Cited By. This article is cited by 12 publications. Abul Fazal, Annette F. Raigoza, Christen M. Strollo, Alicia A. Journal of Chemical Education , 97 4 , Enthalpy and the Second Law of Thermodynamics.
Journal of Chemical Education , 96 7 , Raff, , William R. Journal of Chemical Education , 96 2 , In more general terms though, entropy is really a measure of the system disorder; the more particles we have, the more possible arrangements we have, and essentially the more mess we can make. Imagine a bedroom: Take out all the clothes and put them on the floor. The more clothes we own, the more of a disordered mess the floor of the room will be.
The same is true of molecules. The distribution of gas particles is just one way to see the effects of entropy. As we will see in the next section, entropy determines not only how particles arrange themselves in space, but also how heat flows between objects. In the previous section, we saw how the random movement of gas particles leads to an even distribution of those particles inside a container.
In other words, the spread-out macrostate has the most entropy. Energy Quanta Like particles of gas, energy quanta also distribute themselves according to statistical mechanics. A similar analysis explains why heat flows from hot objects to cold objects. When two objects of different temperature are brought into contact, the quanta of energy distribute themselves uniformly throughout just like gas particles spreading throughout their container.
Just as the most probable macrostate for the gas particles was , the most probable macrostate for the energy quanta is As noted in the introduction to this unit, exothermic reactions are often but not always spontaneous.
The underlying reason for this is that exothermic reactions increase entropy by releasing quanta of energy. The quanta spread out, and entropy increases.
Thus, exothermic reactions tend to be spontaneous. Energy quanta can spread by transferring from one particle to another throughout an object, but they can also spread out in a different sense. Not only can a quantum jump between particles, but it can also cause the particle to move in different ways. Figure A quantum of energy might make a particle move through space faster; this is called translational energy. It also might cause a molecule to rotate in place; this is called rotational energy.
Finally, a quantum of energy might cause the bonds of a molecule to vibrate. This vibrational energy causes chemical bonds to stretch and contract, or to bend and straighten. Energies Energy can cause a molecule to move in different ways: vibration of its bonds, rotation of the molecule as a whole, or translation movement through space. The more ways a molecule can move, the more ways quanta of energy can be distributed.
The water molecules in an ice cube can only vibrate in place. Quanta of energy are restricted to vibrational energy, and therefore ice has a low entropy value. In liquid water, the quanta can spread out to cause vibration and rotation; liquid water has higher entropy.
Gaseous water steam has the highest amount of entropy because the molecules possess vibrational, rotational, and translational energies. In the previous sections, we saw that high entropy is associated with two things: a wide distribution of particles and a wide distribution of energy quanta.
The more particles and energy quanta can spread out, the more entropy there is. Bearing this in mind, it should make sense that a substance in the solid phase would have relatively low entropy. In a solid, the particles are locked in place and highly ordered, the clear opposite of disorder or entropy.
The quanta of energy in a solid are restricted mainly to vibration, so the distribution of quanta is also minimized. Entropy and the States of Matter Entropy increases as temperature increases and as a substance changes from solid to liquid to gas.
The entropy of the liquid phase is higher. The particles are no longer locked in place. Because they are now free to move, they can distribute themselves in more ways. The energy quanta can distribute themselves in a greater variety of ways as well. Like a solid, the molecules can vibrate; but because they have more freedom of movement, molecules have rotational and some translational energy, too.
Gases have the highest entropy values because they have the greatest freedom of movement. Gas particles are separate and distribute themselves throughout their container see Section 2: Microstates, Macrostates, and Matter.
And, gases also possess all three types of energy: translational, rotational, and vibrational. Finally, a substance that is dissolved in a liquid also has a high level of entropy for reasons similar to gases. Dissolved particles are free to not only move throughout the volume of the liquid, but also to move in all three ways. Generally speaking, the entropy value of a dissolved substance is higher than pure liquids but less than gases. To summarize, the entropy of the phases of matter are:. Using this information, we can make an educated guess about whether entropy is increasing or decreasing when a chemical reaction occurs.
Consider the following reaction in which solid table salt dissolves in water:. In this case, a solid low entropy is turning into two aqueous ions higher entropy. We can reasonably assume that entropy increases. As we know, this reaction is spontaneous; salt dissolves in water. Consider another spontaneous process, the sublimation of dry ice solid CO 2 :. Both of the above reactions are spontaneous, and both produce products with higher entropy than the reactants.
It may be tempting, then, to assume that all such reactions are spontaneous. But consider the burning of hydrogen gas:. Yet, the reaction is spontaneous; hydrogen is highly flammable. As the previous sections have shown, chemical reactions that increase entropy tend to be spontaneous. Section 3 demonstrated that exothermic reactions increase entropy by allowing a wider distribution of energy quanta. Section 4 illustrated how reactions that create liquids and gases also tend to increase entropy.
What now remains is to combine these two factors to create a complete picture—a way to definitively determine if a reaction will be spontaneous.
When they both oppose spontaneity, the reaction is never spontaneous. In the s, American mathematician Josiah Willard Gibbs — developed the concept of Gibbs free energy given the variable G and an equation that determines whether or not a reaction will happen spontaneously.
