In the presence of excess thiocyanate ion, SCN−, the following reaction is first order in chromium(III) ion, Cr3−; the rate constant is 2.0 × 10−6/s.
What is the half-life in hours? How many hours would be required for the initial concentration of Cr3− to decrease to each of the following values: 25.0% left, 12.5% left, 6.25% left, 3.125% left?
Interpretation:
The half-life of
Concept Introduction:
Half life period:
The time taken by the concentration of reaction to get reduced of its original concentration is called as half-life reaction.
Half life period can be calculated using the equation,
The half-life period of substance is related to rate constant but it is independent of concentration of reactants.
Answer to Problem 13.65QP
The half life of
The time duration for decrease in concentration of
The time duration for decrease in concentration of
The time duration for decrease in concentration of
The time duration for decrease in concentration of
Explanation of Solution
To calculate the half-life of
Substitute
Half life period can be calculated using the equation,
The half life of
To calculate time duration for decrease in concentration of
For the concentration to decrease by
To calculate time duration for decrease in concentration of
For the concentration to decrease by
To calculate time duration for decrease in concentration of
For the concentration to decrease by
To calculate time duration for decrease in concentration of
For the concentration to decrease by
The half-life of
Want to see more full solutions like this?
Chapter 13 Solutions
Lab Manual Experiments in General Chemistry
- In the presence of excess thiocyanate ion, SCN, the following reaction is first order in iron(III) ion, Fe3+; the rate constant is 1.27/s. Fe3+(aq)+SCN(aq)Fe(SCN)2+(aq) What is the half-life in seconds? How many seconds would be required for the initial concentration of Fe3+ to decrease to each of the following values: 25.0% left, 12.5% left, 6.25% left, 3.125% left? What is the relationship between these times and the half-life?arrow_forwardThe catalyzed decomposition of hydrogen peroxide is first-order in [H2O2]. It was found that the concentration of H2O2 decreased from 0.24 M to 0.060 M over a period of 282 minutes. What is the half-life of H2O2? What is the rate constant for this reaction? What is the initial rate of decomposition at the beginning of this experiment (when [H2O2] = 0.24 M)?arrow_forwardSucrose, a sugar, decomposes in acid solution to give glucose and fructose. The reaction is first-order in sucrose, and the rate constant at 25 C is k = 0.21 h1. If the initial concentration of sucrose is 0.010 mol/L, what is its concentration after 5.0 h?arrow_forward
- Hydrogen peroxide, H2O2(aq), decomposes to H2O() and O2(g) in a reaction that is first-order in H2O2 and has a rate constant k = 1.06 103 min1 at a given temperature. (a) How long will it take for 15% of a sample of H2O2 to decompose? (b) How long will it take for 85% of the sample to decompose?arrow_forwardThe decomposition of SO2Cl2 is a first-order reaction: SO2Cl2(g) SO2(g) + Cl2(g) The rate constant for the reaction is 2.8 103 min1 at 600 K. If the initial concentration of SO2Cl2 is 1.24 103 mol/L, how long will it take for the concentration to drop to 0.31 103 mol/L?arrow_forwardThe compound Xe(CF3)2 decomposes in a first-order reaction to elemental Xe with a half-life of 30. minutes. If you place 7.50 mg of Xe(CF3)2 in a flask, how long must you wait until only 0.25 mg of Xe(CF3)2 remains?arrow_forward
- The Raschig reaction produces the industrially important reducing agent hydrazine, N2H4, from ammonia, NH3, and hypochlorite ion, OCl−, in basic aqueous solution. A proposed mechanism is Step 1: Step 2: Step 3: What is the overall stoichiometric equation? Which step is rate-limiting? What reaction intermediates are involved? What rate law is predicted by this mechanism?arrow_forwardThe dimerization of butadiene, C4H6, to form 1,5-cyclooctadiene is a second-order process that occurs when the diene is heated. In an experiment, a sample of 0.0087 mol of C4H6 was heated in a 1.0-L flask. After 600. seconds, 21% of the butadiene had dimerized. Calculate the rate constant for this reaction.arrow_forwardAn excellent way to make highly pure nickel metal for use in specialized steel alloys is to decompose Ni(CO)4 by heating it in a vacuum to slightly above room temperature. Ni(CO)4(g) Ni(s) + 4 CO(g) The reaction is proposed to occur in four steps, the first of which is Ni(CO)4(g) Ni(CO)3(g) + CO(g) Kinetic studies of this first-order decomposition reaction have been carried out between 47.3 C and 66.0 C to give the results in the table. (a) Determine the activation energy for this reaction. (b) Ni(CO)4 is formed by the reaction of nickel metal with carbon monoxide. Suppose that 2.05 g CO is combined with 0.125 g nickel metal. Determine the maximum mass (g) of Ni(CO)4 that can be formed. Replacement of CO by another molecule in Ni(CO)4 was studied in the nonaqueous solvents toluene and hexane to understand the general principles that govern the chemistry of such compounds. Ni(CO)4(g) + P(CH3)3 Ni(CO)3P(CH3)3 + CO A detailed study of the kinetics of the reaction led to the mechanism Step1:(slow)Ni(CO)4Ni(CO)3+COStep2:(fast)Ni(CO)3+P(CH3)3Ni(CO)3P(CH3)3 (c) Which step in the mechanism is unimolecular? Which is bimolecular? (d) Add the steps of the mechanism to show that the result is the balanced equation for the observed reaction. (e) Is there an intermediate in this reaction? If so, what is it? (f) It was found that doubling the concentration of Ni(CO)4 increased the reaction rate by a factor of 2. Doubling the concentration of P(CH3)3 had no effect on the reaction rate. Based on this information, write the rate equation for the reaction. (g) Does the experimental rate equation support the proposed mechanism? Why or why not?arrow_forward
- General Chemistry - Standalone book (MindTap Cour...ChemistryISBN:9781305580343Author:Steven D. Gammon, Ebbing, Darrell Ebbing, Steven D., Darrell; Gammon, Darrell Ebbing; Steven D. Gammon, Darrell D.; Gammon, Ebbing; Steven D. Gammon; DarrellPublisher:Cengage LearningChemistry & Chemical ReactivityChemistryISBN:9781133949640Author:John C. Kotz, Paul M. Treichel, John Townsend, David TreichelPublisher:Cengage LearningChemistry & Chemical ReactivityChemistryISBN:9781337399074Author:John C. Kotz, Paul M. Treichel, John Townsend, David TreichelPublisher:Cengage Learning
- ChemistryChemistryISBN:9781305957404Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCostePublisher:Cengage LearningChemistry: An Atoms First ApproachChemistryISBN:9781305079243Author:Steven S. Zumdahl, Susan A. ZumdahlPublisher:Cengage Learning