Question

1. Given the reaction 2A + B à C, with the rate law: Rate = k[A]0[B]2

a. When the concentration of A and B were 0.023M and 0.054M, the reaction rate was 8.31 X 10-2M/sec, calculate the value for k (with units).
b. Given the same amount of the reactants shown in part B, calculate the concentration of A when the concentration of B is 0.050M.

Answer 1

To calculate the rate constant (k) in the given rate law and the concentration of A when the concentration of B is known, we can use the provided values and plug them into the rate law equation. Using the given values, the value of k is approximately 270 M-1sec-1, and the concentration of A when [B] = 0.050 M is approximately 0.992 M.

Step-by-step explanation:

To calculate the value of the rate constant (k) in the given rate law, we can use the values of the concentration of A, the concentration of B, and the reaction rate provided.

a. Using the given values, we can plug them into the rate law equation and solve for k:

Rate = k[A]0[B]2

8.31 x 10-2 M/sec = k x (0.023 M)0 x (0.054 M)2

k = 8.31 x 10-2 M/sec / (0.054 M)2

k ≈ 270 M-1sec-1

b. To calculate the concentration of A when the concentration of B is 0.050 M, we can rearrange the rate law equation and solve for [A]:

Rate = k[A]0[B]2

8.31 x 10-2 M/sec = (270 M-1sec-1) x [A]0 x (0.050 M)2

Simplifying the equation, we get:

[A] ≈ 0.992 M

Answer 2

a. The value for k is 192 M⁻¹ sec⁻¹.

b. When the concentration of B is 0.050M, the concentration of A will be 0.016M.

Explanation

a. To determine the value of k, using the provided rate law equation Rate = k[A]⁰[B]², the rate constant (k) can be calculated using the given values of concentrations and the rate of the reaction. Since the order of A is 0, the rate of the reaction is independent of the concentration of A. Using the rate equation, k = Rate / ([A]⁰ * [B]²), substituting the given values: k = (8.31 x 10⁻² M/sec) / (0.023 M)⁰ * (0.054 M)² = 192 M⁻¹ sec⁻¹.

b. For the second part, if the concentration of B is 0.050M and the rate law remains the same, substituting the known values into the rate law equation allows for solving for the concentration of A. Using the rate law equation Rate = k[A]⁰[B]² and the obtained value of k (192 M⁻¹ sec⁻¹), rearranging the equation gives [A] = √(Rate / (k * [B]²)). Plugging in the values: [A] = √(8.31 x 10⁻² M/sec / (192 M⁻¹ sec⁻¹ * (0.050 M)²)) = 0.016M.

Understanding the rate law equation's dependency on concentrations allows us to calculate the rate constant (k) based on the given concentrations and rate of the reaction. Additionally, using the rate law equation, the concentration of A can be determined when the concentration of B is altered, providing insight into the relationship between reactants and their impact on the reaction rate.