Ch.14 - Chemical Kinetics

Problem 22a

Chapter 14, Problem 22a

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.

Verified step by step guidance

Identify the concentration of HCl at different time intervals. For example, at time 0.0 minutes, the concentration of HCl is 1.85 M, and at 54.0 minutes, it is 1.58 M.

Calculate the change in concentration of HCl (\(\Delta [HCl]\)) for each time interval by subtracting the final concentration from the initial concentration. For instance, between 0.0 and 54.0 minutes, \(\Delta [HCl] = 1.58 \text{ M} - 1.85 \text{ M}\).

Determine the change in time (\(\Delta t\)) for each interval by subtracting the initial time from the final time. For the first interval, \(\Delta t = 54.0 \text{ min} - 0.0 \text{ min}\).

Calculate the average rate of reaction for each interval using the formula: \(\text{Average Rate} = \frac{\Delta [HCl]}{\Delta t}\). Convert the time from minutes to seconds by multiplying by 60, as the rate should be expressed in M/s.

Repeat the calculations for each time interval to find the average rate of reaction for each.

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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 as the change in concentration of a reactant or product per unit time, often in units of molarity per second (M/s). Understanding how to calculate the average rate of reaction over specific time intervals is crucial for analyzing kinetic data.

Average Rate Calculation

The average rate of a reaction over a time interval can be calculated by taking the change in concentration of a reactant or product and dividing it by the time interval. For example, if the concentration of HCl decreases from 1.85 M to 1.58 M over a certain time, the average rate can be calculated as the difference in concentration divided by the time elapsed. This method provides a straightforward way to quantify the speed of the reaction.

Concentration Units

Concentration is a measure of the amount of a substance in a given volume of solution, commonly expressed in molarity (M), which is moles of solute per liter of solution. In the context of reaction rates, understanding how to interpret and manipulate these units is essential for accurate calculations. Changes in concentration over time directly relate to the kinetics of the reaction being studied.

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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

(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

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 (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 (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.