The tabulated data show the concentration of cyclobutane (C4H8) versus time for this reaction: C4H8 -> 2 C2H4. Time (s) [C4H8] (M) 0 1.000 10 0.894 20 0.799 30 0.714 40 0.638 50 0.571 60 0.510 70 0.456 80 0.408 90 0.364 100 0.326. Determine the order of the reaction and the value of the rate constant. What is the rate of reaction when [C4H8] = 0.25 M?

Verified step by step guidance

1. insert step 1> Start by plotting the concentration of cyclobutane, [C_4H_8], versus time to visually inspect the data and determine if it fits a zero, first, or second-order reaction.
2. insert step 2> For a zero-order reaction, a plot of [C_4H_8] versus time should be linear. For a first-order reaction, a plot of ln[C_4H_8] versus time should be linear. For a second-order reaction, a plot of 1/[C_4H_8] versus time should be linear.
3. insert step 3> Calculate the natural logarithm of the concentration, ln[C_4H_8], and the reciprocal of the concentration, 1/[C_4H_8], for each time point.
4. insert step 4> Plot ln[C_4H_8] versus time and 1/[C_4H_8] versus time to determine which plot is linear. The linear plot will indicate the order of the reaction: first-order if ln[C_4H_8] is linear, second-order if 1/[C_4H_8] is linear.
5. insert step 5> Once the order is determined, use the slope of the linear plot to calculate the rate constant, k. For a first-order reaction, the slope of ln[C_4H_8] versus time is -k. For a second-order reaction, the slope of 1/[C_4H_8] versus time is k. Then, use the rate law to calculate the rate of reaction when [C_4H_8] = 0.25 M.

Key Concepts

Reaction Order

The order of a reaction refers to the power to which the concentration of a reactant is raised in the rate law. It indicates how the rate of reaction depends on the concentration of reactants. For example, a first-order reaction has a rate directly proportional to the concentration of one reactant, while a second-order reaction depends on the square of the concentration. Determining the order helps in understanding the kinetics of the reaction.

Rate Constant (k)

The rate constant (k) is a proportionality factor in the rate law that relates the rate of a reaction to the concentrations of the reactants. It is specific to a given reaction at a particular temperature and is influenced by factors such as temperature and the presence of catalysts. The value of k can be determined experimentally and is crucial for calculating reaction rates at different concentrations.

Integrated Rate Laws

Integrated rate laws are mathematical expressions that relate the concentration of reactants to time, allowing for the determination of reaction order and rate constants. For zero, first, and second-order reactions, these laws take different forms, enabling the calculation of concentration at any given time. By analyzing concentration data over time, one can derive the order of the reaction and the rate constant, which are essential for predicting future concentrations.