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Chapter 14: Problem 3

In the reaction \(A \longrightarrow\) products, \([A]\) is found to be \(0.485 \mathrm{M}\) at \(t=71.5 \mathrm{s}\) and \(0.474 \mathrm{M}\) at \(t=82.4 \mathrm{s} .\) What is the average rate of the reaction during this time interval?

Short Answer

Expert verified
The average rate of the reaction for this time interval is \( -0.001 \, M/s \).

Step by step solution

01

Identify the Variables

The initial concentration of A is 0.485 M at t = 71.5 s and the final concentration of A is 0.474 M at t = 82.4 s. Here, it is important to note that since A is being consumed to form the product, the rate will be negative.
02

Substitute into the formula

Substitute the initial and final concentrations and time into the average rate formula: \[Average \;Rate = \frac{(0.474 \, M - 0.485 \, M)}{(82.4 \, s - 71.5 \, s)}\]
03

Do the arithmetic

Perform the arithmetic in the numerator and the denominator of the fraction separately before dividing them.
04

Calculate the average rate

Finally, perform the division to calculate the average rate of reaction during the given time interval. The unit of rate would be M/s.

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Most popular questions from this chapter

Ammonia decomposes on the surface of a hot tungsten wire. Following are the half-lives that were obtained at \(1100^{\circ} \mathrm{C}\) for different initial concentrations of \(\mathrm{NH}_{3}:\left[\mathrm{NH}_{3}\right]_{0}=0.0031 \mathrm{M}, t_{1 / 2}=7.6 \mathrm{min} ; 0.0015 \mathrm{M}\) \(3.7 \mathrm{min} ; 0.00068 \mathrm{M}, 1.7 \mathrm{min.}\) For this decomposition reaction, what is (a) the order of the reaction; (b) the rate constant, \(k ?\)

In the first-order decomposition of substance A the following concentrations are found at the indicated times: \(t=0 \mathrm{s},[\mathrm{A}]=0.88 \mathrm{M} ; t=50 \mathrm{s},[\mathrm{A}]=0.62 \mathrm{M} ; t=100 \mathrm{s},[\mathrm{A}]=0.44 \mathrm{M} ; t=150 \mathrm{s},[\mathrm{A}]=0.31 \mathrm{M}.\) Calculate the instantaneous rate of decomposition at \(t=100 \mathrm{s}.\)

The half-lives of both zero-order and second-order reactions depend on the initial concentration, as well as on the rate constant. In one case, the half- life gets longer as the initial concentration increases, and in the other it gets shorter. Which is which, and why isn't the situation the same for both?

Certain gas-phase reactions on a heterogeneous catalyst are first order at low gas pressures and zero order at high pressures. Can you suggest a reason for this?

In three different experiments, the following results were obtained for the reaction \(A \longrightarrow\) products: \([\mathrm{A}]_{0}=1.00 \mathrm{M}, t_{1 / 2}=50 \mathrm{min} ;[\mathrm{A}]_{0}=200 \mathrm{M}, t_{1 / 2}=\) \(25 \min ;[\mathrm{A}]_{0}=0.50 \mathrm{M}, t_{1 / 2}=100 \mathrm{min} .\) Write the rate equation for this reaction, and indicate the value of \(k.\)
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