For the reaction S2O82 (aq) + 3 I(aq) --> ? 2 SO4^-2(aq) + I3^-(aq), the followi

Question

For the reaction S2O82 (aq) + 3 I(aq) --> ? 2 SO4^-2(aq) + I3^-(aq), the following data were collected at a particular temperature:

Experiment [S2O8^-2] [I^-] Initial Rate (M/s) of disappearance of S2O82
1 0.054 0.048 1.6 x 10^-5
2 0.054 0.019 6.3 x 10^-6
3 0.030 0.030 5.5 x 10^-6

Determine a) the complete rate law showing the order with respect to each reactant and the rate constant with proper units b) the overall reaction order and c) the rate of disappearance of I when [S2O8^-2] = 0.075 M and [I^-] = 0.060 M (hint: you should get around 6.2 x 103 for the rate constant value)

Careful with Part c: the rate law gives disappearance of S2O8^-2 but the question asks for the rate of disappearance of I?


an added question:

For a hypothetical gas-phase reaction that is second order in A and third order in B, by what factor does the rate change if pA is decreased by 4 times and pB is doubled?

Explanation / Answer

a) From Experiments 1 and 2, holding [S2O8] constant while decreasing [I-] by a factor of about 2.5 also lowers the disappearance of S2O8 by 2.5. This means that the rate of disappearance of S2O8 with respect to I- is first order. So we have:

rate of S2O8 = k[S2O8]x[I-]

From the table, it's hard to use the same reasoning as above to get the value of x (i.e. the reaction order for S2O8). Here we plug in the numbers from the table instead. Let's take Experiments 1 and 3.

For Experiment 1: rate = k[0.054]x[0.048]=1.6x10-5

For Experiment 3: rate = k[0.030]x[0.030]=5.5x10-6

Divide the two equations above and use some algebra to find that:

(1.8)x=1.81

Here we can approximate that x 1.

Now we have our rate equation:

rate of S2O8 = k[S2O8][I-].

To find the value of k, we simply choose a single experiment from the table and plug in the values.

Let's choose Experiment 3:

rate = k[0.03]2=5.5x10-6 This gives us k = 6.11x10-3 which is close to the value you gave.

rate of S2O8 = k[S2O8][I-], where k = 6.11x10-3 M-2s-1)

b) The overall reaction order is 2 (1st order for S2O8 and first order for I-)

c) Notice in the reaction that [I-] = 3[S2O8] (i.e. three moles of I- react with each mole of S2O8). This means that the rate of disappearance of I- is 3 times that of S2O8. Using the numbers given, let's first find the rate of disappearance of S2O8:

rate of S2O8 = (6.11x10-3)[0.075][0.060] = 2.75x10-5 M/s

This means the rate of disappearance of I- = 3*2.75x10-5 M/s =8.25x10-5 M/s.

Extra Question:

old rate = k*pA2pB3

new rate = k*((1/4)pA)2(2*pB)3=(1/4)223*k*pA2pB3=(1/2)*old rate.

The rate decreases by a factor of 2.

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