In a reaction A and B react to form product. The initial rate of reaction (ro) was determined using different initial concentrations of A and B as shown below: What is the initial rate of reaction (ro) when the critical concentration of A and B is 0.50 mol/L and 0.50 mol/L, respectively?A/mol L-1 B/mol L-1 ro/mol L-1 s-1 0.10 0.30 6.81 × 10-4 0.10 0.10 2.27 × 10-4 0.20 0.30 13.62 × 10-4
56.75 × 10-4 mol L-1 s-1
Determining Reaction Rate Law and Initial Rate
Understanding the rate of a chemical reaction is fundamental in chemical kinetics. The rate of a reaction is often dependent on the concentration of the reactants. This relationship is described by the rate law, which includes the rate constant and the order of the reaction with respect to each reactant.
Analyzing the Given Initial Rate Data
We are provided with experimental data showing the initial rate of a reaction (A + B → Product) at different initial concentrations of reactants A and B. The data is presented in the table below:
| [A] / mol L\(^{-1}\) | [B] / mol L\(^{-1}\) | ro / mol L\(^{-1}\) s\(^{-1}\) |
|---|---|---|
| 0.10 | 0.30 | 6.81 × 10\(^{-4}\) |
| 0.10 | 0.10 | 2.27 × 10\(^{-4}\) |
| 0.20 | 0.30 | 13.62 × 10\(^{-4}\) |
The general form of the rate law for this reaction can be written as:
\( \text{ro} = k[A]^x [B]^y \)
where:
- ro is the initial rate of reaction
- k is the rate constant
- [A] and [B] are the concentrations of reactants A and B
- x is the order of the reaction with respect to A
- y is the order of the reaction with respect to B
Our task is to determine the values of x, y, and k using the experimental data and then use these values to calculate the initial rate at new concentrations.
Determining the Order of Reaction (x and y)
To find the order of reaction with respect to each reactant, we compare experiments where the concentration of one reactant is changed while the other is kept constant.
Order with Respect to B (Finding y)
Let's compare Experiment 1 and Experiment 2. The concentration of A is constant ([A] = 0.10 M), while the concentration of B changes from 0.30 M to 0.10 M. The initial rate also changes.
Using the rate law:
\( \frac{\text{ro}_1}{\text{ro}_2} = \frac{k[A]_1^x [B]_1^y}{k[A]_2^x [B]_2^y} \)
\( \frac{6.81 \times 10^{-4}}{2.27 \times 10^{-4}} = \frac{k(0.10)^x (0.30)^y}{k(0.10)^x (0.10)^y} \)
Since k and \((0.10)^x\) are the same in both expressions, they cancel out:
\( \frac{6.81}{2.27} = \left(\frac{0.30}{0.10}\right)^y \)
\( 3 = (3)^y \)
From this equation, we can see that \(y = 1\). The reaction is first order with respect to B.
Order with Respect to A (Finding x)
Now let's compare Experiment 1 and Experiment 3. The concentration of B is constant ([B] = 0.30 M), while the concentration of A changes from 0.10 M to 0.20 M. The initial rate also changes.
Using the rate law:
\( \frac{\text{ro}_3}{\text{ro}_1} = \frac{k[A]_3^x [B]_3^y}{k[A]_1^x [B]_1^y} \)
\( \frac{13.62 \times 10^{-4}}{6.81 \times 10^{-4}} = \frac{k(0.20)^x (0.30)^y}{k(0.10)^x (0.30)^y} \)
Since k and \((0.30)^y\) are the same in both expressions, they cancel out:
\( \frac{13.62}{6.81} = \left(\frac{0.20}{0.10}\right)^x \)
\( 2 = (2)^x \)
From this equation, we can see that \(x = 1\). The reaction is first order with respect to A.
The rate law for the reaction is therefore:
\( \text{ro} = k[A]^1 [B]^1 = k[A][B] \)
Calculating the Rate Constant (k)
Now that we know the rate law, we can use the data from any one experiment to calculate the rate constant, k. Let's use the data from Experiment 1:
- [A] = 0.10 mol L\(^{-1}\)
- [B] = 0.30 mol L\(^{-1}\)
- ro = \( 6.81 \times 10^{-4} \) mol L\(^{-1}\) s\(^{-1}\)
Substitute these values into the rate law:
\( 6.81 \times 10^{-4} \text{ mol L}^{-1} \text{ s}^{-1} = k (0.10 \text{ mol L}^{-1}) (0.30 \text{ mol L}^{-1}) \)
\( 6.81 \times 10^{-4} \text{ mol L}^{-1} \text{ s}^{-1} = k (0.030 \text{ mol}^2 \text{ L}^{-2}) \)
Solve for k:
\( k = \frac{6.81 \times 10^{-4} \text{ mol L}^{-1} \text{ s}^{-1}}{0.030 \text{ mol}^2 \text{ L}^{-2}} \)
\( k = \frac{6.81}{0.030} \times 10^{-4} \text{ mol}^{-1} \text{ L s}^{-1} \)
\( k = 227 \times 10^{-4} \text{ L mol}^{-1} \text{ s}^{-1} \)
or
\( k = 0.0227 \text{ L mol}^{-1} \text{ s}^{-1} \)
The units for k depend on the overall order of the reaction. Since the overall order is 1 + 1 = 2 (second order), the units are typically M\(^{-1}\) s\(^{-1}\) or L mol\(^{-1}\) s\(^{-1}\).
