"I lay on my straw, but I could not sleep. I thought of the occurrences of the day. What chiefly struck me was the gentle manners of these people; and I long to join them, but dare not†. The monster wants to merge into a warm family instead of trying to hurt them. It means he also really wants to be loved and love others. The above quotes suggest that the monster’s nature is good, meaning he is not the one to harm another purposefully. How does a nice creature, which goes after love, gradually become an evil devil? Something must have happens and gradually change his thoughts. Look at how he was born. â€Å"It was dark when I awoke; I felt cold also, and half frightened, as it were, instinctively, finding myself so desolate. (71) This description above shows the monster is left alone by Victor because of the monster’s appearance and suffered from coldness and loneliness since the first day when he was created, while it is just the start of his miserable life. Look at the first times when he met a human being. Suffering from hunger, the nameless creature went into a small hut and an old man sat there. â€Å"He turned on hearing a noise, and perceiving me, shrieked loudly, and quitting the hut, ran across the fields with a speed of which his debilitated form hardly appeared capable†(72). Once the old man notices the nameless creature and runs away because the monster’s appearance is terrifying and he assumes the monster will hurt him. We can see the old man as a representative of the ordinary people. He judges the nameless creatures by his appearance instead of quality. Imagine this situation: you are a really nice person and keep trying to make friends with others, but they discriminates you because of your skin color, gender or any other characters you have. This will make every emotional creature hurt. Actually the monster’s situation is even worse than that, because he has no companion and the only reason why everyone in this world discriminate him is his terrifying appearance which is not his fault. Therefore, it is reasonable for his inner world to gradually become dark. If people just try to avoid him, maybe, it is still acceptable. But what if his beloved try to destroy him? Please look at this sentence: â€Å"Agatha fainted, and Safie, unable to attend to her friend, rushed out of the cottage. Felix darted forward, and with supernatural force tore me from his father, to whose knees I clung, in a transport of fury, he dashed me to the ground and struck me violently with a stick. I could have torn him limb from limb, as the lion rends the antelope. But my heart sank within me as with bitter sickness, and I refrained. †(94) At the sight of the monster, worrying about monster will hurt his father, Felix spares no effort to attack the monster , while the monster is the one who had always been trying to help this family alleviate life burden and been eager to become a part to his family. Wronged and beaten by those cottagers, monster still refrained from desire to fight back, even though he is strong enough to tear Felix up. It is not the deed of a killer. How many human beings can be as tolerable as him? In a sense, the monster is even nobler than many of us. However, people regard this creature, which looks scary, as a monster, which is hostile to human. Nobody cares about it comes with a heart of gold. In this case, how does he feel? His feelings are afflicted and intensively contradictory. When I thought of my friends, of the mild voice of De Lacey, the gentle eyes of Agatha, and the exquisite beauty of the Arabian, these thoughts vanished and a gush of tears somewhat soothed me. But again when I reflected that they had spurned and deserted me, anger returned, a rage of anger, and unable to injure anything human, I turned my fury towards inanimate objects. †(97)Through these sentences, we can feel the monster’s inner struggle. He wanted to vent his i ndignation and hatred, but at the thought of his â€Å"protector†, he calmed down. Then, once he thinks of their departure and aversion to him, rage came back. However, he only turned his anger to inanimate stuff. He wants to revenge for what people have done to him but his nature tells him he shouldn’t do that. Even if he can’t control his anger, he still tries to minimize the damage by only destroying inanimate stuff. He wants to be a genuine person and gets along well with human being, but was rejected and hurt again and again. The reality tortured him emotionlessly. He was perplexed at that time. His thought was not as benevolent and pure as before. The discrimination of human being towards him made him started thinking of revenge. However, there is something worse waiting for him. â€Å"This was then the reward of my benevolence! I had saved a human being from destruction, and as recompense I now writhed under the miserable pain of a wound which shattered the flesh and bone. The feelings of kindness and gentleness which I had entertained but a few moments before gave place to hellish rage and gnashing of teeth. Inflamed by pain, I vowed eternal hatred and vengeance to all mankind. † (99) This is the description of the inner world of monster after being shot by a peasant whose daughter was saved by monster. He tried his best to save a girl and it’s the evidence of his heart of gold. However, the girl’s father never thought of why he save her life