A given reaction is fitted into the following Arrhenius form : K2 = 6.0 × 1014 (S-1) . exp \(\left[-\frac{104.4\ (\mathrm{kJ\,mol^{-1}})}{RT}\right]\) Value of the rate constant at very high temperature would be :
5.8 × 1014 S-1
The Arrhenius equation is \(k = A\,e^{-E_a/RT}\), where \(A\) is the pre-exponential (frequency) factor. Here \(A = 6.0 \times 10^{14}\) s-1 and \(E_a = 104.4\) kJ mol-1.
Look at what happens to the exponential term as the temperature rises. The exponent is \(-\frac{E_a}{RT}\); as \(T \to \infty\) the fraction \(\frac{E_a}{RT} \to 0\), and therefore
\(e^{-E_a/RT} \to e^{0} = 1\).
So in the high-temperature limit \(k \to A = 6.0 \times 10^{14}\) s-1, and the value closest to that limit is 5.8 × 1014 s-1.
The physical meaning is worth stating. The exponential term is the fraction of collisions with enough energy to surmount the barrier. At very high temperature essentially every encounter carries sufficient energy, so the activation barrier stops limiting the rate and the reaction proceeds as fast as the molecules can come together and orient correctly. That maximum possible rate is the pre-exponential factor, which is why \(A\) represents the collision frequency weighted by the steric requirement.
It also follows that \(k\) can never exceed \(A\) at any finite temperature, since the exponential is always less than 1. The two options of order 104 are smaller than \(A\) by ten orders of magnitude and correspond to no limit of this expression.
Hence the rate constant at very high temperature is 5.8 × 1014 s-1.
Similar Questions
Analysis of four different samples of an alloy yielded 12.12, 12.14, 12.10 and 12.22% of metal. The mean deviation of the result is :
For the first order consecutive reaction :
Which of the following statement is incorrect ?
E° value for various ions are as follows :
E°(MnO4-) = +1.51 V
E°(Ag/Ag+) = +0.7996 V
E°(Au/Au+) = +1.692 V
E°(Zn/Zn2+) = -0.761 V
Based on this data, permaganate can be used to oxidize :
Vapour pressure of 0.5 molal solution of non-volatile solute in organic solvent at 30°C would be :
(Given : vapour pressure of pure organic solvent is 100 torr; the molecular weight of organic solvent is 100 g mol-1).
The following half cell represents, normal hydrogen electrode (NHE) :
If, we discharge the electrochemical cell rapidly, then :
Consider the reaction :
H2S(g) + \(\tfrac{3}{2}\) O2(g) → SO2(g) + H2O(g), ΔH° = 518.62 kJ
What is the effect of increase of temperature and pressure on the reaction ?
The number of microstates of distributing five quanta of energy among four distinguishable particles is :
The variation of Cp with pressure at constant temperature is given by :
According to the phase diagram given below, the composition of the layer `a' relative to the layer `b' at point `c' is :
Important Questions from Thermodynamics
Two blocks of ice when pressed together join to form one block because
The ratio C p/C vof the specific heats at constant pressure and volume of a monoatomic ideal gas in two dimensions is
The total number of phonon modes in a solid of volume V is \(\int_{\rm{0}}^{{\rm{ω_ D}}} {{\rm{g}}\left( {\rm{ω }} \right)\,} {\rm{dω }}\) = 3N, where N is the number of primitive cells, ω Dis the Debye frequency and density of photon modes is g( ω ) = AV ω2 (with A > 0 a constant). If the density of the solid doubles in a phase transition, the Debye temperature θ D, will
The dispersion relation of a gas of non-interacting bosons in d dimensions is E(k) = ak s, where a and s are positive constants. Bose-Einstein condensation will occur for all values of
Example of thermoplastic among the following is
