Explain the isolation method of determing the rate equation for a chentical reaction between two reactants \( A \) and \( B \)

The isolation method is a technique used to determine the rate equation for a chemical reaction involving two reactants, \( A \) and \( B \). This method allows us to simplify the analysis of the reaction kinetics by focusing on one reactant at a time. Here’s a step-by-step explanation of how the isolation method works: ### Step 1: Understand the Rate Law The rate law for a reaction can generally be expressed as: \[ \text{Rate} = k[A]^m[B]^n \] where: - \( k \) is the rate constant, - \( [A] \) and \( [B] \) are the concentrations of reactants \( A \) and \( B \), - \( m \) and \( n \) are the orders of the reaction with respect to \( A \) and \( B \), respectively. ### Step 2: Initial Conditions To apply the isolation method, you need to set up the reaction under controlled conditions. This typically involves varying the concentration of one reactant while keeping the other reactant's concentration constant. ### Step 3: Isolate One Reactant 1. **Choose a Reactant to Isolate**: Decide whether to isolate \( A \) or \( B \). For example, if you choose to isolate \( A \), you will keep the concentration of \( B \) constant. 2. **Perform Experiments**: Conduct a series of experiments where you measure the initial rate of the reaction while varying the concentration of \( A \) and keeping \( [B] \) constant. ### Step 4: Analyze the Data - **Plot the Data**: Create a plot of the initial rate of reaction versus the concentration of \( A \). - **Determine the Order with Respect to \( A \)**: Analyze the plot to determine how the rate changes with varying concentrations of \( A \). If the plot is linear, the reaction is first order with respect to \( A \). If it is quadratic, it is second order, and so on. ### Step 5: Repeat for the Other Reactant Once you have determined the order with respect to \( A \), repeat the process for \( B \): 1. Keep the concentration of \( A \) constant. 2. Vary the concentration of \( B \) and measure the initial rates. 3. Analyze the data to determine the order with respect to \( B \). ### Step 6: Write the Rate Equation After determining the orders \( m \) and \( n \) for both reactants, you can write the overall rate equation: \[ \text{Rate} = k[A]^m[B]^n \] ### Conclusion The isolation method is a systematic approach to determining the rate equation by focusing on one reactant at a time. This method simplifies the analysis of complex reactions and allows for a clearer understanding of the relationship between reactant concentrations and reaction rates.