Arrhenius equation taking logarithms

From Equations (2.34) and (2.39) for initiation by thermolysis RpArrhenius equations, taking logarithms and differentiating with respect to temperature gives... [Pg.61]

Squation 9.36 is referred to as the Arrhenius equation, and taking logarithms... [Pg.1192]

A change in the temperature at which a reaction is taking place affects the rate constant k. As the temperature increases, the value of the rate constant increases and the reaction is faster. The Swedish scientist Arrhenius derived a relationship in 1889 that related the rate constant and temperature. The Arrhenius equation has the form k= Ae EalPT where k is the rate constant, A is a term called the frequency factor that accounts for molecular orientation, e is the natural logarithm base, R is the universal gas constant 8.314 J mol K-, / is the Kelvin temperature, and Ea is the activation energy, the minimum amount of energy that is needed to initiate or start a chemical reaction. [Pg.202]

Equation 21 has an exponential temperature dependence, which is much stronger than the weak temperature dependence of the collision rate itself. Let s now confirm that our model is consistent with the Arrhenius equation. When we take logarithms of both sides, we obtain... [Pg.767]

As we saw in Section 12.10, the activation energy Ea is one of the most important factors affecting the rate of a chemical reaction. Its value can be determined using the Arrhenius equation if values of the rate constant are known at different temperatures. Taking the natural logarithm of both sides of the Arrhenius equation, we obtain the logarithmic form... [Pg.503]

The Arrhenius equation can be used to determine the activation energy for a reaction. We start by taking the natural logarithm on both sides of the equation. [Pg.33]

Postulation of the Arrhenius equation, Equation (3-18), remains the greatest single step in chemical kinetics, and retains its usefulness today, nearly a century later. The activation energy, E. is determined experimentally Calculation of ifie by carrying out the reaction at several different temperatures. After taking the activation energy natural logarithm of Equation (3-18) we obtain... [Pg.95]

In the previous section, the Arrhenius equation was described. The Arrhenius equation was applied to the prediction of drug degradation in the 1940s and 1950s. Taking the logarithm of both sides ofEq. (2.70) yields... [Pg.62]

Inserting Eq. (6.103) or (6.104) into Eq. (6.102), applying Arrhenius equations for the rate constants, taking logarithms, and finally differentiating with respect to... [Pg.381]

We can calculate a ffoiri the Arrhenius equation by taking the natural logarithm of both sides and recasting the equation into one for a straight line ... [Pg.516]

In order to test the Arrhenius equation, equation (9.39), we first.take logarithms of both sides ... [Pg.388]

MATHS HELP TAKING LOGARITHMS OF THE ARRHENIUS EQUATION... [Pg.68]

Taking logarithms to the base 10 of the Arrhenius equation gives (Equation 6.5)... [Pg.115]

Taking the natural logarithm of each side of the Arrhenius equation yields... [Pg.750]

Insertion of the Arrhenius equation into the rate expression leads to the an expression for the decrease in concentration -d[A]/dt. Taking the logarithm of both sides of the equation removes the exponential, and additional differentiation leads to the second equation with the activation energy, pre-exponential factor, and order of the reaction expressed in terms of measurable quantities. This analysis is known under the name Freeman-CarroU method [33]. [Pg.263]

Arrhenius s Equation I For the first equation, taking the natural logarithm of this equation will give... [Pg.91]

It is useful to recast Arrhenius s equation in logarithmic form. Taking the natural logarithm of both sides of the Arrhenius equation gives... [Pg.585]

If you take natural logarithms of both sides of the original form of the Arrhenius equation and rearrange it, you get ... [Pg.577]

CHAUINGt The Arrhenius equation can be reformulated in a way that permits the experimental determination of activation energies. For this purpose, we take the natural logarithm of both sides and convert into the base 10 logarithm. [Pg.95]

Following the method of analysis used in Section 2.4.11, appropriate Arrhenius expressions can be substituted into Equation (2.61). Taking logarithms and then differentiating with respect to temperature gives... [Pg.72]

Comparison of this equation with the Arrhenius form of the reaction rate constant reveals a slight difference in the temperature dependences of the rate constant, and this fact must be explained if one is to have faith in the consistency of the collision theory. Taking the derivative of the natural logarithm of the rate constant in equation 4.3.7 with respect to temperature, one finds that... [Pg.107]

Taking the logarithm of bromide concentration in the water extracts (normalized to the weight of resin) for the Arrhenius plots in Figure 1 was based on the following assumption the level of Br ions accumulated over the period of extraction was proportional to the rate of RBr hydrolysis. This assumption would hold if the rate of hydrolysis (and hence ion release), Rh, were constant over that period of extraction. Under that assumption the following equation would apply ... [Pg.432]

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