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Ch.14 - Chemical Kinetics
All textbooksBrown 15th EditionCh.14 - Chemical KineticsProblem 22b
Chapter 14, Problem 22b

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.

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Identify the initial and final concentrations of HCl from the data provided. At t = 0.0 min, the concentration of HCl is 1.85 M, and at t = 430.0 min, the concentration is 0.580 M.
Calculate the change in concentration of HCl (\(\Delta [HCl]\)) by subtracting the final concentration at t = 430.0 min from the initial concentration at t = 0.0 min.
Identify the total time over which the reaction occurs, which is from t = 0.0 min to t = 430.0 min. Calculate the change in time (\(\Delta t\)) by subtracting the initial time from the final time.
Calculate the average rate of reaction using the formula: \(\text{Average Rate} = \frac{\Delta [HCl]}{\Delta t}\). Remember that the rate of disappearance of HCl is negative, so take the absolute value if necessary to express the rate as a positive number.
Express the average rate in appropriate units, which in this case would be M/min (molarity per minute).

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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 can be expressed as the change in concentration of a reactant or product over time. In this case, the rate of disappearance of HCl is crucial for understanding the overall reaction kinetics.
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Average Rate of Reaction

Average Rate of Reaction

The average rate of reaction is calculated by taking the total change in concentration of a reactant or product over a specified time interval. It provides a simplified view of the reaction's speed across that period, which is essential for analyzing the data collected from the experiment.
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Concentration Units

Concentration is typically expressed in molarity (M), which is moles of solute per liter of solution. Understanding how to interpret and manipulate these units is vital for calculating rates and determining how the concentration of HCl changes over time in the given reaction.
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SI Units
Related Practice
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.

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 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 (d) Graph [HCl] versus time and determine the instantaneous rates in M>min and M>s at t = 75.0 min and t = 250 min.

Textbook Question

For each of the following gas-phase reactions, indicate how the rate of disappearance of each reactant is related to the rate of appearance of each product:

(a) H2O2(g) → H2(g) + O2(g)

(b) 2 N2O(g) → 2 N2(g) + O2(g)