Ch.14 - Chemical Kinetics

Problem 19b

Chapter 14, Problem 19b

Consider the following hypothetical aqueous reaction: A(aq) → B(aq). A flask is charged with 0.065 mol of A in a total volume of 100.0 mL. The following data are collected: Time (min) 0 10 20 30 40 Moles of A 0.065 0.051 0.042 0.036 0.031 (b) Calculate the average rate of disappearance of A for each 10-min interval in units of M>s.

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insert step 1> Start by understanding that the average rate of disappearance of a reactant is calculated using the formula: \( \text{Rate} = -\frac{\Delta [A]}{\Delta t} \), where \( \Delta [A] \) is the change in concentration of A and \( \Delta t \) is the change in time.

insert step 2> Convert the moles of A to concentration in molarity (M) by dividing the moles by the volume of the solution in liters. Since the volume is 100.0 mL, convert it to liters by dividing by 1000, which gives 0.1 L.

insert step 3> Calculate the concentration of A at each time interval by dividing the moles of A by the volume in liters. For example, at time 0, the concentration is \( \frac{0.065 \text{ mol}}{0.1 \text{ L}} = 0.65 \text{ M} \). Repeat this for each time point.

insert step 4> For each 10-minute interval, calculate \( \Delta [A] \) by subtracting the concentration of A at the end of the interval from the concentration at the beginning of the interval.

insert step 5> Calculate the average rate of disappearance for each interval by dividing \( \Delta [A] \) by \( \Delta t \) (10 minutes converted to seconds, which is 600 seconds) and apply the negative sign to indicate disappearance.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Molarity and Concentration

Molarity (M) is a measure of concentration defined as the number of moles of solute per liter of solution. In this context, understanding molarity is crucial for calculating the concentration of reactants in the reaction. Since the total volume of the solution is given, we can convert moles of A into molarity to analyze its change over time.

Rate of Reaction

The rate of reaction refers to the change in concentration of a reactant or product per unit time. It is typically expressed in terms of molarity per second (M/s). In this question, calculating the average rate of disappearance of A involves determining how much the concentration of A decreases over specified time intervals, which is essential for understanding the kinetics of the reaction.

Average Rate Calculation

The average rate of a reaction over a time interval can be calculated using the formula: average rate = (change in concentration) / (change in time). For this problem, you will subtract the concentration of A at the end of each interval from its initial concentration and divide by the duration of the interval. This calculation provides insight into how quickly the reactant is consumed during the reaction.

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Textbook Question

(b) As the temperature increases, does the reaction rate increase or decrease?

Textbook Question

Consider the following hypothetical aqueous reaction: A(aq) → B(aq). A flask is charged with 0.065 mol of A in a total volume of 100.0 mL. The following data are collected: Time (min) 0 10 20 30 40 Moles of A 0.065 0.051 0.042 0.036 0.031 (a) Calculate the number of moles of B at each time in the table, assuming that there are no molecules of B at time zero and that A cleanly converts to B with no intermediates.

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Textbook Question

Consider the following hypothetical aqueous reaction: A(aq) → B(aq). A flask is charged with 0.065 mol of A in a total volume of 100.0 mL. The following data are collected: Time (min) 0 10 20 30 40 Moles of A 0.065 0.051 0.042 0.036 0.031 (c) Between t = 10 min and t = 30 min, what is the average rate of appearance of B in units of M/s? Assume that the volume of the solution is constant.

Textbook Question

A flask is charged with 0.100 mol of A and allowed to react to form B according to the hypothetical gas-phase reaction A1g2¡B1g2. The following data are collected: Time (s) 0 40 80 120 160 Moles of A 0.100 0.067 0.045 0.030 0.020 (c) Which of the following would be needed to calculate the rate in units of concentration per time: (i) the pressure of the gas at each time, (ii) the volume of the reaction flask, (iii) the temperature, or (iv) the molecular weight of A?

Textbook Question

The isomerization of methyl isonitrile (CH₃NC) to acetonitrile (CH₃CN) was studied in the gas phase at 215°C, and the following data were obtained:

Time (s) [CH₃NC] (M)

0 0.0165

2000 0.0110

5000 0.00591

8000 0.00314

12,000 0.00137

15,000 0.00074

(a) Calculate the average rate of reaction, in M/s, for the time interval between each measurement. (c) Which is greater, the average rate between t = 2000 and t = 12,000 s, or between t = 8000 and t = 15,000 s?