Zeroth-order reaction

For a chemical reaction and zeroth-order rate law of the form 

Equation 6.12d has the form of an exponential decay (Fig. 6.7). A common feature of all first-order reactions, therefore, is that the concentration of the reactant decays exponentially with time. 

Justification 6.1 Rrst-orderintegrated rate laws A first-order rate equation has the form d[A] 

Equation 6.12d lets us predict the concentration of A at any time after the start of the reaction. However, we can also use the result to confirm that a reaction is first order and to determine the rate constant eqn 6.12c shows that if we plot In [A] against f, then we will get a straight line if the reaction is first order (Fig. 6.8). If the experimental data do not give a straight line when plotted in this way, then the reaction is not first order. If the line is straight, then it follows from the same equation that its slope is -k, so we can also determine the rate constant from the graph. 

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First-order nitrations in nitromethane are also markedly accelerated by addition of sulphuric acid, the effect being very similar to that observed with zeroth-order reactions. 

Unlike the effect of sulphuric acid upon nitration in nitric acid ( 2.2.3 where zeroth-order reactions are unknown), the form of the catalysis of zeroth-order nitration in nitromethane by added sulphuric acid does not deviate from a first-order dependence with low concentrations of catalyst. ... 

When large concentrations of water are added to the solutions, nitration according to a zeroth-order law is no longer observed. Under these circumstances, water competes successfully with the aromatic for the nitronium ions, and the necessary condition for zeroth-order reaction, namely that all the nitronium ions should react with the aromatic as quickly as they are formed, no longer holds. In these strongly aqueous solutions the rates depend on the concentrations and reactivities of the aromatic compound. This situation is reminiscent of nitration in aqueous nitric acid in which partial zeroth-order kinetics could be observed only in the reactions of some extremely reactive compounds, capable of being introduced into the solution in high concentrations ( 2.2.4). 

Anisole] = 0 4 mol 1 zeroth-order reactions, except for that with added nitrate, which was of the first order with respect to the concentration of anisole. 

The kinetic effect of increased pressure is also in agreement with the proposed mechanism. A pressure of 2000 atm increased the first-order rates of nitration of toluene in acetic acid at 20 °C and in nitromethane at 0 °C by a factor of about 2, and increased the rates of the zeroth-order nitrations of p-dichlorobenzene in nitromethane at 0 °C and of chlorobenzene and benzene in acetic acid at 0 °C by a factor of about 559. The products of the equilibrium (21a) have a smaller volume than the reactants and hence an increase in pressure speeds up the rate by increasing the formation of H2NO. Likewise, the heterolysis of the nitric acidium ion in equilibrium (22) and the reaction of the nitronium ion with the aromatic are processes both of which have a volume decrease, consequently the first-order reactions are also speeded up and to a greater extent than the zeroth-order reactions. 

Differential temperature method. A differential method has been applied to a study of the iodination of acetone, a pseudo-zeroth-order reaction when [(CHj)2CO] [I2].26 It allows the determination of AW to much higher accuracy than otherwise. The reaction rate is expressed mathematically as... 

Figure 4. Entrance region polymer weight fraction (relative to value at the tube centerline) profiles in the tube cross section for a zeroth order reaction and uniform viscosity at GrSc = 10 and = 0.05 and 0.1.

FIGURE 6.9 Plots of the total current density vs. (or K ) for (1) first-order and (2) zeroth-order reactions. 

Eqs. (19) and (20) were derived applying the steady-state approximation to the oxidized Fe-TAML species and using the mass balance equation [Fe-TAML] = 1 + [oxidized Fe-TAML] ([Fe-TAML] is the total concentration of all iron species, which is significantly lower than the concentrations of H2O2 and ED). The oxidation of ruthenium dye 8 is a zeroth-order reaction in 8. This implies that n[ED] i+ [H202]( i+ m). Eq. (19) becomes very simple, i.e.,... 

This is commonly called the Arrhenius equation. Table 4.1 gives typical values for fuels in terms of the specific rate constant, k. In Equation (4.1), m("r is taken as positive for the mass rate of fuel consumed per unit volume. Henceforth, in the text we will adopt this new sign convention to avoid the minus sign we were carrying in Chapter 3. The quantity A is called the pre-exponential factor and must have appropriate units to give the correct units to m("r. The exponents n and m as well as A must be arrived at by experimental means. The sum (n + m) is called the order of the reaction. Often a zeroth-order reaction is considered, and it will suffice for our tutorial purposes. 

Illustrative values for a zeroth-order reaction are given as follows ... 

Raising a mixture of fuel and oxidizer to a given temperature might result in a combustion reaction according to the Arrhenius rate equation, Equation (4.1). This will depend on the ability to sustain a critical temperature and on the concentration of fuel and oxidizer. As the reaction proceeds, we use up both fuel and oxidizer, so the rate will slow down according to Arrhenius. Consequently, at some point, combustion will cease. Let us ignore the effect of concentration, i.e. we will take a zeroth-order reaction, and examine the concept of a critical temperature for combustion. We follow an approach due to Semenov [3],... 

For zeroth-order reaction steps, we still have linear equations, but for other orders of kinetics we have nonlinear simultaneous equations, which generally have no closed-form analytical solutions. We must solve these sets of equations numerically to find C/i(t), Cfi(r), and Cc(t). 

Elementary reaction 2H20(aq) H30+(aq)+ OH (aq) (Reaction l-9f) is a zeroth-order reaction (or pseudo-zeroth-order reaction) ... 

The net reaction rate does not behave as a simple second-order reaction or as a zeroth-order reaction. The net rate is linear to [Ca +][COf ], but not proportional to [Ca " ][C03 ]. At constant composition, temperature, and pressure, the net reaction rate is constant. The concentrations approach equilibrium and hence the net reaction rate approaches zero as reaction proceeds. 

A zeroth-order reaction of the type A — products is one that has the rate law... 

This is another equation of the form y = mx + b, so a graph of [A] versus time is a straight line with a slope = —k (Figure 12.9). Note that both the rate constant k and the rate of a zeroth-order reaction have a constant value equal to minus the slope of the [A] versus time plot. 

Zeroth-order reactions are relatively uncommon, but they can occur under special circumstances. Take, for example, the decomposition of gaseous ammonia on a hot platinum surface ... 

Concentration of a reactant A as a function of time for a zeroth-order reaction. 

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