Reactant or Product Concentration

A system at dynamic equilibrium is in a state of balance. When the concentrations of species in the reaction are altered, the equilibrium shifts until a new state of balance is attained. What does shift mean It means that reactant and product concentrations change over time to accommodate the new situation. Shift does not mean that the equilibrium constant itself is altered the equilibrium constant remains the same. Le Chatelier s principle states that the shift is in the direction that minimizes or reduces the effect of the change. Therefore, if a chemical system is already at equilibrium and the concentration of any substance in the mixture is increased (either reactant or product), the system reacts to consume some of that substance. Conversely, if the concentration of a substance is decreased, the system reacts to produce some of that substance. 

There is no change in the equilibrium constant when we change the concentrations of reactants or products. As an example, consider our familiar equilibrium mixture of N2,H2,andNH3  

In the Haber reaction, therefore, removing NH3 from an equilibrium mixture of N2, H2, and NH3 causes the reaction to shift right to form more NH3. If the NH3 can be removed continuously as it is produced, the yield can be increased dramatically. In the 

Why does the nitrogen concentration decrease after hydrogen is added  

Adding H2 causes the reaction as written to shift to the right, consuming some H2 to produce more NH3. 

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The rate of reaction is often experimentally determined by relating the reactant (or product) concentration with time. 

In order to determine reaction rate constants and reaction orders, it is necessary to determine reactant or product concentrations at known times and to control the environmental conditions (temperature, homogeneity, pH, etc.) during the course of the reaction. The experimental techniques that have been used in kinetics studies to accomplish these measurements are many and varied, and an extensive treatment of these techniques is far beyond the intended scope of this textbook. It is nonetheless instructive to consider some experimental techniques that are in general use. More detailed treatments of the subject are found in the following books. 

Kinetics is the study of the speed of reactions. The speed of reaction is affected by the nature of the reactants, the temperature, the concentration of reactants, the physical state of the reactants, and catalysts. A rate law relates the speed of reaction to the reactant concentrations and the orders of reaction. Integrated rate laws relate the rate of reaction to a change in reactant or product concentration over time. We may use the Arrhenius equation to calculate the activation... 

The simplest way to determine a rate law is the method of initial rates. If a reaction is slow enough, it can be allowed to proceed for a short time, At, and the change in a reactant or product concentration measured. Repeating the experiment for different concentrations, the concentration-dependence of the rate can be deduced. 

In a photochemical reaction with a complex mechanism, the local rate of change of the reactant or product concentrations might have a nonlinear dependence on the light intensity absorbed locally. For example, the rate to be used in Equation 6.19 can be dependent on the nth power of the light intensity. 

Many techniques have been employed in kinetic studies to determine reaction rate constants and reaction orders from either reactant or product concentrations at known times. The most desirable analytical methods allow continuous and rapid measurement of the concentration of a particular component. Any of the methods used to monitor the course of reaction must satisfy the following criteria ... 

What other reactant or product concentration could be used to measure the isocitrate dehydrogenase activity ... 

Before we go further, we must define exactly what we mean by the term rate in Equation (15.1). In Section 15.1 we saw that reaction rate means a change in concentration per unit time. However, which reactant or product concentration do we choose in defining the rate For example, for the decomposition of N02 to produce 02 and NO considered in Section 15.1, we could define the rate in terms of any of these three species. However, since 02 is produced only half as fast as N02, we must be careful to specify which species we are talking about in a given case. For instance, we might choose to define the reaction rate in terms of the consumption of N02 ... 

Most reactions are characterized by a change in reactant or product concentration that can be described by a single exponential. The differential form of the rate equation contains a single term the integrated form yields a straight line from which the rate constant can be obtained. Some of the more common and useful cases are described. 

All impedance measurements should begin with measurement of a steady-state polarization curve. The steady-state polarization curve is used to guide selection of an appropriate perturbation amplitude and can provide initial hypotheses for model development. The impedance measirrements can then be made at selected points on the polarization curve to explore the potential dependence of reaction rate constants. Impedance measurements can also be performed at different values of state variables such as temperature, rotation speed, and reactant concentration. Impedance scans measured at different points of time can be used to explore temporal changes in system parameters. Some examples include growth of oxide or corrosion-product films, poisoning of catal5dic surfaces, and changes in reactant or product concentration. 

The rate of a chemical reaction is calculated from changes in reactant or product concentration during a small time interval. 

The average reaction rate is the change in reactant (or product) concentration over a change in time, Af. The rate slows as reactants are used up. The instantaneous rate at time t is obtained from the slope of the tangent to a concentration vs. time curve at time t. The initial rate, the instantaneous rate at f = 0, occurs when reactants are just mixed and before any product accumulates. The expression for a reaction rate and its numerical value depend on which reaction component is being monitored. 

