Reactant graph

The chemical reaction C is described completely by the reactant graph M and change of reaction graph AC. Therefore, we call the quintuple (e, y, A, Ay) the reaction graph. Written In the notation introduced in Definition 2.17, this gives ... 

Hence, Cen(C) consists of the atoms whose state is changed by the reaction, or whose bonds are altered. It can be described also by the reactant graph, the center of reaction and the change of atom states and bonds of the center atoms. 

Many reactions in chemistry follow either the same or very similar reaction paths. This manifests itself in similar reaction center graphs for these reactions. This similarity can be used to describe a data structure that represents similar reaction center graphs and thus allows the construction of the underlying chemical reaction from the reactant graph, yielding the reaction center. 

Each reactant and product appears in the Nemst equation raised to its stoichiometric power. Thermodynamic data for cell potentials have been compiled and graphed (3) as a function of pH. Such graphs are known as Pourbaix diagrams, and are valuable for the study of corrosion, electro deposition, and other phenomena in aqueous solutions.Erom the above thermodynamic analysis, the cell potential can be related to the Gibbs energy change... 

The graphs of each of the species concentrations are plotted as a function of position along the tube z and time t. At the edges of the graphs for the concentrations of A and B we see the boundary and initial conditions. All values are unit or zero concentration as we had specified. As we move through time, we see the concentrations of both species drop monotonically at any position. Furthermore, if we take anytime slice, we see that the concentrations of reactants drop exponentially with position—as we know they should. At the longer times the profiles of... 

This form assumes that the effect of pressure on the molar volume of the solvent, which accelerates reactions of order > 1 by increasing the concentrations when they are expressed on the molar scale, has been allowed for. This effect is usually small, ignored but in the most precise work. Equation (7-41) shows that In k will vary linearly with pressure. We shall refer to this graph as the pressure profile. The value of A V is easily calculated from its slope. The values of A V may be nearly zero, positive, or negative. In the first case, the reaction rate shows little if any pressure dependence in the second and third, the applied hydrostatic pressure will cause k to decrease or increase, respectively. A positive value of the volume of activation means that the molar volume of the transition state is larger than the combined molar volume of the reactant(s), and vice versa. 

FIGURE 9.10 These graphs show the changes in composition that can be expected when additional hydrogen and then ammonia are added to an equilibrium mixture of nitrogen, hydrogen, and ammonia. Note that the addition of hydrogen results in the formation of ammonia, whereas the addition of ammonia results in the decomposition of some of the added ammonia as reactants are formed. In each case, the mixture settles into a composition in accord with the equilibrium constant of the reaction. 

FIGURE 13.10 The graph of Ihe concentration of a reactant in a tirst-orrler reaction is an exponential decay, as shown here. The larger the rate constant, the faster the decav from the same initial concentration. 

STRATEGY We need to plot the natural logarithm of the reactant concentration as a function of t. If we get a straight line, the reaction is first order and the slope of the graph is —k. We could use a spreadsheet program or the Living Graph Determination of Rate Constant (first-order rate law) on the Weh site for this book to make the plot. 

FIGURE 13.12 Thu ohange in concentration of the reactant in two first-order reactions plotted on the same graph When the first-order rate constant is large, the half-life of the reactant is short, because the exponential decay of the concentration of the reactant is then fast. 

This graph shows the number of mole ratios that can be determined given the number of reactants and products of a chemical reaction. If this trend continues, how many mole ratios can be formed with a chemical reaction that has a sum of eight reactants and products ... 

Figure 14 is a plot of the optical density of the 2890 cm-1 band center versus time for the spectra shown in Fig. 13. At the point labeled A on this graph, the H2 C2H. stream was changed to a H2 He stream. The decrease in intensity of the spectrum due to this species (hereafter called X) is rapid initially but becomes slower as time proceeds. The initial rate of falloff (based on the first two points) is such that if this rate were maintained (dashed line), it would, take about 2 min in pure hydrogen to remove all of X from the surface. Similar conclusions are reached if the integrated intensity in the 2925-2825 cm-1 region is plotted as a function of time. Corresponding runs were also made for C2H4-D2 reactant mixture.

Note the overall look of the graph. The concentrations of A and B decrease with time and the concentration of C increases with time as the system approaches equilibrium at time, teq. How much the reactants decrease and the products increase depends on the stoichiometric coefficients... 

Figure 1 shows the graphs of the PCL that were recorded with riboflavin as the photosensitizer and luminol as the detector for free radicals [21], The course of the PCL reaction has two maxima at approximately 30 s and 3 min after the start of irradiation. It has been demonstrated by analysis of kinetics after addition of the reactants at varying times that the first maximum is riboflavin-dependent. Luminol is needed only for visualization of the superoxide radicals. 

