Rituraj Tiwari
Last Activity: 4 Years ago
To understand the rate of formation of O2 from the decomposition of hydrogen peroxide (H2O2), we need to delve into the kinetics of the reaction, especially since it follows a first-order rate law. Let's break this down step by step so that it makes sense.
First-Order Kinetics Overview
In a first-order reaction, the rate of reaction is directly proportional to the concentration of one reactant. The general form of the rate equation for a first-order reaction can be expressed as:
Here, k is the rate constant, and [H2O2] is the concentration of hydrogen peroxide at any given time. The important aspect of first-order kinetics is that the concentration decreases exponentially over time.
Calculating the Rate Constant (k)
First, we need to determine the rate constant (k) using the information provided. We know that the concentration of H2O2 decreases from 0.5 M to 0.125 M in 50 minutes. We can use the integrated rate law for a first-order reaction:
Where:
- [A]0 is the initial concentration (0.5 M)
- [A] is the concentration at time t (0.125 M)
- t is the time in minutes (50 minutes)
Plugging in the values:
- ln(0.5/0.125) = k * 50
- ln(4) = k * 50
- 1.386 = k * 50
Now, solving for k gives us:
- k = 1.386 / 50 = 0.02772 min-1
Determining the Rate of Formation of O2
The decomposition of hydrogen peroxide can be represented by the following balanced chemical equation:
This indicates that for every 2 moles of H2O2 that decompose, 1 mole of O2 is produced. Therefore, the rate of formation of O2 is half the rate of the decomposition of H2O2.
Now, when the concentration of H2O2 is at 0.05 M, we can calculate the rate of formation of O2:
- Rate of decomposition of H2O2 = k[H2O2]
- Rate of decomposition = 0.02772 min-1 * 0.05 M = 0.001386 M/min
- Rate of formation of O2 = 0.5 * Rate of decomposition = 0.5 * 0.001386 M/min = 0.000693 M/min
Final Results
Thus, the rate of formation of O2 when the concentration of H2O2 reaches 0.05 M is approximately 0.000693 M/min. This value gives us a clear understanding of how fast oxygen is being produced in the reaction under the specified conditions.