C23J Kinetics

1
C23J Kinetics - 2

• Complex Reactions
• Reversible or Opposing
• Consecutive
• Parallel
• Chain

2
Reversible/Opposing Reactions
k1 k-1

• A B (assume both 1st order)

t 0 ao 0 t t ao x x equilm ao
xe xe (equilm concn of B )
Rate
3
Reversible/Opposing Reactions

• At equilibrium

• Substituting for k-1 into equation (1)

4
Reversible/Opposing Reactions

• Equation (3) can be rearranged and simplified

• Separate variables. Integrate limits t 0, x
  0 t t, x x

5
Reversible/Opposing Reactions

• Integration gives

• From equation (2), it can be shown that

6
Reversible/Opposing Reactions

• Substituting into equation (7)

t
7
Reversible/Opposing Reactions

• Rewrite equation (9) to give

ln(xe x) ln(xe) (k1 k-1)t y
c m x
ln(xe x)
slope -(k1 k-1)
t
8
Reversible/Opposing Reactions
k1 k-1
A B
xe ao - xe
equilm ao xe xe Keq
If Keq is known and, also Keq k1/k-1 then
both k1 and k-1 can be found.
9
Reversible/Opposing Reactions

• More complicated case To simplify, make
  ROHgtgtNOCl, i.e. pseudo-first order
  conditions pseudo-first order rate constant
  k1 kfROH

kf kb
NOCl ROH RONO HCl
Initially ao 0
0 t t ao x x
x t 8 ao xe xe
xe -d(ao x)/dt dx/dt k1(ao x)
kb(x2) (10) At equilibrium k1(ao
xe) kb(xe)2 kb k1 (ao xe)/(xe)2
k1kfROH
10
Reversible/Opposing Reactions

• substituting for kb in equation (10)

• which can be rearranged to give

• and integration by parts gives