Heat of Reaciton; Enthalpy

Supposethat we are interested in studying some physical or chemical change. The substance or mixture of substances in which this change occurs i called the system. The surroundings are everything in the vicinity of this system. For example, if we are interested in the reaction of barium hydroxide octahydrate with ammonium thiocyanate, this reaction mixture is our system, and the reaction vessel and everything outside it are the surroundings. Heat is defined as energy that flows into or out of a system, because of a difference in temperature between the system and its surroundings. As long as a system and its surroundings are in thermal contact (that is, not thermally insulated freom each other), energy-heat-flows between them to establish temperature equality or thermal equilibrium. Heat flows from a system at high temperature to one at low temperature; but once thermal equilibrium is established, heat flow stops.

 Suppose, for example, that a system and its surroundings are both initially at 25 C. They are in thermal equilibirum and no heats flows. Imagine that we initiate a chemical reaction in the system so taht the temperature rises. Heat begins to flow from the system to the surroundings. It continues to flow until the reaction stops and the temperature of the system equals the temperature of the surroundings. If, on the other hand, the temperature of the system falls because of the reaction, heat flows from the surroundings to the system – the system absorbs heat. It will continue to absorb heat until the reaction stops and the temperature of system equals the temperature ef the surroundings

 The total amount of heat that is evolved or absorbed by a system at a particular temperature (25 C in the previous example) because of chemical reaction is called the heat of reaction. A chemical reaction or physical change is exothermic when heat is evolved, and endotermic when heat is absorbed. Experimentally, we note that in the exothermic case the reaction flask warms; in the endothermic case, the reaction flask cools.

 We will use the symbol q to denote heat. When heat is absorbed by a system, energy added to it; by convention, the number assigned to q is positive. Thus, for an endothermic reaction, the heat, q, is a positive quantity. On the other hand, when heat is evolved durin a reaction, energy is substract from the system. The number assigned to q for an exothermic reaction is negative. The sign conventions for q are summarized below.

 Enthalpy

When one mole methane burns in oxsygen to give carbon dioxide and liquid water, the amount of heat that is released depends on how the experiment is carried out. If the reaction occurs in the atmosphere, where the pressure is constant (equal to that of atmosphere), the quantity of heat evolved at 1 atm and 25 C is 890 kj (q= -890kj). On the other hand, if this same reaction is done in a closed container, the heat evolved at 25 C is 883 kj (q = -883 kj). In this cesa, although the volume of the system is constant (equal to the volume of the container), the pressure changes during the reaction.

 Most reactions are carried out in beakers or flasks that are open to the atmosphere. In these cases, the volume changes but the pressure is constant, since it must equal that of the surrounding atmosphere. Yhe heat of reaction at constant pressure,qp, is related to a property of the reactants and products called enthalpy (or heat content). Enthalpy (denoted H) is a property of a substance, like mass and volume. Every substance has a definite quantity of enthalpy, just as it definite mass and definite volume. The enthalpy of a substance depends on the amount of substance. Two moles of substance have twice as much enthalpy as one mole of substance. The quantity of enthalpy in a mol of substance depends only on those variables, such as temperature and pressure, that determine the state of the substance. Therefore, enthalpy is said to be a state function, or a state property.

 Using the symbol  D  (meaning ‘’change in’’), we write the change in enthalpy as DH . The change in enthalpy for a reaction (called the enthalpy of reaction) is obtained by subtracting the enthalpy of the reactants from the enthalpy of the product:

                                   DH   = H (products) – H (reactants)

The heat of reaction at constant pressure equals the enthalpy of a reaction:    qp = DH

Atomic Orbital Shapes

An as orbital has a spherical shape, though specific details of the probability distribution depend on the value of n. Figure shows cross sectional representation of the probability distribtions of a 1s and 2s orbital. The color shading is darker where the electron is more likely to be found. In the case of a 1s orbital (figure left), the electron is most likely to be found near the nucleus. The shading becomes lighter as the distance from the nucleus increases, indicating that the electron is less likely to be found far from the nucleus.

 The orbital does not abruptly end at some particular distance from the nucleus. An atom, therefore, has an indefinite extension or ‘’ size.‘’ We can gauge the ‘’ size‘’ of the orbital by means of the 99% contour. The electron has a 99% probability of being found within the space of the 99% contour (the dashed line in the diagram).

 A 2s orbital differs in detail from a 1s orbital. As shown in figure right, the electron in a 2s orbital is likely to be found in two regions, one near the nucleus and the other in a spherical shell about the nucleus. The 99% contour show that the 2s orbital is larger than the 1s orbital.

