Question

25. Effect of increasing temperature on equilibrium
30
constant is given by log Ką - log Ki
-AH
2.303R
1 1
T, I
then for an endothermic reaction the false
2
statement is:-
1
1
(1)
TT
= positive (2) log K2 > log Ki
(3) AH = positive
(4) K,>K
3
CE0028​

Answer 1

Answer:

In 1889, Svante Arrhenius proposed the Arrhenius equation from his direct observations of the plots of rate constants vs. temperatures:

k=Ae−EaRT(6.2.3.4.1)

(6.2.3.4.1)k=Ae−EaRT

The activation energy, Ea, is the minimum energy molecules must possess in order to react to form a product. The slope of the Arrhenius plot can be used to find the activation energy. The Arrhenius plot can also be used by extrapolating the line back to the y-intercept to obtain the pre-exponential factor, A. This factor is significant because A=p×Z, where p is a steric factor and Z is the collision frequency. The pre-exponential, or frequency, factor is related to the amount of times molecules will hit in the orientation necessary to cause a reaction. It is important to note that the Arrhenius equation is based on the collision theory. It states that particles must collide with proper orientation and with enough energy. Now that we have obtained the activation energy and pre-exponential factor from the Arrhenius plot, we can solve for the rate constant at any temperature using the Arrhenius equation.

The Arrhenius plot is obtained by plotting the logarithm of the rate constant, k, versus the inverse temperature, 1/T. The resulting negatively-sloped line is useful in finding the missing components of the Arrhenius equation. Extrapolation of the line back to the y-intercept yields the value for ln A. The slope of the line is equal to the negative activation energy divided by the gas constant, R. As a rule of thumb in most biological and chemical reactions, the reaction rate doubles when the temperature increases every 10 degrees Celsius.

Looking at the Arrhenius equation, the denominator of the exponential function contains the gas constant, R, and the temperature, T. This is only the case when dealing with moles of a substance, because R has the units of J/molK. When dealing with molecules of a substance, the gas constant in the dominator of the exponential function of the Arrhenius equation is replaced by the Boltzmann constant, kB. The Boltzmann constant has the units J/K. At room temperature, kBT, is the available energy for a molecule at 25 C or 273K, and is equal to approximately 200 wave numbers.

It is important to note that the decision to use the gas constant or the Boltzmann constant in the Arrhenius equation depends primarily on the canceling of the units. To take the inverse log of a number, the number must be unitless. Therefore all the units in the exponential factor must cancel out. If the activation energy is in terms of joules per moles, then the gas constant should be used in the dominator. However, if the activation energy is in unit of joules per molecule, then the constant, K, should be used.

Arrhenius Equation per Mole

k=Ae−EaRT(6.2.3.4.2)

(6.2.3.4.2)k=Ae−EaRT

Arrhenius Equation per Molecule

k=Ae−EaKT(6.2.3.4.3)

(6.2.3.4.3)k=Ae−EaKT

"Linearized" Arrhenius Equation

The Arrhenius equation (Equation 6.2.3.4.16.2.3.4.1 ) can be rearranged to deal with specific situations. For example, taking the logarithm of both sides yields the equation above in the form y=-mx+b.

lnk=−EaRT+lnA(6.2.3.4.4)

(6.2.3.4.4)ln⁡k=−EaRT+ln⁡A

Then, a plot of lnkln⁡k vs. 1/T1/T and all variables can be found.

y=lnky=lnk

m=−Ea/RTm=−Ea/RT

x=1/Tx=1/T

b=lnAb=ln⁡A

This form of the Arrhenius equation makes it easy to determine the slope and y-intercept from an Arrhenius plot. It is also convenient to note that the above equation shows the connection between temperature and rate constant. As the temperature increases, the rate constant decreases according to the plot. From this connection we can infer that the rate constant is inversely proportional to temperature.