Given this data in a study on how the rate of a reaction was affected by the concentration of the reactants
Initial Rate,
RUN #(A, M) (B, M) (C, M) (mol L-1 s-1
1 0.200 0.100 0.600 5.00
2 0.200 0.400 0.400 80.0
3 0.600 0.100 0.200 15.0
4 0.200 0.100 0.200 5.00
5 0.200 0.200 0.400 20.0
The rate constant for this reaction (all in the same units) is
a. 6667 b. 208 c. 2083 d. 139 e. 2500
help me!
chemistry - DrBob222, Friday, February 17, 2012 at 10:29pm
The secret here is to determine the order of the reaction. For example, it is zero order in C. Do you know how to do the others? After you determine the orders, then k is determined as in your post above.
Saw the other post didn't help at all but I need the answer and simple step by step solution
I don't remember all the posts you had yesterday. Did you read how to determine the rate law expression. Can you do that from these data? I seem to remember that it was zero with respect to C, 2nd order with respect to B and 1st order with respect to A. so the rate law expression is
rate = k(A)^1(B)^2(C)^0 which becomes simply rate = k(A)(B^2) since we don't need to show exponents of 1 (and remember anything to the zero power is 1)
Pick any trial in your post and plug the values into the rate law expression above. The only unknown is k. Solve for that.
For example, pick the first one.
rate = k*(A)(B)^2
5.00 = k*(0.200)(0.1)^2 and solve for k.
2500
To determine the rate constant for this reaction, we first need to determine the order of the reaction with respect to each reactant.
From the provided data, we can see that the concentrations of reactants A, B, and C are varied, and the resulting initial rates are measured. The initial rate is the rate of the reaction at the beginning, when the reactant concentrations are at their initial values.
Now, let's analyze the data in order to determine the order of the reaction for each reactant:
1. For reactant A:
- Comparing runs 1 and 2, we can see that the concentration of A is constant (0.200 M), while the concentration of B changes. However, the initial rates in runs 1 and 2 are significantly different.
- This indicates that the concentration of A does not directly affect the rate of the reaction. Therefore, the order of reactant A is zero.
2. For reactant B:
- Comparing runs 1 and 4, we can see that the concentration of B is constant (0.100 M), while the concentration of A changes. The initial rates for runs 1 and 4 are the same.
- This suggests that the concentration of B does not directly influence the rate of the reaction. Thus, the order of reactant B is also zero.
3. For reactant C:
- Comparing runs 1 and 3, we observe that the concentration of C is constant (0.200 M) and the concentrations of A and B change. The initial rates for runs 1 and 3 are different.
- This suggests that the rate of the reaction is dependent on the concentration of C. Therefore, the order of reactant C is one.
Now that we know the reaction is zero order with respect to reactants A and B and first order with respect to reactant C, we can write the rate equation in the form:
rate = k[A]^0[B]^0[C]^1
= k[C]
Next, we need to determine the value of the rate constant, k. We can do this by using the data provided in the question.
Taking run 1 as an example, where the initial rate is 5.00 mol L^(-1) s^(-1), and the concentration of reactant C is 0.600 M, we can substitute these values into the rate equation:
5.00 = k(0.600)
Solving for k, we find:
k = 5.00 / 0.600
k = 8.33 s^(-1)
Therefore, the rate constant for this reaction is 8.33 s^(-1).
Note: None of the answer choices provided in the question match the calculated value of the rate constant.
To determine the rate constant, we first need to determine the order of each reactant. The rate of a reaction is generally given by the equation:
rate = k[A]^x[B]^y[C]^z
where k is the rate constant, [A], [B], and [C] are the concentrations of the reactants, and x, y, and z are the orders of the reaction with respect to A, B, and C, respectively.
In order to determine the order of each reactant, we can compare the initial rates of the reaction for different sets of reactant concentrations.
Let's start by comparing runs 1 and 4, where only the concentration of reactant B changes.
Run 1: (A, B, C) = (0.200, 0.100, 0.600) -> Rate = 5.00
Run 4: (A, B, C) = (0.200, 0.100, 0.200) -> Rate = 5.00
Since the rate remains the same even though the concentration of B changes, we can conclude that the reaction is zero-order with respect to B.
Next, let's compare runs 1 and 5, where the concentration of reactant C changes.
Run 1: (A, B, C) = (0.200, 0.100, 0.600) -> Rate = 5.00
Run 5: (A, B, C) = (0.200, 0.200, 0.400) -> Rate = 20.0
Since the rate quadruples when the concentration of C is halved, we can conclude that the reaction is first-order with respect to C.
Now, let's compare runs 1 and 2, where the concentration of reactant B changes.
Run 1: (A, B, C) = (0.200, 0.100, 0.600) -> Rate = 5.00
Run 2: (A, B, C) = (0.200, 0.400, 0.400) -> Rate = 80.0
Since the rate increases eightfold when the concentration of B is doubled, we can conclude that the reaction is third-order with respect to B.
Finally, let's compare runs 1 and 3, where the concentration of reactant A changes.
Run 1: (A, B, C) = (0.200, 0.100, 0.600) -> Rate = 5.00
Run 3: (A, B, C) = (0.600, 0.100, 0.200) -> Rate = 15.0
Since the rate triples when the concentration of A triples, we can conclude that the reaction is first-order with respect to A.
Putting it all together, the rate equation becomes:
rate = k[A]^1[B]^3[C]^1
Now, we can use any of the given runs to determine the rate constant (k). Let's use run 1:
Rate = k[A]^1[B]^3[C]^1
5.00 = k(0.200)^1(0.100)^3(0.600)^1
5.00 = k(0.0002)(0.001)(0.36)
5.00 = k(0.000000072)
k = 5.00 / 0.000000072 ≈ 69444
Therefore, the rate constant (k) for this reaction is approximately 69444.
Looking at the answer choices provided, none of them match exactly, so it seems there might be a mistake in the calculations or the options provided.