Predicting Initial Rate at New Concentrations
We need to find the initial rate when [A] = 0.50 mol L\(^{-1}\) and [B] = 0.50 mol L\(^{-1}\). We use the rate law \( \text{ro} = k[A][B] \) and the calculated value of k.
\( \text{ro} = (227 \times 10^{-4} \text{ L mol}^{-1} \text{ s}^{-1}) (0.50 \text{ mol L}^{-1}) (0.50 \text{ mol L}^{-1}) \)
\( \text{ro} = (227 \times 10^{-4}) (0.25) \text{ mol L}^{-1} \text{ s}^{-1} \)
\( \text{ro} = 56.75 \times 10^{-4} \text{ mol L}^{-1} \text{ s}^{-1} \)
Thus, the initial rate of reaction when the concentrations of A and B are both 0.50 mol/L is \( 56.75 \times 10^{-4} \) mol L\(^{-1}\) s\(^{-1}\).
Revision Table: Key Steps in Rate Law Determination
| Step | Description | How it was applied here |
|---|---|---|
| 1 | Write the general rate law: \( \text{ro} = k[A]^x[B]^y... \) | \( \text{ro} = k[A]^x[B]^y \) |
| 2 | Use experimental data to find reaction orders (x, y). Compare experiments where one reactant's concentration changes while others are constant. | Compared Exp 1 & 2 (constant [A]) to find y=1. Compared Exp 1 & 3 (constant [B]) to find x=1. |
| 3 | Substitute known orders into the general rate law to get the specific rate law. | Rate Law: \( \text{ro} = k[A][B] \) |
| 4 | Use data from any single experiment and the specific rate law to calculate the rate constant (k). | Used Exp 1 data: \( k = \frac{6.81 \times 10^{-4}}{(0.10)(0.30)} = 227 \times 10^{-4} \) L mol\(^{-1}\) s\(^{-1}\). |
| 5 | Use the specific rate law and calculated k to find the rate under new conditions. | Calculated ro for [A]=0.50, [B]=0.50: \( \text{ro} = (227 \times 10^{-4})(0.50)(0.50) = 56.75 \times 10^{-4} \) mol L\(^{-1}\) s\(^{-1}\). |
Additional Information: Chemical Kinetics Concepts
Initial Rate: The instantaneous rate of a reaction at the very beginning, before the concentrations of reactants have decreased significantly. It is determined by measuring the rate of product formation or reactant disappearance within the first few percent of the reaction.
Rate Law: An equation that relates the rate of a chemical reaction to the concentration of reactants. It is determined experimentally and cannot be predicted from the stoichiometry of the balanced chemical equation in most cases (except for elementary reactions).
Order of Reaction: The power to which the concentration of a reactant is raised in the rate law. It indicates how the rate is affected by changing the concentration of that reactant. The overall order of the reaction is the sum of the orders with respect to each reactant.
- Zero order (order = 0): Rate is independent of the reactant concentration.
- First order (order = 1): Rate is directly proportional to the reactant concentration.
- Second order (order = 2): Rate is proportional to the square of the reactant concentration (or the product of two concentrations raised to the power of 1).
Rate Constant (k): A proportionality constant in the rate law that relates the rate of the reaction to the concentrations of the reactants. The value of k is specific for a particular reaction at a particular temperature. It reflects the intrinsic speed of the reaction.
Factors Affecting Reaction Rate: Apart from reactant concentrations, other factors influence reaction rate, including temperature (rate generally increases with temperature), presence of a catalyst (speeds up rate), surface area (for heterogeneous reactions), and pressure (for gas-phase reactions).
Important Questions from Electrochemistry
Identify transition metal complexes which are not octahedral in shape.
(A) [Co(NH₃)₆]³⁺
(B) [Ni(CO)₄]
(C) [CoCl(NH₃)₅]²⁺
(D) [CoCl₂(NH₃)₄]⁺
(E) [PtCl₄]²⁻
Choose the correct answer from the options given below:
The product of complete hydrolysis of XeF₆ in the following reaction is:
XeF₆ + H₂O → ? HF
In which of the following actinoid elements 6d subshell is vacant?
Which of the following shows both, Frenkel and Schottky defect?
The role of a catalyst is to change:
