CHAP. 9: CHEMICAL KINETICS [CONTENTS] 300
9.4.7 First-order reversible reactions.
9.4.7.1 Type of reaction
A
k 1
→ B,
B
k 2
→ A.9.4.7.2 Kinetic equations.
−
dcA
dτ=k 1 cA−k 2 cB =⇒dx
dτ=k 1 (cA0−x)−k 2 (cB0+x). (9.122)9.4.7.3 Integrated forms of the kinetic equations.
x =k 1 cA0−k 2 cB0
k 1 +k 2[1−exp (−(k 1 +k 2 )τ)], (9.123)cA = cA0−x , cB=cB0+x. (9.124)9.4.8 Reversible reactions and chemical equilibrium
Let us consider the reversible reaction
aA +bB +··· →k^1 sS +tT+···, (9.125)
sS +tT···
k 2
→ aA +bB +··· (9.126)We will assume that, as was mentioned at the beginning of this section, the stoichiometric
coefficients are equal to the partial orders of the reaction, i.e. that both reactions are elementary
[see9.5.1]. The rate of the direct reaction (9.125) isr 1 =k 1 caAcbB···and the rate of the reverse
reaction (9.126) isr 2 =k 2 csSctT···At timeτ → ∞the reaction reaches the state of chemical
equilibrium and we can write
r 1 =r 2 =⇒ k 1 caA,eqcbB,eq···=k 2 csS,eqctT,eq···, [equilibrium], (9.127)