Double arrows

Using this insight Berthollet reasoned that the reaction is reversible, and that the relative amounts of reactants and products determine the direction in which the reaction occurs, and the final composition of the reaction mixture. We recognize a reaction s ability to move in both directions by using a double arrow when writing the reaction. 

The double arrow implies that this reaction does not go to completion. Instead, a mixture is formed containing significant amounts of both products and reactants. With the weak add hydrogen fluoride... 

The double arrow implies that the forward and reverse processes are occurring at the same Liquid-vapor equilibrium. Under the... 

The preceding evolution equations also can be used to generate equations for stationary states by setting the time derivative to zero giving the two equivalent forms (signified by the double arrow) ... 

The double arrows indicate reversibifity, an intrinsic property of all chemical reactions. Thus, for reaction (1), if A and B can form P and Q, then P and Q can also form A and B. Designation of a particular reactant as a substrate or product is therefore somewhat arbitrary since the products for a reaction written in one direction are the substrates for the reverse reaction. The term products is, however, often used to designate the reactants whose formation is thermodynamically favored. Reactions for which thermodynamic factors strongly favor formation of the products to which the arrow points often are represented with a single arrow as if they were irreversible ... 

If the concentration of a solute is lower than its solubility, additional solute can dissolve, but once the concentration of solute reaches the solubility of that substance, no further net changes occur. Individual solute molecules still enter the solution, but the solubility process is balanced by precipitation, as Figure 12-6 illustrates. A saturated solution in contact with excess solute is in a state of dynamic equilibrium. For eveiy molecule or ion that enters the solution, another returns to the solid state. We represent d Tiamic equilibria by writing the equations using double arrows, showing that both processes occur simultaneously ... 

Look again at Figure 16-1 If two NO2 molecules can form a bond when they collide, then that bond also can break apart when an N2 O4 molecule distorts. The concept of reversibility is a general principle that applies to all molecular processes. Every elementary reaction that goes in the forward direction can also go In the reverse direction. As a consequence of reversibility, we can write each step in a chemical mechanism using a double arrow to describe what happens at chemical equilibrium. 

In addition to defined standard conditions and a reference potential, tabulated half-reactions have a defined reference direction. As the double arrow in the previous equation indicates, E ° values for half-reactions refer to electrode equilibria. Just as the value of an equilibrium constant depends on the direction in which the equilibrium reaction is written, the values of S ° depend on whether electrons are reactants or products. For half-reactions, the conventional reference direction is reduction, with electrons always appearing as reactants. Thus, each tabulated E ° value for a half-reaction is a standard reduction potential. 

The double arrow represents the condition of equilibrium that exists between the non-ionized and the ionized species of the electrolyte. Since ionization of strong electrolytes is practically complete there will not be much gain in studying this type of reaction from the point of view of equilibrium. Equilibria involving weak electrolytes, where there is only partial ionization, are of considerable importance. 

The double arrow in the chemical equation above indicates that the reaction is reversible. This means that while some hydrochloric acid molecules are breaking down into hydrogen and chlorine ions, some ions are also combining to produce hydrochloric acid. The same ongoing, continuous process also occurs to the ammonia molecules. Some ammonia molecules accept a hydrogen ion to become an ammonium ion while some ammonium ions give up a hydrogen ion to become an ammonia molecule. 

To save effort, we often write these two exactly opposite equations as one, with double arrows ... 

Figure 8.31. Fiber scattering of PEE 1000/43 (a) at an elongation = 0.88 (b) during relaxation from = 0.88. The fiber direction is indicated by a double-arrow. Visualized region —0.15nm 1 < s 2, sj < 0.15nm 1. = (l l,) /Iq, with Iq and / defined by the initial and the actual distance between two fiducial marks on the sample...

FIGURE 1-5 Detail of the nuclear envelope showing a nuclear pore (single arrow) and the outer leaflet connected to the smooth endoplasmic reticulum (ER) (double arrows). Two cisternae of the rough ER with associated ribosomes are also present. X80,000. 

These two forms of iron are called a redox couple, which is usually expressed by placing a double arrow in the equation, to indicate an equilibrium ... 

Figure 5. Exact (numerical solution, continuous line) and linearised (equation (24), dotted line) velocity profile (i.e. vy of the fluid at different distances x from the surface) at y = 10-5 m in the case of laminar flow parallel to an active plane (Section 4.1). Parameters Dt = 10 9m2 s-1, v = 10-3ms-1, and v = 10-6m2s-1. The hydrodynamic boundary layer thickness (<50 = 5 x 10 4 m), equation (26), where 99% of v is reached is shown with a horizontal double arrow line. For comparison, the normalised concentration profile of species i, ct/ithe linear profile of the diffusion layer approach (continuous line) and its thickness (<5, = 3 x 10 5m, equation (34)) have been added. Notice that the linearisation of the exact velocity profile requires that <5,

A chemical equilibrium results when two exactly opposite reactions are occurring at the same place, at the same time and with the same rates of reaction. When a system reaches the equilibrium state the reactions do not stop. A and B are still reacting to form C and D C and D are still reacting to form A and B. But because the reactions proceed at the same rate the amounts of each chemical species are constant. This state is a dynamic equilibrium state to emphasize the fact that the reactions are still occurring—it is a dynamic, not a static state. A double arrow instead of a single arrow indicates an equilibrium state. For the reaction above it would be ... 

FIGURE 15.13 (a) A representation of a light beam with all wave planes shown as double arrows around the line... 

Figure 1.8. Simplified view of different orientations and two arrangements of molecules in the channels of zeolites. Upper Four representative orientations of molecules and their electronic transition moments, indicated by the double arrow. Middle Orientation of large molecules that align parallel to the channel axis and that have no electronic interaction because of their size and shape. Bottom Orientation of large molecules that align parallel to the channel axis and that have some electronic interaction because of their shape.

Figure 5-16. The Lawton-Sylvestre analysis in action. The double arrows cover the feasible regions of positive absorbances.

Fig. 3.6. Stereoelectronic control of the cleavage of the tetrahedral intermediate during hydrolysis of a peptide bond by a serine hydrolase. The thin lines represent the reactive groups of the enzyme (serine, imidazole ring of histidine) the thick lines represent the tetrahedral intermediate of the transition state. The full circles are O-atoms open circles are N-atoms. The dotted lines represent H-bonds the thick double arrow indicates an unfavorable dipole-dipole interaction [21]. A (R)-configured N-center B (S)-configured N-center.

Equilibrium is achieved in a reversible process when the rates of opposing changes are equal. A double arrow, indicates reversible changes. For example ... 

Figure 9.4. Schematic description of the solute-solvent pair potential. The double-arrowed line indicates the hard (repulsive) interaction between a and a water molecule. The dashed lines indicate the interaction between groups on the surface of a and a water molecule, the sum of which is the last term on the rhs of Eq. (9.4.1).

The double arrows in the methanol reaction indicate that the reaction can go in either direction. There is a principle here that is taught in the sophomore P-chem class (Physical chemistry) of every chemical engineer. Methanol, in the vapor state, takes up only one-third the volume as the equivalent amounts of CO and H2. So in order to "push the reaction to the right," the process is run under pressure. That causes the compound that takes up less volume to be favored—synthesis gas to methanol rather than methanol to synthesis. 

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