A general reaction written as 1A + 2B --> C + 2D is studied and yields the following data:
Expt (A). (B) initial (C)/t
1. 0.150. 0.150. 8.00 x10^-3
2. 0.150. 0.300. 1.60 x10^-2
3. 0.300. 0.150. 8.00 x10^-3
What is the order of the reaction with respect to B?
What is the order of the reaction with respect to A?
Determine the initial rate of B consumption (delta(B)/delta t) for the first trial?
a7a I can't
To determine the order of the reaction with respect to B, we can compare the initial rates of reaction for trials 1 and 2.
Using the initial concentrations of A and B from trial 1 (0.15 M and 0.15 M, respectively) and the initial rate from trial 1 (8.00 x 10^-3 M/s), we can set up the following ratio:
(initial rate of trial 1) / (initial rate of trial 2) = (concentration of B for trial 1)^(order of reaction with respect to B) / (concentration of B for trial 2)^(order of reaction with respect to B)
Plugging in the values, we have:
(8.00 x 10^-3 M/s) / (1.60 x 10^-2 M/s) = (0.15 M)^(order of reaction with respect to B) / (0.30 M)^(order of reaction with respect to B)
Simplifying the equation, we get:
1/2 = (0.15/0.30)^(order of reaction with respect to B)
Taking the logarithm of both sides and solving for the order, we have:
log(1/2) = (order of reaction with respect to B) * log(0.15/0.30)
Simplifying further:
(order of reaction with respect to B) = log(1/2) / log(0.15/0.30)
Calculating this expression gives:
(order of reaction with respect to B) ≈ -1
So, the order of the reaction with respect to B is approximately -1.
To determine the order of the reaction with respect to A, we can similarly compare the initial rates of reaction for trials 1 and 3.
Using the initial concentrations of A and B from trial 1 (0.15 M and 0.15 M, respectively) and the initial rate from trial 1 (8.00 x 10^-3 M/s), we can set up the following ratio:
(initial rate of trial 1) / (initial rate of trial 3) = (concentration of A for trial 1)^(order of reaction with respect to A) / (concentration of A for trial 3)^(order of reaction with respect to A)
Plugging in the values, we have:
(8.00 x 10^-3 M/s) / (8.00 x 10^-3 M/s) = (0.15 M)^(order of reaction with respect to A) / (0.30 M)^(order of reaction with respect to A)
Simplifying the equation, we get:
1 = (0.15/0.30)^(order of reaction with respect to A)
Taking the logarithm of both sides and solving for the order, we have:
log(1) = (order of reaction with respect to A) * log(0.15/0.30)
(order of reaction with respect to A) = log(1) / log(0.15/0.30)
Calculating this expression gives:
(order of reaction with respect to A) = 0
So, the order of the reaction with respect to A is 0.
Lastly, to determine the initial rate of B consumption (delta(B)/delta t) for the first trial, we can refer to the given data:
Initial concentration of B for trial 1 = 0.150 M
Initial concentration of B for trial 2 = 0.300 M
Time taken to reach concentration C for trial 1 = 8.00 x 10^-3 s
Delta(B)/Delta t = (Change in concentration of B) / (Change in time)
Based on the stoichiometry of the reaction, we know that the coefficient of B is 2. Therefore, the change in concentration of B can be calculated by subtracting the final concentration of B (which is 0) from the initial concentration of B for trial 1:
Change in concentration of B = 0.150 M - 0 M = 0.150 M
Plugging in the values, we have:
Delta(B)/Delta t = (0.150 M) / (8.00 x 10^-3 s)
Calculating this expression gives:
Delta(B)/Delta t ≈ 18.8 M/s
Therefore, the initial rate of B consumption for the first trial is approximately 18.8 M/s.
To determine the order of the reaction with respect to each reactant, you can use the method of initial rates.
1. Order of the reaction with respect to B:
To determine the order of the reaction with respect to B, you will compare experiments 1 and 2. In both experiments, the initial concentration of A is the same (0.150 M), while the concentration of B doubles from 0.150 M in experiment 1 to 0.300 M in experiment 2. By comparing the change in the rate of the reaction with the change in the concentration of B, you can determine the order.
From experiments 1 and 2, you can observe that the rate of the reaction doubles when the concentration of B doubles. This indicates that the reaction rate is directly proportional to the concentration of B. Therefore, the order of the reaction with respect to B is 1 (first order).
2. Order of the reaction with respect to A:
To determine the order of the reaction with respect to A, you will compare experiments 1 and 3. In both experiments, the initial concentration of B is the same (0.150 M), while the concentration of A doubles from 0.150 M in experiment 1 to 0.300 M in experiment 3. Again, comparing the change in the rate of the reaction with the change in the concentration of A will allow you to determine the order.
From experiments 1 and 3, you can observe that the rate of the reaction remains constant when the concentration of A doubles. This indicates that the concentration of A does not affect the rate of the reaction. Therefore, the order of the reaction with respect to A is 0 (zero order).
3. Determining the initial rate of B consumption:
The initial rate of B consumption can be calculated by taking the slope of the concentration of B with respect to time at the beginning of the reaction. Looking at experiment 1, where the initial concentrations of A and B are both 0.150 M, you can calculate the initial rate.
By observing the change in concentration of B over time in experiment 1, you can calculate the slope (delta(B)/delta t). Dividing the change in concentration of B by the change in time from the initial state will give you the initial rate of B consumption.
rate exp 2 = k1*(A)^x(B)^y
--------------------------
rate exp 1 = k1*(A)^x(B)^y
Now plug in values for exp 1 and exp 2. That will give you
1.60E-2 = k1*(0.300)^x*(0.0.150)^y
--------=-------------------------8.00E-3 = k1*(0.15o)^x(0.150)^y
k1 cancels.
0.150)^y cancels and you are left
2 = (0.300)^x/(0.150)^y and becomes
2 = 2^x so x must be 1 and that's the order of B.
Can you handle the rest of it. This is how you do it.