Ch.14 - Chemical Kinetics

Problem 19c

Chapter 14, Problem 19c

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.

Verified step by step guidance

First, understand that the average rate of appearance of B is related to the rate of disappearance of A. Since the reaction is A(aq) → B(aq), the rate of appearance of B is equal to the rate of disappearance of A.

Calculate the change in moles of A between t = 10 min and t = 30 min. This is done by subtracting the moles of A at t = 30 min from the moles of A at t = 10 min: Δ[A] = [A] at 10 min - [A] at 30 min.

Convert the change in moles of A to concentration change in molarity (M). Since the volume is constant at 100.0 mL (or 0.100 L), use the formula: Δ[A] (M) = Δ[A] (moles) / Volume (L).

Determine the time interval in seconds between t = 10 min and t = 30 min. Since 1 minute equals 60 seconds, the time interval Δt = (30 - 10) minutes × 60 seconds/minute.

Calculate the average rate of appearance of B in M/s using the formula: Rate = -Δ[A] / Δt. The negative sign indicates the disappearance of A, but since we are interested in the appearance of B, the rate will be positive.

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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 and products in the reaction. Since the volume of the solution is constant, changes in the number of moles directly affect the molarity, which is essential for determining the rate of reaction.

Average Rate of Reaction

The average rate of a reaction is defined as the change in concentration of a reactant or product over a specific time interval. It can be calculated using the formula: average rate = (change in concentration) / (change in time). In this case, the average rate of appearance of B can be derived from the decrease in moles of A over the time interval from 10 to 30 minutes, which is key to solving the problem.

Stoichiometry

Stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. In this scenario, the stoichiometric coefficients indicate that for every mole of A that reacts, one mole of B is produced. This relationship is vital for converting the change in moles of A into the change in moles of B, allowing for the calculation of the average rate of appearance of B.

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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 (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 (b) Calculate the average rate of disappearance of A for each 10-min interval in units of M>s.

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?

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

(b) Calculate the average rate of reaction over the entire time of the data from t = 0 to t = 15,000 s.