For liquid-phase reactions, the densities of reactants and products are often nearly the same, and the slight change in volume of the solution is usually neglected. Then for a batch reaction in a perfectly mixed tank, the reaction rate is the same as the rate of change of reactant or product concentration. To prove this, consider a stirred batch reactor with V liters of solution and a reactant concentration C mol/L. The amount reacted in time dt is V —dCji), and the reaction rate is —dC ldt, a positive term ... 

The rate of a reaction depends on many factors such as the concentration of reactants, the temperature at the time of the reaction, the states of reactants, and catalysts. The rate of a reaction is defined as the change of reactant or product concentration in unit time. If we were to define the rate of a reaction in terms of the reactants, we should define the rate as the rate of disappearance of reactants. If we were to define the rate in terms of the products formed, we should define it as the rate of appearance of products. 

The total reaction can be followed by monitoring the reactant or product concentration as a function of time. Then the following overall expression can be derived for the total product concentration [/ ] as a function of time (Miyake et al 1991) ... 

The next question is how do the coefficients of a polynomial describing reactant or product concentration as a function of time change with process temperature Thermodynamics suggests that the reaction rate constant is proportional to the exponential of inverse process temperature T, namely... 

The determination of a given species using a kinetic method based on direct or indirect measurements of its reaction rate entails monitoring changes in the reactant or product concentration. The reaction rate is defined as the number of moles of substance that is consumed or formed per unit volume per unit time. Thus, for a straightforward reaction of the type... 

The concentrations in eqn [1] can be replaced with any measurable quantity R provided it is directly proportional to concentration. Temporal changes in the reactant or product concentrations can be monitored physically or chemically. Physicochemical techniques (e.g., those based on absorbance, potential, temperature, luminescence, and conductivity measurements) are more commonly used for this purpose. Figure 1 shows the variation of a measured property, R (a signal), as a function of time. The reaction rate is given by the slope of the rising exponential cmwe at each point. 

Differential kinetic methods for the determination of a single species rely on measurements made at the start of reaction, i.e. when changes in the reactant or product concentrations are still negligible and hence the reaction rate is not influenced by the concentration of either reactant, so eqn [2] can be simplified to a pseudo zero-order expression... 

According to the permeation model, the driving forces for transport are phase partitioning and reactant or product concentration gradients. Electrochemical... 

The average reaction rate is the change in reactant (or product) concentration over a change in time. At. The rate slows as the reaction proceeds because reactants are used up. 

Knowledge of the value of the rate of the reaction at different reactant concentrations would allow for determination of the rate and order of a chemical reaction. For the reaction A B, for example, reactant or product concentration-time curves are determined at different initial reactant concentrations. The absolute value of slope of the curve at t = 0, d[A]/dt)o or rf[B]/rft)o, corresponds to the initial rate or initial velocity of the reaction (Fig. 1.8). 

To use integrated rate equations, knowledge of reactant or product concentrations is not an absolute requirement. Any parameter proportional to reactant or product concentration can be used in the integrated rate equations (e.g., absorbance or transmittance, turbidity, conductivity, pressure, volume, among many others). However, certain modifications may have to be introduced into the rate equations, since reactant concentration, or related parameters, may not decrease to zero—a miiumum, nonzero value (Amin) might be reached. For product concentration and related parameters, a maximum value (Pmax) may be reached, which does not correspond to 100% conversion of reactant to product. A certain amount of product may even be present at t = 0 (Pq). The modifications introduced into the rate equations are straightforward. For reactant (A) concentration. 

This equation tells us that during the course of a reaction, reactants are consumed while products are formed. We can follow the progress of a reaction by monitoring either the decrease in concentration of the reactants or the increase in the concentrations of the products. The method used to monitor changes in reactant or product concentrations depends on the specific reaction. In a reaction that either consumes or produces a colored species, we can measure the intensity of the color over time with a spectrometer. In a reaction that either consumes or produces a gas, we can measure the change in pressure over time with a manometer. Electrical conductance measurement can be used to monitor the progress if ionic species are consumed or produced. 

The classical way to evaluate a first order rate constant from an exponential record, is to plot the logarithm (base e) of the reactant or product concentration against time to obtain the slope —k. The fact that the units of first order rate constants are s and do not contain a concentration term, has simplifying consequences. The quantity on the Y ordinate of the plot need not be the logarithm of concentration of one of the reactants, but can be any measurement on the logarithmic scale (absorbance, fluorescence, conductivity, etc.) which is directly proportional to it. 

We will solve the set of kinetic equations for the catalytic process in (2.102) and (2.103) using the steady-state approximation. As before, we wish to compute the rate of product formation as a function of reactant or product concentration by elimination of the concentration of the intermediate from the rate expressions. The rate equations are... 

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