 A cross-sectional diagram cannot portray the three-dimensional aspect of the 1s and 2s atomic orbital.

 There are three p orbitals in each subshell, starting with the 2p subshell. All p orbitals have the same basic shape (two lobes arranged along a straight line with the nucleus between the lobes) but differ in their orientations in space. Since the three orbitals are set at right angles to each other, we can show each one as oriented along a different coordinate axis . We denote these orbitals as 2px, 2py, and 2pz. A 2px orbital has its greatest electron probability along the x-axis, a 2py orbital along the y-axis, and a 2pz orbital along the z-axis. Other p orbitals, such as 3p, have this same general shape, with differences in detail depending on n. We will discuss s and p orbital shapes again on chemical bonding.

  

There are five d orbitals, which have more complicated shapes than s and p orbitals. These are represented in figure. 

 

Sodium Acetate (Hot ice) & Sulphuric Acid and Sugar

   Providing you kept it perfectly straight and thus balanced the quantity of the CH3COONa on either side, could you literally keep on going forever until the force of gravity acting on it became too strong for the top and it collapsed... 

  Thank you for interest... See you all friends... : )

Quantum Numbers and Atomic Orbitals

According to quantum mechanics, each electron in an atom is described by four different quantum numbers. There of the quantum numbers (n, 1, and ml) specify the wave function that gives the probability of finding the electron at various points in space. A wave function for an electron in an atom is called an atomic orbital. An orbital should not be confused with a bohr orbit. An atomic orbital is pictured qualitatively by describing the region of space where there is high probability of finding the electrons. The atomic orbital so pictured has a definite shape. A fourth quantum number (ms) refers to a magnetic property of electrons called spin. In this sections we will first look at quantum numbers, then at atomic orbitals.

 Quantum Numbers

 The allowed values and general meaning of each of the four different quantum numbers of an electron in an atom are as follows:

1.       Principal quantum number (n) This quantum number is the modern equivalent of the n quantum number in Bohr’s theory. It can have any positive whole number value, 1, 2, 3, and so on.

The energy of an electron in an atom depends principally on n. The snaller n is, the lower the energy. In the case of the hydrogen atom or any other single-electron atom (such as Li +2 or  He + ), it is the only quantum number determining the energy (which is given by Bohr’s formula, discussed. For other atoms, the energy also depends to a slight extent on the l quantum number.

 The size of an orbital also depends on n. The larger the value of n is, the larger the orbital. Orbitals of the same quantum state n are said to belong to the same shell. Shells are sometimes designated by the following letters:

           Letter   K   L   M   N…

             n        1   2   3    4…

2.       Angular momentum quantum number (l) (also called azimuthal quantum number) Within each shell of quantum number n, there are n different kinds of orbitals, each with a distinctive shape, denoted by the l quantum number. The allowed values of the l quantum number are the integers from 0 to n-1(Note that the value 0 is allowed for l.). For example, if anelectron has a principal quantum number of 3, the possible values for l are 0, 1, and 2. Thus, within the M shell (n=3), there are three kinds of orbitals, each of which has a different shape for the region where the electron is most likely found.

Orbitals of the same n, but different l, are said to belong to different subshells of a given shell. The different subshells are usually denoted by letters.

              Letter    s   p   d    f   g…

                  l        0   1   2   3   4…

To denote a subshell within a particular shell, we write the value of the n quantum number for the shell followed by the letter designation for the subshell. For example, 2p denotes a subshell with quantum number n=2  and l=1.

3.       Magnetic quantum number (ml)  Except for an s subshell, there is more than one orbital for each subshell. For a p subshell, for example, there are three different orbitals l. There are always 2l + 1 orbitals in each subshell of quantum number l. Thus, for l=2 (the d subshell), there are (2*2) + 1 = 5 orbitals. One way of designating these orbitals within a subshell is with the magnetic quantum number, ml. The magnetic quantum number can have any whole number value from –l  to  +l . For l = 2, the possible values of ml are -2, -1, 0, 1, and 2.

Essentionally each of these orbitals of a subshell has the same shape, but a different orientation, or direction, in space. Each orbital of a particular subshell (no matter how it is oriented in space) has the same energy.

4.       Spin quantum number (ms) An electron acts as though it were spinning on its axis like the earth. Such an electron spin would give rise to a circulatin electrical charge that would generate a magnetic field. Thus, an electron behaves like a small bar magnet, with a north and south pole. The spin quantum number , ms, refers to the two possible orientations that are allowed im quantum mechanics for this magnet or spin. Values for the spin quantum number are +1/2 and

-1/2.

