Question

given the following laboratory data containing the disappearance of a chemical in water, do the data fit a zero-order, first- order, or second-order rate expression? provide sufficient justification for your answer, and report the correct rate constant in the correct units. (10 points) time, h 0 0.5 1 2 3 5 concentration, mg/l 100 61 37 14 5.0

Answer 1

The data provided can be analyzed by plotting concentration versus time for zero-order, the natural logarithm of concentration versus time for first-order, and the inverse of concentration versus time for second-order reactions. If the plot for second-order is linear, the reaction follows a second-order rate law, and the rate constant can be calculated using the corresponding data and the appropriate rate law formula.

Step-by-step explanation:

To determine whether the data fit a zero-order, first-order, or second-order rate expression, we may plot the concentration versus time for each and analyze the linearity of the plots. For a zero-order reaction, a plot of concentration ([C]) versus time (t) should give a straight line. In contrast, a first-order reaction yields a straight line when plotting the natural logarithm (ln) of concentration versus time, and a second-order reaction yields a straight line when plotting the inverse of the concentration (1/[C]) versus time.

In this scenario, if we prepare these plots and the second-order plot is linear, it would suggest that the reaction follows a second-order rate law. Using the rate law and the given data, we would then calculate the rate constant (k). The units of k for zero-order, first-order, and second-order reactions are M s⁻¹, s⁻¹, and M⁻¹ s⁻¹ respectively.

Using a suitable equation, such as the second-order half-life equation, we can calculate the half-life (t1/2) for a second-order reaction, given the initial concentration and the rate constant. For example, for a second-order reaction initiated with a 0.200 mol L⁻¹ reactant solution and a rate constant of 0.0576 L mol⁻¹ min⁻¹, we could calculate the half-life by substituting these values into the second-order half-life formula.

Answer 2

To ascertain the order of the reaction and whether the disappearance of a chemical in water fits a zero-order, first-order, or second-order rate, concentration changes over time should be graphed according to each order's characteristics. The pattern that produces a straight line will indicate the order of the reaction, and thereafter the rate constant can be determined accordingly.

Step-by-step explanation:

To determine whether the disappearance of a chemical in water fits a zero-order, first-order, or second-order rate expression, we analyze the pattern of concentration changes over time. For a zero-order reaction, the concentration of the reactant decreases linearly over time. In a first-order reaction, the natural logarithm (ln) of the concentration of the reactant decreases linearly over time. Finally, for a second-order reaction, the inverse of the concentration of the reactant decreases linearly over time.

In analyzing the given data, the concentration change does not seem linear, which suggests the reaction is not zero-order. Performing a graphical analysis by plotting possible graphs for both first-order and second-order reactions and checking for linearity will be critical to determine the order. For example, graphing natural log of concentration vs. time for a first-order reaction or graphing 1/concentration vs. time for a second-order reaction.

Without performing the actual graphing or calculations here, if the data were found to best fit a second-order expression, as the provided information implies, we would use the integrated second-order rate law to calculate the rate constant (k). Using visual analysis or graphical methods to plot the mentioned relationships is a common strategy when dealing with rate laws and determining the order of reaction.