Chemistry: Atoms First
Chemistry: Atoms First
2nd Edition
ISBN: 9780073511184
Author: Julia Burdge, Jason Overby Professor
Publisher: McGraw-Hill Education
Question
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Chapter 19, Problem 19.2KSP
Interpretation Introduction

Interpretation:

The original mass of sample of 61Cu has to be determined from the given option.

Concept introduction:

  • Unstable nuclei emit radiation spontaneously to become stable nuclei by losing energy. This process of emission of radiation by unstable nuclei is known as radioactive decay.
  • Radioactive decay is in the first order kinetics. Rate of radioactive decay at a time t is,

lnNtN0=ktwhere,k=FirstorderrateconstantN0=number of radioactive nuclei at time zeroNt=number of radioactive nuclei at a time,t

  • Half-life of radioactive decay is the time required for a radioactive sample to decay to one half of the atomic nucleus.

t1/2=0.693k

Expert Solution & Answer
Check Mark

Answer to Problem 19.2KSP

The correct answer is option (e) 8.78×104mg

Explanation of Solution

Reason for correct option

To find: The original mass of sample of 61Cu

The original mass of sample of 61Cu is 8.78×104mg

Original mass of 61Cu is calculated

Given,

Half-life=3.35hTime=24hMassofsampleafter24h=612.8mg

Half-life of a first order reaction is t1/2=0.693k

Hence,

The rate constant of the reaction is,

k=0.693t1/2=0.6933.35h=0.207h1

Suppose the number of radioactive nuclei at time zero is N0 and at a time t is Nt,

lnNtN0=kt

Radioactive nuclei at time zero and time t are the initial concentration and the final concentration.

So the equation can also be written as,

ln[A]t[A]0=kt

Therefore,

The original mass of sample of 61Cu is,

ln[A]t[A]0=ktln612.8mg[A]0=(0.207h1)(24h)ln612.8mg[A]0=(4.968)612.8mg[A]0=6.957×103[A]0=8.78×104mg

The original mass of sample of 61Cu is 8.78×104mg

Hence the correct option for the original mass of sample of 61Cu is option e.

Reasons for incorrect options:

Writes all original mass of sample of 61Cu given in the options except option e.

  1. a) 85.5mg
  2. b) 4.39×103mg
  3. c) 736mg
  4. d) 6.40×103mg

The original mass of sample of 61Cu is found as 8.78×104mg

So, this value of original mass of sample of 61Cu is not matching with any of the above given original mass of sample of 61Cu in remaining options.

Hence the incorrect options are a, b, c and d.

Conclusion

The correct option for original mass of sample of 61Cu is identified from the given options. The original mass of sample of 61Cu is determined by using the data’s given for the radioactive decay.

