The tabulated data show the concentration of N2O5 versus time for this reaction: N2O5(g) → NO3(g) + NO2(g). Time (s) [N2O5] (M): 0 - 1.000, 25 - 0.822, 50 - 0.677, 75 - 0.557, 100 - 0.458, 125 - 0.377, 150 - 0.310, 175 - 0.255, 200 - 0.210. Determine the order of the reaction and the value of the rate constant. Predict the concentration of N2O5 at 250 s.

Verified step by step guidance

1. insert step 1: Determine the order of the reaction by analyzing the concentration data. Test for zero, first, and second order reactions by plotting [N2O5] vs. time, ln[N2O5] vs. time, and 1/[N2O5] vs. time, respectively. The plot that yields a straight line indicates the order of the reaction.
2. insert step 2: Once the order is determined, use the appropriate integrated rate law to calculate the rate constant (k). For a first-order reaction, use ln[N2O5] = -kt + ln[N2O5]_0. For a second-order reaction, use 1/[N2O5] = kt + 1/[N2O5]_0.
3. insert step 3: Calculate the slope of the straight line from the plot that determined the order of the reaction. This slope is equal to the rate constant (k) for the reaction.
4. insert step 4: Use the integrated rate law with the calculated rate constant to predict the concentration of N2O5 at 250 s. Substitute the time (t = 250 s) into the equation and solve for [N2O5].
5. insert step 5: Verify the calculated concentration by checking if it aligns with the trend observed in the data. This ensures the accuracy of the determined reaction order and rate constant.

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 provides insight into the relationship between the concentration of reactants and the rate of the reaction. For example, a first-order reaction depends linearly on 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 predicting how the concentration of reactants changes over time.

Integrated Rate Laws

Integrated rate laws are mathematical expressions that relate the concentration of reactants to time, allowing for the prediction of concentration at any given time. Different orders of reactions have distinct integrated rate laws, such as for first-order reactions, the equation is ln([A]0/[A]) = kt. Understanding these equations is essential for calculating concentrations at specific times and for determining the order of the reaction based on experimental data.