Question

Determine the rate law and the value of k for the following reaction using the data provided.

S₂O₈^2-(aq)+3I^-(aq) --------> 2SO₄^2-(g)+I₃^-(aq)

[S₂O₈^2-]i (M) [I^-]i (M) Initial Rate (M^-1s^-1)

0.30 0.42 4.54

0.44 0.42 6.65

0.44 0.21 3.33

Answer is Rate = 36 M^-1s^-1 [S₂O₈^2-] [I^-]

Please show work

Answer 1

Given that the reaction is,

S2O8 2-(aq)+3I-(aq) --------> 2SO4 2-(g)+I3-(aq)

Let us assume,

Rate = K [S2O8 2-]^x [I-]^y

From 1st data provided in the data table,

4.54 = K (0.30)^x (0.42)^y ............(1)

From the second data

6.65 = K (0.44)^x (0.42)^y ............(2)

Dividing equation (2) by (1) we get

1.465 = (1.466)^x

=> x = 1

From the 3rd data in the data table,

3.33 = K (0.44)^x (0.21)^y ............(3)

Dividing equation (2) by equation (3) we get

2 = (2)^y

=> y = 1

Therefore,

Rate = K [S2O8 2-] [I-]

Now from equation (1)

4.54 = K (0.30) (0.42)

=> K = 36 M^-1 s^-1

=> Rate = 36 M^-1s^-1 [S₂O₈^2-] [I^-]