In: Chemistry
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 × 10−6 |
2 |
0.350 |
55.5 |
8.05 × 10−6 |
3 |
0.100 |
40.0 |
2.30 × 10−6 |
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)
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