and try to restore her animation, but shot him because his appearance makes him look like a monster which will hurt human being. What if it is a human being that saves the girl? Usually, the peasant will show his gratitude and might even ask him to have a meal. If we compare these two conditions, we will find the deed of the saver is the same and but the attitude of peasant will be different. What determines the differences is the appearance of the saver. Humanlike saver is regarded as a nice person and creature which has strange or frightening appearance is regarded as devil. Isn’t that a kind of discrimination? The cruelty of reality kept swallowing his benevolence until the only thing left him to do is revenge. When the monster compromised to victor at the condition of creating a female companion for him, Victor broke his promise because he thought creating another creature like monster can only bring troubles. It is a reflection of discrimination. â€Å"As I looked on him, his countenance expressed the utmost extent of malice and treachery. I thought with a sensation of madness on my promise of creating another like to him, and trembling with passion, tore to pieces the thing on which I was engaged. † (119)This scene happened after Victor seeing the face of monster. When Victor was about to finish his work, he started to think creating another creature like monster can only bring more tragedies and decided to destroyed the monster’s female companion. It is true that the monster killed his brothers, but it is because there are too many miseries happened, revenge becomes the only thing he want to do to vent his indignation. We should notice that the monster can bring more sorrow to Victor and even other human beings, if only he wanted. However, if he didn’t do that, it means, in his deep heart, he is still benevolent creature. Nevertheless, Victor never care about how many good deeds the monster has done or the happiness of the creature he create, but only thought that the negative consequence of what the creature would make. Victor assumed the monster can never be a good creature, so his thought and decision are the reflection of discrimination on the monster. When we try to synthesis every part of novel I mentioned before, we will find the nature of this monster is good, but, gradually, the only thing in his mind is to revenge. What kind of thing makes a so nice creature become an evil? The answer is countless misery and injustice he experienced. Why does a nice creature have to suffer so much? Is that because of the fault of God? No! It is because of the discrimination. No matter how many times the monster help people, everyone in the novel, even children, thinks this creature is evil and tries to hurt people, so they avoid him, hurt him and even try to kill im. A nice creature never receives love or even sympathy because of his appearance, and, regardless of how the monster felt, his creator destroyed his last hope of being loved, so he wanted to see his creator was as painful as he was and decided to murder victors’ beloved. Now we can see that discrimination makes the nameless benevolent creature become a devil, contributing to the death of innocent people. So the real killer should be human being’s discrimination.

The Infection And Prevalence Of Hiv Among Adults And...

The Infection and Prevalence of HIV among Adults and Adolescents in the United States Kuljit Kaur Sidhu I.D. #16822472 Summer Session I 2015 Professor Jaime Allgood I. The Public Health Problem The United States is facing a flourishing epidemic of Human Immunodeficiency Virus (HIV) infections which is rapidly progressing and contributing to the rising mortality rates. HIV is an infection that is caused when a virus attacks the immune system which is the body’s natural defense system and without a strong immune system, an individual’s body is too weak to fight off infections. The strongest component of the immune system to fight off infectious diseases is white blood cells. HIV infects and destroys†¦show more content†¦Individuals with HIV may not notice and/or realize their symptoms because they may not appear for up to 10 years (CDC, 2013). The symptoms include rapid weight loss, recurring fever and/or profuse night sweats, extreme and unexplained tiredness, prolonged swelling of the lymph glands in the armpits, groin, or neck, and/or diarrhea that lasts for more than a week. Within the United States, over 1.2 million people are living with HIV infection and about 13% of them are unaware of their infection. Additionally, it is estimated that 50,000 new HIV infections are developing each year (CDC,2013). In the year 2013, about 47,352 people were newly diagnosed with HIV infections and overall 1,194,039 have been diagnosed with AIDS (CDC, 2013). Unfortunately in the year 2012, about 13,712 people with AIDS and about 670,000 people in the United States have died overall because they were unaware of their infection which caused them to develop AIDS, the untreatable disease (CDC, 2012). In regards to a concentrated population, adolescents/adults (age 13 years and over), carry the highest risk for HIV infections (Campsmith,2010) . In the year 2006, about 1,106,400 adolescents/adults were diagnosed and living with HIV in the United States and about 232,700 individuals who were unaware of their infection and went undiagnosed