Sample Exercise 14.1 Calculating an Average Rate of Reaction

Sample Exercise 14.1 Calculating an Average Rate of Reaction

From the data in Figure 14.2, calculate the average rate at which A disappears over the time interval from 20 s to 40 s.

Solution

Analyze We are given the concentration of A at 20 s (0.54 M) and at 40 s (0.30 M) and asked to calculate the average rate of reaction over this time interval.

Plan The average rate is given by the change in concentration, [A], divided by the change in time, t. Because A is a reactant, a minus sign is used in the calculation to make the rate a positive quantity.

Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus

? 2018 Pearson Education, Inc.

Sample Exercise 14.1 Calculating an Average Rate of Reaction

Continued Solve

Practice Exercise 1

If the experiment in Figure 14.2 is run for 60 s, 0.16 mol A remain. Which of the following statements is or are true? (i) After 60 s there are 0.84 mol B in the flask. (ii) The decrease in the number of moles of A from t1 = 0 s to t2 = 20 s is greater than that from t1 = 40 to t2 = 60 s. (iii)The average rate for the reaction from t1 = 40 s to t2 = 60 s is 7.0 ? 10?3 M/s.

(a) Only one of the statements is true. (b) Statements (i) and (ii) are true. (c) Statements (i) and (iii) are true. (d) Statements (ii) and (iii) are true. (e) All three statements are true.

Practice Exercise 2

Use the data in Figure 14.2 to calculate the average rate of appearance of B over the time interval from 0 s to 40 s.

Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus

? 2018 Pearson Education, Inc.

Sample Exercise 14.2 Calculating an Instantaneous Rate of Reaction

Using Figure 14.3, calculate the instantaneous rate of disappearance of C4H9Cl at t = 0 s (the initial rate).

Solution

Analyze We are asked to determine an instantaneous rate from a graph of reactant concentration versus time.

Plan To obtain the instantaneous rate at t = 0 s, we must determine the slope of the curve at t = 0. The tangent is drawn on the graph as the hypotenuse of the tan triangle. The slope of this straight line equals the change in the vertical axis divided by the corresponding change in the horizontal axis (which, in the case of this example, is the change in molarity over change in time).

Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus

? 2018 Pearson Education, Inc.

Sample Exercise 14.2 Calculating an Instantaneous Rate of Reaction

Continued

Solve The tangent line falls from [C4H9Cl] = 0.100 M to 0.060 M in the time change from 0 s to 210 s. Thus, the initial rate is

Practice Exercise 1

Which of the following could be the instantaneous rate of the reaction in Figure 14.3 at t = 1000 s? (a) 1.2 ? 10?4 M/s (b) 8.8 ? 10?5 M/s (c) 6.3 ? 10?5 M/s (d) 2.7 ? 10?5 M/s (e) More than one of these.

Practice Exercise 2

Using Figure 14.3, determine the instantaneous rate of disappearance of C4H9Cl at t = 300 s.

Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus

? 2018 Pearson Education, Inc.

Sample Exercise 14.3 Relating Rates at Which Products

Appear and Reactants Disappear

(a) How is the rate at which ozone disappears related to the rate at which oxygen appears in the

reaction 2 O3(g)

3 O2(g)?

(b) If the rate at which O2 appears, [O2]/t, is 6.0 ? 10?5 M/s at a particular instant, at what rate is O3

disappearing at this same time, ?[O3]/t?

Solution

Analyze We are given a balanced chemical equation and asked to relate the rate of appearance of the product to the rate of disappearance of the reactant.

Plan We can use the coefficients in the chemical equation as shown in Equation 14.4 to express the relative rates of reactions.

Solve (a) Using the coefficients in the balanced equation and the relationship given by Equation 14.4, we have:

(b) Solving the equation from part (a) for the rate at which O3 disappears, ?[O3]/t, we have:

Chemistry: The Central Science, 14th Edition Brown/LeMay/Bursten/Murphy/Woodward/Stoltzfus

? 2018 Pearson Education, Inc.

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