5. Consider the reaction: C12H22O11 + H2O 2C6H12O6 Some data for this reaction f

Question

5. Consider the reaction: C12H22O11 + H2O 2C6H12O6 Some data for this reaction follows:

Experiment

[C12H22O11] (M)

[H2O] (M)

Initial Rate of Appearance of C6H12O6 (M/s)

1

0.100

55.5

2.30 × 106

2

0.350

55.5

8.05 × 106

3

0.100

40.0

2.30 × 106

a. Write the rate law for this reaction.

b. Calculate the rate constant.

c. At what rate does C12H22O11 disappear if the initial concentrations are [C12H22O11] = 0.250 M and [H2O] = 45.0 M?

(show work)

Experiment

[C12H22O11] (M)

[H2O] (M)

Initial Rate of Appearance of C6H12O6 (M/s)

1

0.100

55.5

2.30 × 106

2

0.350

55.5

8.05 × 106

3

0.100

40.0

2.30 × 106

Explanation / Answer

In order to calculate the rate law expression for a A+B reaction, we need to apply Initial Rates Method.

Note that the generic formula goes as follows:

r = k [A]^a [B]^b

Note that if we got at least 3 sets of point, in which we have A and B constant, then we could use:

r1 / r2 = (k1 [A]1^a [B]1^b) / (k2 [A]2^a [B]2^b)

If we assume K1 and K2 are constant, then K1= K2 cancel each other

r1 / r2 = ([A]1^a [B]1^b) / ( [A]2^a [B]2^b)

Then, order according to [A] and [B]

r1 / r2 = ([A]1/[A2])^a * ([B]1/[B]2)^b

If we get two points in which A1 = A2, then we could get B, and vise versa for A...

From the data shown in YOUR table

Choose point 1 and 2...

r1 / r2 = ([A]1/[A2])^a * ([B]1/[B]2)^b

substitute

(2.3) / (8.05) = (0.1/0.35)^a * (55.5/55.5)^b

Cleary, the coefficient cancels:

0.287 = 0.287 ^a

solve,

a = 1

Choose now points 2 and 3:

r3 / r3 = ([A]2/[A]3)^a * ([B]2/[B]3)^b

substitute

(2.3)/(2.3) = (0.1/0.1)^a * (55.5/40)^b

Cleary, the coefficient cancels:

1= (1.387 )^b

solve,

ln(1) / ln(1.387 ) = b

b= 0

so...

a = 1, b = 0

then

r = k [A]^a [B]^b

so

r = k [A]^1 [B]^0

r = k*[A]

b)

For "k" value... choose any point in your set of data, I will choose 1 for simplicity

substitute data

r = k*[A]^2

2.3*10^-6 = k*(0.1)

K = (2.3*10^-6)/(0.1 ) = 2.3*10^-5 1/s

c)

rate for [C12H22O11] = 0.25 and [H2O ] = 0.45

we just care on C12H22O11

so

RAte = (2.3*10^-5 )(0.25 ) = 0.00000575 M/s

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