At 400 K, oxalic acid decomposes according to the reaction: H2C2O4(g) → CO2(g) + HCOOH(g). In three separate experiments, the initial pressure of oxalic acid and the final total pressure after 20,000 seconds are measured. Experiment: 1) PH2C2O4 at t = 0: 65.8, PTotal at t = 20,000 s: 94.6; 2) PH2C2O4 at t = 0: 92.1, PTotal at t = 20,000 s: 132; 3) PH2C2O4 at t = 0: 111, PTotal at t = 20,000 s: 160. Find the rate law of the reaction and its rate constant.
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Identify the reaction: \( \text{H}_2\text{C}_2\text{O}_4(g) \rightarrow \text{CO}_2(g) + \text{HCOOH}(g) \). Note that the decomposition of one mole of \( \text{H}_2\text{C}_2\text{O}_4 \) produces one mole of \( \text{CO}_2 \) and one mole of \( \text{HCOOH} \).
Calculate the change in pressure (\( \Delta P \)) for each experiment by subtracting the initial pressure of \( \text{H}_2\text{C}_2\text{O}_4 \) from the total pressure at \( t = 20,000 \) seconds.
Determine the concentration of \( \text{H}_2\text{C}_2\text{O}_4 \) that has decomposed in each experiment using the relation: \( \Delta P = P_{\text{CO}_2} + P_{\text{HCOOH}} = 2x \), where \( x \) is the change in pressure due to the decomposition of \( \text{H}_2\text{C}_2\text{O}_4 \).
Use the initial pressures and the changes in pressure to determine the order of the reaction by comparing the ratios of the rates of reaction (\( \Delta P / \Delta t \)) to the initial pressures raised to the power of the reaction order (\( n \)).
Once the order is determined, use the rate law \( \text{Rate} = k [\text{H}_2\text{C}_2\text{O}_4]^n \) to calculate the rate constant \( k \) for each experiment and find an average value.
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Rate Law
The rate law of a chemical reaction expresses the relationship between the rate of the reaction and the concentration of its reactants. It is typically formulated as rate = k[A]^m[B]^n, where k is the rate constant, and m and n are the orders of the reaction with respect to reactants A and B. Understanding the rate law is essential for determining how changes in concentration affect the reaction rate.
Partial pressure is the pressure exerted by a single component of a gas mixture. In the context of the given reaction, the initial and final partial pressures of oxalic acid and the products are crucial for calculating the changes in concentration over time. This concept is vital for applying the ideal gas law and understanding how gas behavior relates to reaction kinetics.
Integrated rate laws relate the concentration of reactants to time, allowing for the determination of the rate constant (k) from experimental data. Depending on the order of the reaction, different integrated forms are used, such as for zero, first, or second-order reactions. Analyzing the data from the experiments will help identify the order of the reaction and calculate the rate constant.
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