Ch.14 - Chemical Kinetics

Brown - Chemistry: The Central Science 15th Edition

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Brown 15th Edition

Ch.14 - Chemical Kinetics

Problem 21d

Chapter 14, Problem 21d

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.

Verified step by step guidance

Step 1: Start by plotting the concentration of CH3NC (y-axis) against time (x-axis). You can use any graphing tool or software to do this. The concentration of CH3NC should decrease over time as it is converted to CH3CN.

Step 2: To find the instantaneous rate at a specific time, you need to determine the slope of the tangent line to the curve at that point. This represents the rate of change of concentration at that specific time.

Step 3: To find the instantaneous rate at t = 5000 s, draw a tangent line to the curve at t = 5000 s and calculate its slope. The slope of the tangent line is equal to the change in concentration divided by the change in time (Δ[CH3NC]/Δt).

Step 4: Repeat the process for t = 8000 s. Draw a tangent line to the curve at t = 8000 s and calculate its slope. This will give you the instantaneous rate at t = 8000 s.

Step 5: Remember that the instantaneous rate of a reaction at a particular time is the slope of the tangent to the curve of concentration versus time at that time. It represents the speed of the reaction at that specific moment.

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Key Concepts

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

Isomerization

Isomerization is a chemical process where a compound is transformed into one of its isomers, which are molecules with the same molecular formula but different structural arrangements. In this case, methyl isonitrile is converted to acetonitrile, highlighting the importance of understanding structural differences and their implications on chemical properties and reactivity.

Reaction Rate

The reaction rate refers to the speed at which reactants are converted into products in a chemical reaction. It can be expressed in terms of concentration change over time, typically in units of molarity per second (M/s). Understanding how to calculate and interpret reaction rates is crucial for analyzing kinetic data, such as the provided concentration values over time.

Graphical Analysis of Kinetics

Graphical analysis in kinetics involves plotting concentration versus time to visualize the reaction's progress and determine instantaneous rates. By analyzing the slope of the concentration-time graph at specific time points, such as 5000 s and 8000 s, one can derive the rate of reaction at those moments, which is essential for understanding the dynamics of the isomerization process.

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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 (b) Calculate the average rate of reaction for the entire time for the data from t = 0.0 min to t = 430.0 min.

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.

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 (c) Which is greater, the average rate between t = 54.0 and t = 215.0 min, or between t = 107.0 and t = 430.0 min?

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.

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?