Initial Reaction Rates For A And B Were Studied
The Initial Rates For a Reaction A And B Were Studied Using The Follow
The initial rates for a reaction involving reactants A and B were studied using specific initial concentrations. Three experiments provided the following data: Experiment 1 with [A] = 0.300 mol/L, [B] = 0.400 mol/L, and rate = 2.80×10-4 M/s; Experiment 2 with [A] = 1.04 mol/L, [B] = 0.400 mol/L, and rate = 2.80×10-4 M/s; and Experiment 3 with [A] = 0.695 mol/L, [B] = 1.63 mol/L, and rate = 4.65×10-3 M/s. The key objective is to determine the reaction order with respect to B based on the provided experimental data and analyze the relationship between concentrations and reaction rates.
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The determination of the reaction order with respect to reactant B in a chemical reaction is fundamental for understanding the reaction mechanism and predicting how variations in concentration influence the rate. The provided data from experiments involving reactants A and B allow for the calculation of the reaction order concerning B by analyzing the changes in rate relative to changes in B’s concentration.
Given the rate law in a general form: Rate = k [A]^m [B]^n, where m and n are the reaction orders with respect to A and B, respectively, and k is the rate constant, we analyze the data to find n, the order with respect to B. Notably, Experiments 1 and 2 have the same [B], but different [A], and demonstrate identical rates. Since the rate remains unchanged despite a significant increase in [A], the reaction appears to be zero-order with respect to A under these conditions. Consequently, the rate is independent of [A] at constant [B], implying that m = 0.
To determine n, compare Experiments 2 and 3, where [A] varies while [B] also changes. In Experiment 2, [A] = 1.04 mol/L, [B] = 0.400 mol/L, with a rate of 2.80×10-4 M/s. In Experiment 3, [A] = 0.695 mol/L, [B] = 1.63 mol/L, with a rate of 4.65×10-3 M/s. The change in [A] between experiments 2 and 3 is from 1.04 to 0.695 mol/L, approximately a 1.5-fold decrease, while [B] increases from 0.400 to 1.63 mol/L, roughly a 4.1-fold increase.
The reaction rate change from 2.80×10-4 to 4.65×10-3 M/s corresponds to a ratio of approximately 16.6. Assuming the rate law rate ∝ [B]^n, the rate ratio (R) relates to the concentration ratio (C) as R = (CB3/CB2)^n. Substituting the values, 16.6 ≈ (4.1)^n, taking logarithms yields:
log(16.6) ≈ n · log(4.1), so n ≈ log(16.6)/log(4.1) ≈ 1.22/0.61 ≈ 2.0.
This indicates that the reaction is second order with respect to B, as n ≈ 2.0. Therefore, the reaction rate significantly depends on the square of the concentration of B, consistent with the rate law: Rate = k [A]^0 [B]^2, or simply Rate = k [B]^2, since m = 0.
In conclusion, the reaction exhibits zero order with respect to A and second order with respect to B. This insight into the reaction kinetics aids in elucidating the reaction mechanism, suggesting that B participates in the rate-determining step more directly than A under the experimental conditions. Further kinetic studies could involve varying temperature and examining the temperature dependence to extract activation energy or exploring intermediate steps of the reaction pathway.
References
- Atkins, P., & de Paula, J. (2010). Physical Chemistry (9th ed.). Oxford University Press.
- Moore, J. W., & Pearson, R. G. (1981). Kinetics and Mechanism. John Wiley & Sons.
- Laidler, K. J. (1987). Chemical Kinetics (3rd ed.). Harper & Row.
- Levine, R. D. (2009). Quantum Chemistry (6th ed.). Pearson Education.
- House, J. E. (2007). Principles of Chemical Kinetics (2nd ed.). Academic Press.
- Anslyn, E. V., & Dougherty, D. A. (2006). Modern Physical Organic Chemistry. University Science Books.
- Pilling, M. J., & Seakins, P. W. (2013). Reaction Kinetics. Oxford University Press.
- Johnson, C. R. (2011). Introduction to Chemical Kinetics. CRC Press.
- McMurry, J., & Fay, R. C. (2015). Chemistry (6th ed.). Pearson Education.
- Solomons, T. W., & Frye, C. H. (2011). Organic Chemistry (10th ed.). John Wiley & Sons.