A typical graph of k as a function of temperature is shown in Figure 3.6. The increasing slope shows the importance of determining a maximum allowable temperature in process equipment so that the heat removal capacity is not exceeded. Under adiabatic conditions, the temperature will reach the calculated maximum only if the reactants are depleted. The actual maximum temperature in a system with some heat dissipation will, of course, be somewhat lower than the calculated value. 

Some data of the rate as a function of the concentration of C are represented by the graph, when starting with pure reactant A0 = 3. Two points off this curve are... 

Figure 6.2 Graph of Gibbs function G (as y ) against the extent of reaction f (as V). The minimum of the graph corresponds to the position of equilibrium the position of equilibrium for a weak acid, such as ethanoic acid, lies near the un-ionized reactants the position of equilibrium for a strong acid, like sulphuric acid, lies near the ionized products...

Worked Example 8.2 yields a value for the rate constant k, but an alternative and usually more accurate way of obtaining k is to prepare a series of solutions, and to measure the rate of each reaction. A graph is then plotted of reaction rate (as y ) against concentration(s) of reactants (as V) to yield a linear graph of gradient equal to k. 

Figure 8.1 shows such a graph. The gradient of the graph is 1.09 x 106 dm3 s-1 (which is the same value as that cited in Worked Example 8.1). Notice how the intercept is zero, which confirms the obvious result that the rate of reaction is zero (i.e. no reaction can occur) when no reactants are present. 

Also depicted on the graph in Figure 8.5 is the number of moles of magnesium sulphate produced. It should be apparent that the two concentration profiles (for reactant and product) are symmetrical, with one being the mirror image of the other. This symmetry is a by-product of the reaction stoichiometry, with 1 mol of sulphuric acid forming 1 mol of magnesium sulphate product. 

We call a graph of concentration of reactant or product (as y ) against time (as ) a concentration profile. 

Graphs such as those in Figures 8.5 and 8.6 are an ideal means of determining the rates of reaction. To obtain the rate, we plot the concentration of a reactant or product as a function of time, and measure the slope. (Strictly, since the slopes are negative for reactants, so the rate is slope x —1 .)... 

Accordingly, we perform the kinetic experiment with a series of concentrations [B]0, the reactant in excess, and then plot a graph of k (as y ) against [B]0 (as V). The gradient will have a value of k2. 

Figure 8.15 The rate constant of a pseudo-order reaction varies with the concentration of the reactant in excess graph of k (as V) against [alkene]0 (as V). The data refer to the formation of a 1,2-diol by the dihydrolysis of an alkene with osmium tetroxide. The gradient of the graph yields k2, with a value of 3.2 x 10 2 dm3 mol-1 s-1...

Figure 8.23 During a reaction, the participating species approach, collide and then interact. A seamless transition exists between pure reactants and pure products. The rearrangement of electrons requires large amounts of energy, which is lost as product forms. The highest energy on the activation energy graph corresponds to the formation of the transition-state complex. The relative magnitudes of the bond orders are indicated by the heaviness of the lines...

Figure 8.24 Reaction profile of energy (as v j against reaction coordinate (as x ). The activation energy Ea is obtained as the vertical difference between the reactants and the peak of the graph,...

Referring to the graph produced, what is the limiting reactant on the line with the positive slope With the negative slope ... 

The rate of reaction is the change in concentration per change in time. It is possible to find the rate of reaction from a graph of concentration of a reactant versus time. The procedure involves drawing a tangent to the curve at the point in the reaction where we wish to know the rate. 

Calculate the flame temperature of normal octane (liquid) burning in air at an equivalence ratio of 0.5. For this problem assume there is no dissociation of the stable products formed. All reactants are at 298 K and the system operates at a pressure of 1 atm. Compare the results with those given by the graphs in the text. Explain any differences. 

Use a graph to describe the rate of reaction as a function of the change of concentration of a reactant or product with respect to time. 

Plot a graph of the data you collected. Put transfer number on the x-axis and volume of water on the y-axis. Use different symbols or colours to distinguish between the reactant volume and the product volume. Draw the best smooth curve through the data. 

In an acid-base titration, you carefully measure the volumes of acid and base that react. Then, knowing the concentration of either the acid or the base, and the stoichiometric relationship between them, you calculate the concentration of the other reactant. The equivalence point in the titration occurs when just enough acid and base have been mixed for a complete reaction to occur, with no excess of either reactant. As you learned in Chapter 8, you can find the equivalence point from a graph that shows pH versus volume of one solution added to the other solution. To determine the equivalence point experimentally, you need to measure the pH. Because pH meters are expensive, and the glass electrodes are fragile, titrations are often performed using an acid-base indicator. 

---