Table 5.2 lists the permissible quantum numbers for all orbitals through the n = 4 shell. These velues follow from the rules just given. Note that all orbitals with the same principal quantum number, n, have the same energy. For atoms with more than one electron, however, only orbitals in the same subshell (denoted by a given n and l) have the same energy

Chromatography

Chromatography is the name given to a group of similar, very useful seperation techniques that involve a stationary phase and a moving, or mobile, phase. The seperation of dye pigments by chromatography can be seen if a drop of ink is placed on a sheet of paper. The spot grows our –tword by capillary action or wetting, each dye moving with the solution at a different, but characteristic, rate. The result is a dark disk surrounded by colored rings. Wetted paper fibers form the stationary phase, and the ink solution is the mobile phase. The rate at which each dye moves depends upon how strongly the dye is attracted to the wet fşbers in the paper.

 The Russian botanist Mikhail Tswett was the first to seperate chemical substances by chromatography. He described the use of column chromatography in 1906. Tswett disvolved the pigments from plant leaves with the liquid petroleum ether.  After packing a glass tube or column with powdered chalk (calcium carbonate, CaCO3 ), he poured the solution of plant pigments into the top of the column. When he washed, or eluted, the column by pouring in more pure petroleum ether after the solution, it began to show distinct yellow and gren bands. These bands, each containing a pure pigment, became well separated as they moved down the column, so that the pure pigments could be obtained.

 Vapor phase chromatography (VPC), also called gas chromatography (GC), is a more recent separation method. Here the mobile phase consists of a mixture of gaseous or vaporized substance plus a gas such as helium, called the carrier, that acts as an eluting agent. The stationary phase consists of a solid or a liquid adhering to a solid, packed in a column. As the gas passes through the column, substances in the mixture are attracted differently to the stationary phase and thus are separated.

 Vapor phase chromatography is a rapid method of separating mixtures and has become important in chemical synthesis, the preparation of complicated substances from simpler ones. A synthesis may require many chemical reactions, each one followed by the separation of product. With vapor phase chromatography, a synthesis that formerly took months might instead be complated in days. Vapor phase chromatography can also be used to detect minute quantities of sunstances. For example, as little as a picogram of amphetamine can be detected in urine using vapor phase chromatography with a special detector.

Diffusion and Effusion

Gaseous diffusion is the process whereby a gas spreads out through another gas to occupy a space with uniform partial pressure. A gas or vapor having a relatively high partial pressure will spread out toward regions of lower partial pressure of that gas until the partial pressure becomes equal everywhere in the space. Thus, if we release an odorous substance at one corner of a room, minutes later it will be detected at the opposite corner. (It is well known, for example, how quickly the smell of baking apple pie draws people to the kitchen.)

We might consider the spread of an odor in minutes to be fast yet when we think about our kinetic-theory calculations of molecular speed, we might ask why diffusion is not even much faster than it is. Why does it take minutes for the gas to diffuse throughout a room when the molecules are moving at perhaps a thousand miles per hour? This was in fact one of the first criticisms of kinetic theory. The answer is simply that a molecule never travels very far in one direction (at ordinary pressures) before it collides with another molecules and moves off in another direction. If we could trace out the path of an individual molecule, it would be a zigzagging trail reminiscent of Brownian motion. For a molecule to cross a room, it has to travel many times the straight-line distance.

Although the rate of diffusion certainly depends in part on the average molecular speed, the effect of molecular collisions makes the theoretical Picture a bit complicated. Effusion, like diffusion, is a process involving the flow of a gas, but is theoretically much simpler.

If we place a container of gas in a vacuum and then make a very small hole in the container, the gas escapes through the hole at the same speed it had in the container. The proses is called effusion. It was first studied by Thomas Graham who, in 1846, discovered the law that bears his name. Graham’s law of effusion states: The rate of effusion of gas molecules from a partivular hole is inversely proportional to the square root of the molecular weight of the gas at constant temperature and pressure.

Let us consider a kinetic-theory analysis of an effusion experiment. Suppose the hole in the container is made small enough so that the gas molecules continue to move randomly (rather than moving together as they would in a wind). When a molecule happens to encounter the hole, it leaves the container. The collection of molecules leaving the container by chance encounters with the hole constitutes the effusing gas. All we have to consider for effusion is the rate at which molecules encounter the hole in the container.

The rate of effusion of molecules from a container depends on three factors: (1) the cross-sectional area of the hole (the larger this is, the more likely molecules are to escape); (2) the number of molecules per unit volume (the more crowded the molecules are, the more likely they are to encounter the hole); and (3) the average molecular speed (the faster the molecules are moving, the sooner they will escape).

If we compare the effusion of different gases from the same container, at the same temperature and pressure, factors (1) and (2) will be the same. The average molecular speeds will be different, however.

