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Mechanism of a hypothetical reaction X 2 + Y 2 → 2 X Y X_2 + Y_2 \rightarrow 2XY X 2 + Y 2 → 2 X Y is given below: \newline (i) X 2 → X + X X_2 \rightarrow X + X X 2 → X + X (fast) \newline (ii) X + Y 2 ⇌ X Y + Y X + Y_2 \rightleftharpoons XY + Y X + Y 2 ⇌ X Y + Y (slow) \newline (iii) X + Y → X Y X + Y \rightarrow XY X + Y → X Y (fast) \newline The overall order of the reaction will be
hard
ChemicalKinetics
2017
chemistry
Explanation To determine the overall order of the reaction, we need to analyze the given reaction mechanism.
\newline The mechanism consists of three steps:
\newline (i) X 2 → X + X ( X_2 \rightarrow X + X \, ( X 2 → X + X ( fast ) )
\newline )
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(ii)
X + Y 2 ⇌ X Y + Y ( X + Y_2 \rightleftharpoons XY + Y \, ( X + Y 2 ⇌ X Y + Y ( slow
(iii)
X + Y → X Y ( X + Y \rightarrow XY \, ( X + Y → X Y ( fast
The rate-determining step is the slowest step, which is step (ii).
The rate law for the rate-determining step is determined by the reactants involved in that step.
In step (ii), the reactants are
and
Therefore, the rate law can be written as:
Rate
= k [ X ] [ Y 2 ] = k[X][Y_2]
\newline = k [ X ] [ Y 2 ] To find the overall order of the reaction, we need to sum the exponents of the concentration terms in the rate law.
The order with respect to
is 1, and the order with respect to
is 1.
Thus, the overall order of the reaction is:
1 + 1 = 2
\newline 1 + 1 = 2
\newline 1 + 1 = 2 However, we need to consider the equilibrium in step (ii).
The equilibrium constant for the reversible step (ii) can affect the concentration of
If we assume that the concentration of
is in equilibrium with
then:
[ X ] = K [ X 2 ] 1 / 2
\newline [X] = K[X_2]^{1/2}
\newline [ X ] = K [ X 2 ] 1/2 Substituting this into the rate law gives:
Rate
= k ( K [ X 2 ] 1 / 2 ) [ Y 2 ] = k(K[X_2]^{1/2})[Y_2]
\newline = k ( K [ X 2 ] 1/2 ) [ Y 2 ] This simplifies to:
Rate
= k ′ [ X 2 ] 1 / 2 [ Y 2 ] = k'[X_2]^{1/2}[Y_2]
\newline = k ′ [ X 2 ] 1/2 [ Y 2 ] where
k ′ = k K . k' = kK.
\newline k ′ = k K . Now, the order with respect to
is
and the order with respect to
is 1.
Therefore, the overall order of the reaction is:
1 2 + 1 = 1.5
\newline \frac{1}{2} + 1 = 1.5
\newline 2 1 + 1 = 1.5 Thus, the correct option is Option 3.