Equations for a first order reaction

The half life of a first order reaction is given as  

To determine B(t), the following equation should be used A(t) B(t) Ainitial B initial 

An excavated bone of a prehistoric elephant contains 10 % of the eC of a living animal. Calculate, how old this fossil is. The half-life of carbon-14 is 5,700 years. 

You measure the decay of a sample of fluorine-18, which has just been delivered, and these are your data  

Graph In (fluorine) versus time gives a straight line Half life = 110 minutes, k = 6.3 jc 10 min  

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Solve the above equation for a first-order reaction under steady-state conditions, and obtain an expression for the mass transfer rate per unit area at the surface of a catalyst particle which is in the form of a thin platelet of thickness 2L. 

When only taking into account the concentration polarization in the pores (disregarding ohmic potential gradients), we must use an equation of the type (18.15). Solving this equation for a first-order reaction = nFhjtj leads to equations exactly like (18.18) for the distribution of the process inside the electrode, and like (18.20) for the total current. The rate of attenuation depends on the characteristic length of the diffusion process ... 

This is the integrated rate equation for a first-order reaction. When dealing with first-order reactions it is customary to use not only the rate constant, k for the reaction but also the related quantity half-life of the reaction. The half-life of a reaction refers to the time required for the concentration of the reactant to decrease to half of its initial value. For the first-order reaction under consideration, the relation between the rate constant k and the half life t0 5 can be obtained as follows ... 

Referring back to the rate equation for a first-order reaction (Equation A1.2), we have a differential equation for which the derivative of the variable ([S]) is proportional to the variable itself. Such a system can be described by an infinite series with respect to time ... 

Hence we can express the rate equation for a first-order reaction also as... 

From the design equation for a first-order reaction, eqn. (11), it follows that the reaction time is equal to the area under the curve of l/fe(l — Xa) plotted against Xa- This integral may be obtained graphically by counting squares or by a numerical method. 

Since this reaction has a first-order rate law, — A[H202]/Af = k[H202], we can use the corresponding concentration-time equation for a first-order reaction ... 

Solution to the Differential Equation for a First-Order Reaction 746... 

Mole Balances on the (1) Bubble, (2) Cloud, and (3) Emulsion Solution to the Balance Equations for a First Order Reaction Example CD12-3 Catalytic Oxidation of Ammonia Limiting Situations... 

The grain model gas phase material balance and boundary equations for a first-order reaction are... 

The rate constants (Table 1.) for the peroxidase oxidation of phenol at various tenqreratures were calculated by the kinetic equation for a first order reaction (Fig.4). From the data in Table 1 is seen that on peroxidase oxidation of phenol, the catalase immobilized on "NORIT" soot shows a higher catalytic activity than the catalase in solution. It can be explained first, with the fact that the values in Table 1 are not the values for the specific rate constants, and secondly, as the catalase peroxidase fiuiction is characteristic of its subunits, with the complete or partial dissociation of catalase on its immobilization on "NORIT" soot. In this... 

E. Solution 10 the Balance Equations for a First Order Reaction... 

A dramatic reduction in dimensionality is often possible by converting a design equation from dimensioned to dimensionless form. Equation 1.62 contains the dependent variable a and the independent variable z. The process begins by selecting characteristic values for these variables. By characteristic value we mean some known parameter that has the same dimensions as the variable and that characterizes the system. Eor a PER, the variables are concentration and length. A characteristic value for concentration is flin and a characteristic value for length is L. These are used to define the dimensionless variables a = ala-m and zIL. The governing equation for a first-order reaction in an ideal PER becomes... 

Table 7.4 Intraphase diffusion parameters and equations for a first-order reaction (A — products) for different catalyst shapes... 

In this chapter I will show, how we can formulate the typical rate equation for a first order reaction. Using examples I will develop the equations for this kind of kinetics. By the end of this chapter you should be able to ... 

This equation should look familiar to you - it is the rate equation for a first order reaction. However, it is important to remember that it is only apparently a first order reaction - it truly is a second order reaction disguised as a first order reaction. In this case we call this kind of reaction a pseudo-first order reaction . 

Calculations to estimate a shelf life at a different temperature can only be made when the active substance is not subject to degradations other than chemical degradation, such as physical or microbiological degradation. In addition, calculations are only possible for relatively small differences in temperature. Data from stability studies that have actually been performed are preferred over estimations. Moreover, the equation for a first-order reaction can only be used for the first 10 % degradation for any other type of reaction. 

A first-order reaction rate is obtained by plotting the natural logarithm (In) of the concentration of a starting material versus time. The rate of a second-order reaction is obtained by plotting the In of a concentration term that includes both reactants versus time. The rate equation for a first-order reaction is rate = k [A], where k is the rate constant. The rate equation for a second-order reaction is rate = k [A] [B], where k is the rate constant. 

The reactant concentration-time curve for a typical first-order reaction, A -> products, is shown in Fig. 1.1(a). The rate equation for a first-order reaction can be expressed as... 

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