The bromination of acetone is acid-catalyzed.
CH3COCH3 + Br2 CH3COCH2Br + H+ + Br -
The rate of disappearance of bromine was measured for several different concentrations of acetone, bromine, and H+ ions at a certain temperature.
[CH3COCH3] [Br2] [H+] rate of disappearance of Br2 (M/s)
0.30 0.050 0.050 5.7 10-5
0.30 0.10 0.050 5.7 10-5
0.30 0.050 0.10 1.2 10-4
0.40 0.050 0.20 3.1 10-4
0.40 0.050 0.050 7.6 10-5
(a) What is the rate law for the reaction?
(b) Determine the rate constant. answer in M·s
You really need to tell us what you don't understand about this.
To get you started, we can look at reaction 1 and reaction 2. Acetone is same concn, Br2 is different, H^+ is same and rate is same. So the only difference in concn is Br2 (change from 0.05 to 0.10) but rate remains the same. What does that tell you about the order with respect to (Br2)?
Then compare reaction 1 with reaction 3. Acetone is same, Br2 is same, H^+ is different (0.05 vs 0.1). That should give you the exponent (order) for (H^+). If I didn't goof that will be 1. Clarify your thoughts in a repost if this doesn't help.
To determine the rate law for the reaction, we need to examine how the rate of disappearance of bromine (Br2) changes with changes in the concentrations of acetone (CH3COCH3), bromine (Br2), and H+ ions.
(a) The rate law is expressed in the form:
rate = k [CH3COCH3]^a [Br2]^b [H+]^c
From the given data, we can compare two sets of conditions where only one concentration changes while keeping the others constant. Let's compare the first and second rows of data. In both cases, [CH3COCH3] and [H+] are constant, while only [Br2] changes. We can see that the rate of disappearance of Br2 (M/s) remains the same. This suggests that the concentration of Br2 doesn't affect the rate, indicating that the reaction is zero-order with respect to [Br2]. Therefore, b = 0.
Now, let's compare the first and third rows of data. In both cases, [CH3COCH3] and [Br2] are constant, while only [H+] changes. We observe that the rate of disappearance of Br2 changes. Specifically, as [H+] doubles, the rate of disappearance of Br2 doubles as well. This indicates that the rate is directly proportional to the concentration of H+. Therefore, c = 1.
Finally, let's compare the third and fourth rows of data. In both cases, [Br2] and [H+] are constant, while only [CH3COCH3] changes. We can see that when [CH3COCH3] doubles, the rate of disappearance of Br2 doubles as well. This suggests that the rate is directly proportional to the concentration of CH3COCH3. Therefore, a = 1.
Thus, the rate law for the reaction is:
rate = k [CH3COCH3] [H+]
(b) To determine the rate constant (k), we can choose any set of data from the table and substitute the values into the rate law equation, along with the corresponding rate of disappearance of Br2. Let's choose the first row of data:
rate = k [CH3COCH3] [H+]
5.7 × 10^-5 M/s = k (0.30 M) (0.050 M)
We can rearrange the equation to solve for the rate constant (k):
k = rate / ([CH3COCH3] [H+])
Substituting the values:
k = (5.7 × 10^-5 M/s) / (0.30 M × 0.050 M)
k ≈ 3.8 M^-1 s^-1
Therefore, the rate constant is approximately 3.8 M^-1 s^-1.
(a) To determine the rate law for the reaction, we can look at the effect of changing the concentrations of acetone, bromine, and H+ ions on the rate of disappearance of bromine.
From the given data, we can see that when the concentration of acetone ([CH3COCH3]) and the concentration of bromine ([Br2]) are constant, and only the concentration of H+ ions ([H+]) changes, the rate of disappearance of bromine remains constant. From this, we can conclude that the concentration of H+ ions does not affect the rate of the reaction. Therefore, the reaction is zero-order with respect to [H+].
Next, we can compare the effects of changing the concentrations of acetone and bromine while keeping the concentration of H+ ions constant. From the data, we can observe that when the concentration of acetone is doubled and the concentration of bromine is kept constant, the rate of disappearance of bromine remains constant. This indicates that the reaction is zero-order with respect to [CH3COCH3].
Similarly, when the concentration of bromine is doubled with the concentration of acetone kept constant, the rate of disappearance of bromine remains constant. Hence, the reaction is also zero-order with respect to [Br2].
Combining the information, we can conclude that the rate law for the reaction is:
Rate = k[CH3COCH3]^0[Br2]^0[H+]^0
Simplifying, we get:
Rate = k
(b) Since the order of the reaction with respect to all the reactants is zero, the rate constant (k) can be determined directly from the given data by choosing any set of concentrations and the corresponding rate. Let's select the last set of concentrations:
[CH3COCH3] = 0.40 M
[Br2] = 0.050 M
[H+] = 0.050 M
rate = 7.6 × 10-5 M/s
Substituting these values into the rate equation, we have:
7.6 × 10-5 M/s = k
Therefore, the rate constant (k) for the reaction is 7.6 × 10-5 M/s.