Ch.14 - Chemical Kinetics

Problem 21a,c

Chapter 14, Problem 21a,c

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?

Verified step by step guidance

To calculate the average rate of reaction for each time interval, use the formula: \( \text{Average Rate} = -\frac{\Delta [\text{CH}_3\text{NC}]}{\Delta t} \), where \( \Delta [\text{CH}_3\text{NC}] \) is the change in concentration and \( \Delta t \) is the change in time.

For the interval between 0 and 2000 seconds, calculate \( \Delta [\text{CH}_3\text{NC}] = [\text{CH}_3\text{NC}]_{2000} - [\text{CH}_3\text{NC}]_{0} \) and \( \Delta t = 2000 - 0 \). Substitute these values into the rate formula to find the average rate.

Repeat the calculation for each subsequent interval: 2000 to 5000 seconds, 5000 to 8000 seconds, 8000 to 12000 seconds, and 12000 to 15000 seconds, using the same formula.

To compare the average rates between t = 2000 and t = 12000 s, and t = 8000 and t = 15000 s, calculate the average rate for each of these intervals using the same method: \( \Delta [\text{CH}_3\text{NC}] \) and \( \Delta t \) for each interval.

Compare the calculated average rates for the intervals t = 2000 to t = 12000 s and t = 8000 to t = 15000 s to determine which is greater.

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Key Concepts

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

Reaction Rate

The reaction rate is a measure of how quickly reactants are converted into products in a chemical reaction. It is typically expressed in terms of concentration change over time, such as molarity per second (M/s). Understanding how to calculate the average rate of reaction between specific time intervals is crucial for analyzing kinetic data.

Average Rate Calculation

To calculate the average rate of a reaction over a specific time interval, one can use the formula: average rate = (change in concentration) / (change in time). This involves determining the concentration of the reactant at the beginning and end of the interval and dividing the difference by the time elapsed, allowing for a clear comparison of rates across different intervals.

Isomerization Reaction

Isomerization is a type of chemical reaction where a molecule is transformed into one of its isomers, which have the same molecular formula but different structural arrangements. In this case, methyl isonitrile is converting to acetonitrile, and understanding the nature of isomerization helps in analyzing the kinetics and mechanisms involved in the reaction.

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Related Practice

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

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

(b) Calculate the average rate of reaction over the entire time of the data from t = 0 to 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

(d) Graph [CH₃NC] versus time and determine the instantaneous rates in M/s at t = 5000 s and t = 8000 s.

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Textbook Question

The rate of disappearance of HCl was measured for the following reaction: CH3OH1aq2 + HCl1aq2¡CH3Cl1aq2 + H2O1l2 The following data were collected: Time (min) 3HCl 4 1M2 0.0 1.85 54.0 1.58 107.0 1.36 215.0 1.02 430.0 0.580 (a) Calculate the average rate of reaction, in M>s, for the time interval between each measurement.