Textbook Question
The reaction 2 NO2¡2 NO + O2 has the rate constant k = 0.63 M- 1s - 1. (b) If the initial concentration of NO2 is 0.100 M, how would you determine how long it would take for the concentration to decrease to 0.025 M?
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Ch.14 - Chemical Kinetics
Chapter 14, Problem 98
The reaction H₂O₂(aq) → H₂O(l) + 1/2 O₂(g) is first order. At 300 K, the rate constant equals 7.0 * 10⁻⁴ s⁻¹. If the activation energy for this reaction is 75 kJ/mol, at what temperature would the reaction rate be doubled?
Verified step by step guidance1
Step 1: Understand the relationship between temperature and reaction rate. The Arrhenius equation, k = A * e^(-Ea/(RT)), describes how the rate constant k depends on temperature T, where A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.
Step 2: Use the Arrhenius equation to express the rate constant at two different temperatures. Let k1 be the rate constant at the initial temperature T1 (300 K), and k2 be the rate constant at the new temperature T2, where the reaction rate is doubled (k2 = 2 * k1).
Step 3: Set up the equation for the two rate constants using the Arrhenius equation: k1 = A * e^(-Ea/(R * T1)) and k2 = A * e^(-Ea/(R * T2)). Since k2 = 2 * k1, you can write: 2 * A * e^(-Ea/(R * T1)) = A * e^(-Ea/(R * T2)).
Step 4: Simplify the equation by canceling out the pre-exponential factor A and taking the natural logarithm of both sides to solve for T2: ln(2) = Ea/R * (1/T1 - 1/T2).
Step 5: Rearrange the equation to solve for the new temperature T2: 1/T2 = 1/T1 - (R/Ea) * ln(2). Substitute the known values (Ea = 75,000 J/mol, R = 8.314 J/(mol*K), T1 = 300 K) to find T2.
Related Practice
Textbook Question
Consider two reactions. Reaction (1) has a constant halflife, whereas reaction (2) has a half-life that gets longer as the reaction proceeds. What can you conclude about the rate laws of these reactions from these observations?
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Open Question
A first-order reaction A → B has the rate constant k = 3.2 * 10^-3 s^-1. If the initial concentration of A is 2.5 * 10^-2 M, what is the rate of the reaction at t = 660 s?
Textbook Question
Americium-241 is used in smoke detectors. It has a first-order rate constant for radioactive decay of k = 1.6 * 10-3 yr-1. By contrast, iodine-125, which is used to test for thyroid functioning, has a rate constant for radioactive decay of k = 0.011 day-1. (b) Which one decays at a faster rate?
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Textbook Question
Americium-241 is used in smoke detectors. It has a first-order rate constant for radioactive decay of k = 1.6 * 10-3 yr-1. By contrast, iodine-125, which is used to test for thyroid functioning, has a rate constant for radioactive decay of k = 0.011 day-1. (c) How much of a 1.00-mg sample of each isotope remains after three half-lives?
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Textbook Question
The rate of a first-order reaction is followed by spectroscopy, monitoring the absorbance of a colored reactant at 520 nm. The reaction occurs in a 1.00-cm sample cell, and the only colored species in the reaction has an extinction coefficient of 5.60 * 103 M-1 cm-1 at 520 nm. (a) Calculate the initial concentration of the colored reactant if the absorbance is 0.605 at the beginning of the reaction.
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