3.1.9 - 3.1.10 Rate Equations and Kₚ
Rate equation: Rate = [A]ᵐ [B]ⁿ
[A] = concentration of reactant A
[B] = concentration of reactant B
m = order of reaction with respect to A
n = order of reaction with respect to B
k = rate constant; varies with temperature
Sammer Sheikh
Arrhenius equation: k = Ae⁻ᴱᵃ/ᴿᵀ
k = constant
A = Arrhenius constant
Eₐ = activation energy J mol⁻¹
T = temperature (K)
R = gas constant 8.31 J K⁻¹mol⁻¹
rearranged in the form: ln k = –Eₐ /RT + ln A
y = ln k
m = –Eₐ /RT
x = time
c = ln A
Kp
The equilibrium constant Kp is deduced from the equation for a reversible reaction occurring in the gas phase.
Kp is the equilibrium constant calculated from partial pressures for a system at constant temperature.
catalyst does not affect the value of the equilibrium constant.
Rate of reaction
equation: aX + bY --> cZ
expression: rate = k [X]ᵃ [Y]ᵇ
a species not present in the equation may appear in the rate equation; a species present in the equation may not appear in the rate equation
k = rate constant; units are variable depending on overall order of reaction
ᵃ and ᵇ = order of reaction with respect to X and Y;
overall order of reaction = ᵃ + ᵇ
rate concentration graphs:
concentration time graphs:
effect of changing temperature on k
decrease temperature = k decreases
increase temperature = k increases
change in concentration of either reactants or products with unit time
rate of reaction at an instant = change in concentration / time
temperature is a measure of the average kinetic energy of particles; as temperature increases, greater proportion of molecules have enough energy to react
order of reaction restricted to 0, 1, 2
zero order: rate not affected by concentration of a species; not in rate equation
first order: rate directly proportional to concentration of species
second order: rate proportional to the square of the concentration of the species
overall order of reaction = ᵐ + ⁿ
e⁻ᴱᵃ/ᴿᵀ = fraction of molecules with energy greater than the activation energy
Rate determining step
reactions take place in different steps; product of one step in the reactant of the next reaction
rate of slowest step is the rate determining step / rate limiting step
steps after the rate determining step will not affect the rate of reaction, so will not appear in the rate equation
species in or before the rate determining step could appear in the rate equation; could affect overall rate of reaction
partial pressure: contribution of a gas to the total pressure in a mixture of gases; pressure that the gas would exert if it occupied the container by itself
partial pressure (p) of A = mole fraction of A x total pressure
mole fraction of gas A: number of moles of A in mixture / total number of moles of gas in the mixture
similar to Kc calculations; concentrations are replaced by partial fractions
changing total pressure only affects equilibrium constant when there is different numbers of moles of gas on either side of the equation
if increase temperature, equilibrium move in endothermic direction
if decrease temperature, equilibrium move in exothermic direction