Reactivity 2.2.6—Many reactions occur in a series of elementary steps. The slowest step determines the rate of the reaction. (AHL)
Reactivity 2.2.7—Energy profiles can be used to show the activation energy and transition state of the rate-determining step in a multistep reaction. (AHL)
Reactivity 2.2.8—The molecularity of an elementary step is the number of reacting particles taking part in that step. (AHL)
Reactivity 2.2.9—Rate equations depend on the mechanism of the reaction and can only be
determined experimentally. (AHL)
Reactivity 2.2.10—The order of a reaction with respect to a reactant is the exponent to which the
concentration of the reactant is raised in the rate equation. The order with respect to a reactant can describe the number of particles taking part in the rate determining step. The overall reaction order is the sum of the orders with respect to each reactant. (AHL)
Reactivity 2.2.11—The rate constant, k, is temperature dependent and its units are determined
from the overall order of the reaction. (AHL)
Reactivity 2.2.12—The Arrhenius equation uses the temperature dependence of the rate constant to determine the activation energy. (AHL)
Reactivity 2.2.13—The Arrhenius factor, A, takes into account the frequency of collisions with
proper orientations. (AHL)
Rate expression & order of reaction
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The rate of reaction between reactants (e.g. A and B) can be followed experimentally.
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The mathematical relationship between the rate of reaction and the concentration of reactants can be expressed as a rate expression:
xA + yB → zC + D
r = k [A]x[B]y:
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k is the rate constant
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X and Y is the order of reaction with respect to A and B
Graphical Representation of Orders of Reactions
Rate constant units
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Rate unit = mol dm-3 s-1
Order | Zero | First | Second | Third |
units of k | mol dm-3 s-1 | s-1 | mol-1 dm3 s-1 | mol-2 dm6 s-1 |
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Increases in intervals of mol-1 dm3
Factor change calculation
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r=k[X][Y]2
Change | Applied | Result |
[X] doubles and [Y] no change | k[2X][Y]2 = 2 k[X][Y]2 | 2 r (rate doubles) |
[X] no change and [Y] doubles | k[X][2Y]2 = 4 k[X][Y]2 | 4 r (rate quadruples) |
[X] doubles and [Y] halves | k[2X][½Y]2 = 2 x ½ k[X][Y]2 | 2 x ½ r (no change in rate) |
[X] halves and [Y] doubles | k[½X][2Y]2 = ½ x 4 k[X][Y]2 | ½ x 4 r (rate doubles) |
Finding the rate expression
1.
Select 2 experiments that have the same concentration for one reactant and different for the other
2.
Compare the magnitude of rate change relative to [reactant] change
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As we double [X], the initial rate also doubles therefore the reaction is first order with respect to [X]
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As we double [Y], the initial rate quadruples therefore the reaction is second order with respect to [Y]
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As we double [Z], the initial rate stays the same, therefore the reaction is zero order with respect to [Z]
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Hence, the rate expression is written as r = k [x][y]2 → Reaction is third order overall
Calculating the rate constant, k
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r=k[X][Y]2
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k= r[X][Y]2
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k=5.00 10-4[0.100][0.100]2
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k = 500 mol-2 dm6 s-1
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you can use any of the experiment values to calculate k (e.g. experiment 1)
Reaction mechanisms
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Many reactions do not proceed in one step. When there are more than 2 reactant molecules, it is too improbable for all the reactants to collide at the same time.
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When there is more than one step to a reaction, each step will proceed at its own rate
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The overall rate of reaction will always depend on the slowest step: rate-determining step
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The RDS has the highest Ea out of the steps in the mechanism
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The Ea for the overall reaction = the Ea of RDS
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The number of molecules involved in the RDS determines the reaction’s molecularity
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unimolecular = 1, bimolecular = 2, trimolecular = 3
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Intermediate: a species formed during the steps of the reaction but does not appear in the overall rxn
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Formed and then consumed in the duration of the reaction
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Rate expression cannot be deduced from reactant coefficients of the overall rxn (different to single-step rxn)
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Example: NO2(g) + CO(g) → NO(g)+ CO2(g)
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step 1: NO2(g) + NO2(g)→ NO(g) + NO3(g)
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step 2: NO3(g)+ CO(g) → NO2(g) + CO2(g)
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overall reaction: NO2(g) + CO(g) → NO(g) + CO2(g)
<Determining the Rate Expression when there are multiple steps in a reaction>
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Reactants in a fast step before the RDS are included in the rate expression but not after
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Common rate expression pitfall = reactants in a fast step before the slow step not included, intermediate included
<Confirm Rate Expression>
1.
Test effect of independently varying [reactant] on rxn rate
2.
Check if rate changes proportionally to change in [reactant] according to rxn order
a.
Doubling first order [reactant A] doubles rate
b.
Tripling zero order [reactant B] doesn’t affect rate
Arrhenius Equation
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k = Ae−Ea/RT
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A = Arrhenius constant (or frequency factor) that accounts for geometry and orientation requirements of successful collision.
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R = gas constant (= 8.31 J K–1 mol–1)
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T = temperature (K)
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Ea = activation energy (J)
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Temp ↑ = rate constant ↑ (non linearly)
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Molecule complexity ↑ = Arrhenius constant ↓ (chances of successful collision ↓)
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k dependent on both [reactant] via rate expression and temp. via arrhenius equation
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ln k=-EaRT+ln A
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Ea is always +ve
Graphical method | Simultaneous equation method |
Plot ln k values against 1/T and calculate gradient | Calculate from a table of k and T values |
“Arrhenius Plot”
Y-axis = ln k
X-axis = 1/T
Gradient = -Ea/RT | ln k1=-EaRT1+ln A
ln k2=-EaRT2+ln A
Subtracting the equations above gives:
ln (k1k2)=EaR(1T2-1T1) |
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Always convert oC into K
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No need to know A value