Question

Consider the reaction, S₂O₈^2-   +    3 I^-  à    2 SO₄^2-  +  I₃^-. Data obtained in measuring rate of formation of I₃^- are listed in the table.

Experiment	[S2O82-], M	[I‑], M	Initial rate, Ms-1
1	0.035	0.055	1.5 x 10-5
2	0.070	0.055	3.0 x 10-5
3	0.070	0.110	6.0 x 10-5

1. Determine the order of reaction with respect to S₂O₈^2-.

2. What is the order of reaction with respect to I^-?

3. Give the overall order of reaction.

4. Write the rate law for the reaction.

5. Determine the value for the rate constant, k.

6. What is the initial rate of reaction if [S₂O₈^2-] = 0.030M and [I^-] = 0.050 M?

7. When the rate of formation of I₃^-is 3.0 x 10^-5 M/s, what is the rate of disappearance of I^-?

Answer 1

Solution :-

Suppose, the order with respect to S₂O₈^2- is p and with respect to I^- is q. The rate law can thus be written as: Rate = k [S​​​​​​​​​​​​​​_{2​​​​​​​}O​​​​​​​₈]^p [I^-]^q

Substituting the values of rate, [S​​​​​​​_{2​​​​​​​}O​​​​​​​₈] and [I^-] for various sets of experiments, we have

1.5 × 10^-5 = k [0.035]^p [0.055]^q ............….(i)

​​​​​​3.0 × 10^-5 = k [0.070]^p [0.055]^q ................(ii)

6.0 × 10^-5 = k [0.070]^p [0.110]^q ...............(iii)

Dividing eq. (ii) by eq. (i) , we get,

(3.0 × 10^-5) / (1.5 × 10^-5) = (0.070)^p / (0.035)^p

2 = 2^p

p = 1

Dividing eq. (iii) by eq. (ii), we get,

(6.0 × 10^-5) / (3.0 × 10^-5) = (0.110)^q / (0.055)^q

2 = 2^q

q = 1

1) Thus, the order of reaction with respect to S₂O₈^2- is = 1

2) The order of reaction with respect to l^- is = 1

3) Overall rate of reaction = (p + q) = (1 + 1) = 2

4) Rate Law ,

Rate = k [S​​​​​​​_{2​​​​​​​}O​​​​​​​_{8​​​​​​​​}^2-​​​​​​]¹ [I^-]¹

5) Putting values of order of reactants in equation 1, we get,

1.5 × 10^-5 = k [0.035]¹ [0.055]¹

or, k (Rate constant) = (1.5 × 10^-5) / (0.035 × 0.055) = 7.8 × 10^-3  M^-1 s^-1

6) If [S2O82-​​​​​​] = 0.030 M, and [I​​​​​​​^-] = 0.050 M

k = 7.8 × 10^-3  M^-1 s^-1

Rate =?

Rate = (7.8 × 10^-3) × (0.030)× (0.050)

Rate = 1.17 × 10^-5 M s^-1

7) Rate of formation of I₃^- = 1/3 × Rate of disappearance of I^-

or , Rate of disappearance of I^- = 3 × Rate of formation of I₃^-

or, Rate of disappearance of I​​​​​​​^- = 3 × (3.0 × 10^-5) = 9.0 × 10^-5 M/s

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