The Gibbs free energy of a system depends on the enthalpy, entropy, and absolute temperature of the system the derivation of this equation is beyond the scope of this text :.
Although the entropy of the system decreases in this reaction, it is more than offset by the heat released to the surroundings. Again, this conforms to experience; below its melting point, a solid will not melt. Indeed, the reverse reaction is spontaneous at these lower temperatures; liquid water turns to ice.
Neither the forward nor the reverse reaction is spontaneous. At this particular temperature, the reaction is held in a kind of limbo between the forward and reverse. Osmosis and Entropy The natural progression toward greater entropy sometimes produces surprising results.
The diagram below shows a U-shaped tube divided into two halves by a semipermeable membrane. When the tube is filled with water, the levels on the right and the left are the same, just as one would expect. However, if salt is added to the left side, a strange thing occurs. Water will pass from the right side to the left side across the membrane, and the two levels will become uneven.
Greater mixing occurs when water moves toward the side with salt, and therefore the entropy increases. It may seem that this kind of diffusion due to entropy is a passive process and not important outside of the laboratory. In fact, semipermeable membranes are ubiquitous in living things. The membrane that surrounds all cells is semipermeable; water passes freely but larger molecules do not. The consequences are enormous. Without knowing how it works, humankind has been taking advantage of osmosis for centuries by salting food for preservation.
Putting salt on the surface of food pulls moisture out, making it a less hospitable environment for bacteria. A high-salt environment also kills bacteria outright, as osmosis pulls their water out causing the bacteria to shrivel and die.
Sugar need not be refrigerated for the same reason; although it is a rich source of energy for microorganisms, such a high concentration of sugar would kill any bacteria attempting to live on it. Osmosis also plays an important role in some human diseases. The bacterium that causes cholera, Vibrio cholerae , secretes a toxin that binds to the surface of cells in the intestine. The toxin stimulates cells to secrete large amounts of Cl — ions into the intestinal cavity.
While too much osmosis is a bad thing, too little can be bad too. Patients suffering from cystic fibrosis have a defect in a chloride channel in the cell membrane.
Various mutations in this channel cause it to malfunction, and it does not release enough Cl — ions onto the membranes lining the pancreas, lungs, sweat glands, salivary glands, and other organs. Because Cl — ions remain trapped inside the cells, water also remains inside the cell. Thus, the mucus coating these membranes lacks water and becomes too viscous.
The symptoms of cystic fibrosis are the result of thick, sticky mucus clogging the channels of the affected organs. Thus the equilibrium constant for the formation of ammonia at room temperature is favorable. As we saw in Chapter 15 "Chemical Equilibrium" , however, the rate at which the reaction occurs at room temperature is too slow to be useful. Answer: 2. Although K p is defined in terms of the partial pressures of the reactants and the products, the equilibrium constant K is defined in terms of the concentrations of the reactants and the products.
We described the relationship between the numerical magnitude of K p and K in Chapter 15 "Chemical Equilibrium" and showed that they are related:. For all reactions that do not involve a change in the number of moles of gas present, the relationship in Equation Only when a reaction results in a net production or consumption of gases is it necessary to correct Equation Although we typically use concentrations or pressures in our equilibrium calculations, recall that equilibrium constants are generally expressed as unitless numbers because of the use of activities or fugacities in precise thermodynamic work.
Systems that contain gases at high pressures or concentrated solutions that deviate substantially from ideal behavior require the use of fugacities or activities, respectively. Combining Equation Thus the magnitude of the equilibrium constant is also directly influenced by the tendency of a system to seek the lowest energy state possible. The magnitude of the equilibrium constant is directly influenced by the tendency of a system to move toward maximum disorder and seek the lowest energy state possible.
This relationship is shown explicitly in Equation The quantitative relationship expressed in Equation Because heat is produced in an exothermic reaction, adding heat by increasing the temperature will shift the equilibrium to the left, favoring the reactants and decreasing the magnitude of K.
Conversely, because heat is consumed in an endothermic reaction, adding heat will shift the equilibrium to the right, favoring the products and increasing the magnitude of K. Equation Suppose, for example, that K 1 and K 2 are the equilibrium constants for a reaction at temperatures T 1 and T 2 , respectively. Applying Equation Subtracting ln K 1 from ln K 2 ,. Use the data from Example However, nitrogen monoxide is capable of being produced at very high temperatures, and this reaction has been observed to occur as a result of lightning strikes.
One must be careful not to confuse the term spontaneous with the notion that a reaction occurs rapidly. A spontaneous reaction is one in which product formation is favored, even if the reaction is extremely slow. You do not have to worry about a piece of paper on your desk suddenly bursting into flames, although its combustion is a spontaneous reaction. What is missing is the required activation energy to get the reaction started.
If the paper were to be heated to a high enough temperature, it would begin to burn, at which point the reaction would proceed spontaneously until completion. In a reversible reaction, one reaction direction may be favored over the other. Carbonic acid is present in carbonated beverages.
It decomposes spontaneously to carbon dioxide and water according to the following reaction. The forward reaction is spontaneous because the products of the forward reaction are favored at equilibrium.
In the reverse reaction, carbon dioxide and water are the reactants, and carbonic acid is the product. The reverse of the above reaction is not spontaneous.
This illustrates another important point about spontaneity.
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