Since the average molecular speed essentially equals , where is the molar mass, we see that the rate of effusion is proportional to 1/ . That is, the rate of effusion is inversely proportional to the square root of the molar mass (or molecular weight), as Graham’s law states. The derivation of Graham’s law from kinetic theory was considered a triumph of the theory, and greatly strengthened confidence in its validity.

 

Graham’s law effusion:

Rate of effusion of molecules α 1/ (for the same container at constant T and P)

Grahams law has practical application in the preparation of fuel rods for nuclear fission reactors. Such reactors depend on the fact that the uranium-235 nucleus undergoes fission (splits) when bombarded with neutrons. When the nucleus splits, several neutrons are emitted and a large amount of energy is liberated. These neutrons bombard more urenium-235 nuclei, and the process continues with the evolution of more energy. However, natural uranium consist of 99.27% uranium-238 (which does not undergo fission) and only 0.72% uranium-235 (which does undergo fission). A uranium fuel rod must contain about 3% uranium-235 to sustain the nuclear reaction.

To increase the percentage of uranium-235 in a sample of uranium (a process called enrichment), one first prepares uranium hexafluoride, U , a white, crystalline solid that is easily vaporized.

Uranium hexafluride vapor is allowed to pass through a series of porous membranes. Each membrabe has many small holes through which the vapor can effuse. Since the U molecules with the lighter isotope of uranium travel about 0.4% faster than the U molecules with the heavier isotope, the gas that passes through first will be somewhat richer in uranium-235 vapor becomes further concentrated. It takes many effusion stages to reach the necessary enrichment; for complete sepetaration of the isotopes, as required for bomb-grade uranium, about two million effusion stages are needed.

Separation Of Mixtures

The separation of mixtures into their components is of great commercial importance, as well as a necessary step in the preparation of a pure compound in the laboratory. A raw ore is often treated to obtain the pure metal compound before subsequent steps are undertaken to isolate the desired metal. The juice of sugar beets ore cane is concentrated, crystallized, an centrifuged to give white table sugar. Steel objects are picked out by magnetic separators from other refuse at recycling plants. In this, we will discuss three common methods for separating mixtures: filtration, distillation, and chromatography.

Filtration is the process of seperating solid particles suspended in a liqued solution by pouring the mixture through a filter. For example, photografic developing solution contains silver compounds. If sodium chloride is added to the devoloping solution, fine crystals of silver chloride form. When this mixture is pured in to a cone made of filter paper, the solution passes throug, leaving the silver chloride behind. In this way, the silver can be recovered from the developing solution (as silver chloride)

A liquid or solid that changes readily to the gaseous state is said to be volatile, When the temperature of a volatile liquid is increased sufficiently, the liquid boils, changing rapidly to the gaseous or vapor state. Distillation uses the differences in volatility of substances to seperate a solution into its components. For example, if a solution of sodium chloride in water is heated, the water (which is fairly volatile) boils off, leaving behind sodium chloride (which is not volatile)



Figure 1: A simple distilation apparatus. Volatile components pass from the flask into the condenser. There the vapor changes back to liquid, which is collected in the receiver. Less volatile components remain in the distillation flask.

Figure 1 shows a typical laboratory distillation apparatus. The sodium chloride solution is placed in the distillation flask and heated. The water vaporizes and passes into the condenser, leaving sodium chloride crystals in the flask. In the condenser, the water vapor is cooled and changes back to a liquid. The pure (distilled) water is collected in the receiver.

Fractional distillation is useful when the solution consists of two or more volatile components. The temperature at which a liquid boils is known as its boiling point. When a solution containing liquid substances of different boiling points is distilled, the substance whith the lowest boiling point normally distills over first. A fractionating column, containing glass beads, is placed at the top of the column, being hotter at the bottom and cooler at the top. The substances with the lowest boiling point passes over into the condenser from the top of the column, whereas substances with higher boiling points condence on the beads in the column or remain in the distillation flask. As the substance of lowest boiling liquid increases and the next substance, now the one with the lowest boiling point, begins to distill. Fractional distillation is employed commercially to seperate crude oil or petroleum in to useful product. For this, the distillation is operated continuously, various fractions being takeb off at different heights up the fractionating column. Thus the lowest boiling fraction (20 -60 C), called petroleum ether, is obtained near the top of column. Light naphtha or ligroin is a fraction with a slightly higher boiling point (60 -100 C), and it is taken off the column just below the petroleum ether. Gasoline boils between 50 C and 20 C, and kerosene between 175 C and 275 C; these come off even lower on the column. Furnace and diesel fuels boil at stil higher temperatures.