For the reaction 2H2O2 + 2HI -> 2H2O + I2, the following mechanism is proposed: 1. H2O2 + HI -> H2O + HOI 2. HOI -> H2O + I2 3. H2O2 + I2 -> 2H2O + O2 Derive an expression for the rate of formation of I2 using the steady-state approximation.
The Correct Answer and Explanation is:
To derive an expression for the rate of formation of I2I_2I2 in the given reaction using the steady-state approximation, let’s first break down the reaction and its proposed mechanism.
Given Reaction:
2H2O2+2HI→2H2O+I22H_2O_2 + 2HI \rightarrow 2H_2O + I_22H2O2+2HI→2H2O+I2
Proposed Mechanism:
- H2O2+HI→H2O+HOIH_2O_2 + HI \rightarrow H_2O + HOIH2O2+HI→H2O+HOI (Step 1)
- HOI→H2O+I2HOI \rightarrow H_2O + I_2HOI→H2O+I2 (Step 2)
- H2O2+I2→2H2O+O2H_2O_2 + I_2 \rightarrow 2H_2O + O_2H2O2+I2→2H2O+O2 (Step 3)
Step-by-Step Approach Using the Steady-State Approximation:
- Steady-State Approximation:
The steady-state approximation assumes that the concentration of intermediates (in this case, HOIHOIHOI and I2I_2I2) remains approximately constant throughout the reaction. This means that the rate of formation of these intermediates equals the rate of their consumption. - Rate of Formation and Consumption of HOIHOIHOI:
From Step 1, HOIHOIHOI is produced by the reaction:
H2O2+HI→H2O+HOIH_2O_2 + HI \rightarrow H_2O + HOIH2O2+HI→H2O+HOI
The rate of this step is proportional to the concentrations of H2O2H_2O_2H2O2 and HIHIHI:
Rate of formation of HOI=k1[H2O2][HI]\text{Rate of formation of } HOI = k_1[H_2O_2][HI]Rate of formation of HOI=k1[H2O2][HI] From Step 2, HOIHOIHOI is consumed in the reaction:
HOI→H2O+I2HOI \rightarrow H_2O + I_2HOI→H2O+I2
The rate of consumption of HOIHOIHOI is proportional to the concentration of HOIHOIHOI:
Rate of consumption of HOI=k2[HOI]\text{Rate of consumption of } HOI = k_2[HOI]Rate of consumption of HOI=k2[HOI] Using the steady-state approximation for HOIHOIHOI, we set the rate of formation equal to the rate of consumption:
k1[H2O2][HI]=k2[HOI]k_1[H_2O_2][HI] = k_2[HOI]k1[H2O2][HI]=k2[HOI]
Solving for [HOI][HOI][HOI]:
[HOI]=k1[H2O2][HI]k2[HOI] = \frac{k_1[H_2O_2][HI]}{k_2}[HOI]=k2k1[H2O2][HI] - Rate of Formation of I2I_2I2:
From Step 2, I2I_2I2 is produced from the reaction of HOIHOIHOI (which we’ve already solved for):
HOI→H2O+I2HOI \rightarrow H_2O + I_2HOI→H2O+I2
The rate of formation of I2I_2I2 is proportional to the concentration of HOIHOIHOI:
Rate of formation of I2=k2[HOI]\text{Rate of formation of } I_2 = k_2[HOI]Rate of formation of I2=k2[HOI] Substituting the expression for [HOI][HOI][HOI] into this rate equation:
Rate of formation of I2=k2×k1[H2O2][HI]k2=k1[H2O2][HI]\text{Rate of formation of } I_2 = k_2 \times \frac{k_1[H_2O_2][HI]}{k_2} = k_1[H_2O_2][HI]Rate of formation of I2=k2×k2k1[H2O2][HI]=k1[H2O2][HI]
Thus, the rate of formation of I2I_2I2 is given by:
Rate of formation of I2=k1[H2O2][HI]\text{Rate of formation of } I_2 = k_1[H_2O_2][HI]Rate of formation of I2=k1[H2O2][HI]
Final Answer:
The rate of formation of I2I_2I2 is k1[H2O2][HI]k_1[H_2O_2][HI]k1[H2O2][HI], where k1k_1k1 is the rate constant for the first step in the reaction mechanism. This expression indicates that the rate depends on the concentrations of H2O2H_2O_2H2O2 and HIHIHI.
