Increasing the concentration, increases the number of reactant particles per unit volume, so there are more collisions, and a greater chance of a successful collision.
Increasing the surface area of a solid increases the number of solid reactant particles in contact with the other reactants, so the number of collisions increase, and there is a greater chance of a successful collision.
Adding a catalyst increases the rate by providing a new reaction pathway with lower activation energy than the uncatalyzed pathway.
Activation energy­­the minimum energy required for a successful collision.
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[A] [B] Rate (M/s) 0.1
0.02 4.8 x 10­3 0.3 0.02 4.3 x 10­2 0.6 0.06 5.2 x 10­1
Experiment 1 and 2. [A] tripled and rate increased nine times so 2nd order with respect to A.
Expt 2 and 3. We already know that its 2nd order with respect to A, so the rate will be at a minimum 4.3 x 10­2 x 4 = 1.7 x 10­1. Tripling the conc of B caused the rate to be triple or 1.7 x 10­1 x 3 = 5.2 x 10­1. So it is 1st order in B.
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This graph is the function [A]=[A]oe­kt
This means that the loss of reactant in a first order reaction is an exponential decay.
This line is the function ln[A]=ln[A]o ­ kt
Note the slope of this line is the rate constant k
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A
product
If this is a first order reaction, then the relationship between [A] and time is given by
ln[A] = ln[A]o ­ kt
Lets do our first problem. How long will it take for half of the reactant to react?
If [A]o is the concentration at time = 0, then 0.5 [A]o is the concentration when half of A has reacted. So substitute into the 1st order rate equation.
Solve for time
half of A has reacted.
Using ln(AB) = lnA + lnB
Note that ­ln(A/B) = ln(B/A)
This is an interesting result. This means that ln 2 divided by the rate constant is the time it takes for half of the reactant to be consumed. We call this the half life of the reaction, and it is a constant at a constant temperature (because k is temperature dependent)
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13.89 pg. 556
The C­14 decay rate of a sample obtained from a young tree is 0.260 disintegrations per second per gram. Another wood sample prepared from an object recovered from an excavation gives a decay rate of 0.186 disintegrations per second per gram. What is the age of the object? The half life of C­
14 is 5.73 x 103 years.
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13.98 Pu­239 (t1/2 = 2.44 x 105 yr) is used in nuclear reactors and atomic bombs. If there are 5.0 x 102 g of the isotope in a small atomic bomb, how long will it take for the substance to decay to 1.0 x 102 g?
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