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Chapter 19 Solutions

Chemistry: Atoms First

Ch. 19.4 - The gas-phase reaction of nitric oxide with...Ch. 19.4 - Prob. 3PPACh. 19.4 - Prob. 3PPBCh. 19.4 - Prob. 3PPCCh. 19.4 - Prob. 19.4.1SRCh. 19.4 - Prob. 19.4.2SRCh. 19.4 - Prob. 19.4.3SRCh. 19.4 - Prob. 19.4.4SRCh. 19.4 - Prob. 19.4.5SRCh. 19.5 - Prob. 19.4WECh. 19.5 - Prob. 4PPACh. 19.5 - Prob. 4PPBCh. 19.5 - Prob. 4PPCCh. 19.5 - Prob. 19.5WECh. 19.5 - Prob. 5PPACh. 19.5 - Prob. 5PPBCh. 19.5 - Prob. 5PPCCh. 19.5 - Prob. 19.6WECh. 19.5 - Prob. 6PPACh. 19.5 - Calculate the rate constant for the first-order...Ch. 19.5 - Prob. 6PPCCh. 19.5 - Prob. 19.7WECh. 19.5 - The reaction 2A B is second order in A with a rate...Ch. 19.5 - Prob. 7PPBCh. 19.5 - Prob. 7PPCCh. 19.5 - Prob. 19.5.1SRCh. 19.5 - Prob. 19.5.2SRCh. 19.5 - Prob. 19.5.3SRCh. 19.5 - Prob. 19.5.4SRCh. 19.6 - Prob. 19.8WECh. 19.6 - Prob. 8PPACh. 19.6 - Prob. 8PPBCh. 19.6 - Prob. 8PPCCh. 19.6 - Prob. 19.9WECh. 19.6 - Prob. 9PPACh. 19.6 - Prob. 9PPBCh. 19.6 - Prob. 9PPCCh. 19.6 - Prob. 19.10WECh. 19.6 - Prob. 10PPACh. 19.6 - Prob. 10PPBCh. 19.6 - Prob. 10PPCCh. 19.6 - Prob. 19.6.1SRCh. 19.6 - Prob. 19.6.2SRCh. 19.7 - Prob. 19.11WECh. 19.7 - Prob. 11PPACh. 19.7 - Prob. 11PPBCh. 19.7 - Prob. 11PPCCh. 19.7 - Consider the gas-phase reaction of nitric oxide...Ch. 19.7 - Prob. 12PPACh. 19.7 - Prob. 12PPBCh. 19.7 - Prob. 12PPCCh. 19.7 - Prob. 19.7.1SRCh. 19.7 - Prob. 19.7.2SRCh. 19.7 - Prob. 19.7.3SRCh. 19.7 - Prob. 19.7.4SRCh. 19 - The rate of a reaction in which the reactant...Ch. 19 - The rate of a reaction in which the reactant...Ch. 19 - The rate of a reaction in which the reactant...Ch. 19 - Increasing the temperature of a reaction increases...Ch. 19 - Define activation energy. What role does...Ch. 19 - Sketch a potential energy versus reaction progress...Ch. 19 - The reaction H + H2 H2 + H has been studied for...Ch. 19 - What is meant by the rate of a chemical reaction?...Ch. 19 - Distinguish between average rate and instantaneous...Ch. 19 - What are the advantages of measuring the initial...Ch. 19 - Prob. 19.7QPCh. 19 - Consider the reaction N2(g)+3H2(g)2NH3(g) Suppose...Ch. 19 - Prob. 19.9QPCh. 19 - Prob. 19.10QPCh. 19 - Prob. 19.11QPCh. 19 - Prob. 19.12QPCh. 19 - Prob. 19.13QPCh. 19 - What are the units for the rate constants of...Ch. 19 - Consider the zeroth-order reaction: A product....Ch. 19 - Prob. 19.16QPCh. 19 - Prob. 19.17QPCh. 19 - Prob. 19.18QPCh. 19 - Prob. 19.19QPCh. 19 - Prob. 19.20QPCh. 19 - Prob. 19.21QPCh. 19 - Prob. 19.22QPCh. 19 - Prob. 19.23QPCh. 19 - Prob. 19.24QPCh. 19 - Prob. 19.25QPCh. 19 - Prob. 19.26QPCh. 19 - Prob. 19.27QPCh. 19 - Prob. 19.28QPCh. 19 - Prob. 19.29QPCh. 19 - Prob. 19.30QPCh. 19 - Prob. 19.31QPCh. 19 - Prob. 19.32QPCh. 19 - Prob. 19.33QPCh. 19 - Consider the first-order reaction X Y shown here,...Ch. 19 - Prob. 19.35QPCh. 19 - Consider the first-order reaction A B in which A...Ch. 19 - Prob. 19.37QPCh. 19 - Prob. 19.38QPCh. 19 - Prob. 19.39QPCh. 19 - Prob. 19.40QPCh. 19 - Prob. 19.41QPCh. 19 - Prob. 19.42QPCh. 19 - Prob. 19.43QPCh. 19 - Prob. 19.44QPCh. 19 - Prob. 19.45QPCh. 19 - The rate at which tree crickets chirp is 2.0 102...Ch. 19 - Prob. 19.47QPCh. 19 - The activation energy for the denaturation of a...Ch. 19 - Variation of the rate constant with temperature...Ch. 19 - Prob. 19.50QPCh. 19 - Prob. 19.51QPCh. 19 - Prob. 19.52QPCh. 19 - Prob. 19.53QPCh. 19 - What is an elementary step? What is the...Ch. 19 - Prob. 19.55QPCh. 19 - Determine the molecularity, and write the rate law...Ch. 19 - What is the rate-determining step of a reaction?...Ch. 19 - Prob. 19.58QPCh. 19 - Prob. 19.59QPCh. 19 - Classify each of the following elementary steps as...Ch. 19 - Prob. 19.61QPCh. 19 - Prob. 19.62QPCh. 19 - Prob. 19.63QPCh. 19 - Prob. 19.64QPCh. 19 - Prob. 19.65QPCh. 19 - What are the characteristics of a catalyst?Ch. 19 - Prob. 19.67QPCh. 19 - Prob. 19.68QPCh. 19 - The concentrations of enzymes in cells are usually...Ch. 19 - Prob. 19.70QPCh. 19 - Prob. 19.71QPCh. 19 - Prob. 19.72QPCh. 19 - Prob. 19.73QPCh. 19 - Prob. 19.74QPCh. 19 - Prob. 19.75QPCh. 19 - In a certain industrial process involving a...Ch. 19 - Prob. 19.77QPCh. 19 - Prob. 19.78QPCh. 19 - Explain why most metals used in catalysis arc...Ch. 19 - Prob. 19.80QPCh. 19 - Prob. 19.81QPCh. 19 - Prob. 19.82QPCh. 19 - Prob. 19.83QPCh. 19 - Prob. 19.84QPCh. 19 - The bromination of acetone is acid-catalyzed. The...Ch. 19 - The decomposition of N2O to N2 and O2 is a...Ch. 19 - Prob. 19.87QPCh. 19 - Prob. 19.88QPCh. 19 - The integrated rate law for the zeroth-order...Ch. 19 - Prob. 19.90QPCh. 19 - Prob. 19.91QPCh. 19 - Prob. 19.92QPCh. 19 - The reaction of G2 with E2 to form 2EG is...Ch. 19 - Prob. 19.94QPCh. 19 - Prob. 19.95QPCh. 19 - Prob. 19.96QPCh. 19 - Strictly speaking, the rate law derived for the...Ch. 19 - Prob. 19.98QPCh. 19 - The decomposition of dinitrogen pentoxide has been...Ch. 19 - Prob. 19.100QPCh. 19 - Prob. 19.101QPCh. 19 - Prob. 19.102QPCh. 19 - To prevent brain damage, a standard procedure is...Ch. 19 - Prob. 19.104QPCh. 19 - Prob. 19.105QPCh. 19 - Prob. 19.106QPCh. 19 - Prob. 19.107QPCh. 19 - Prob. 19.108QPCh. 19 - Prob. 19.109QPCh. 19 - Prob. 19.110QPCh. 19 - (a) What can you deduce about the activation...Ch. 19 - Prob. 19.112QPCh. 19 - Prob. 19.113QPCh. 19 - Prob. 19.114QPCh. 19 - Prob. 19.115QPCh. 19 - Prob. 19.116QPCh. 19 - Prob. 19.117QPCh. 19 - Prob. 19.118QPCh. 19 - Prob. 19.119QPCh. 19 - Prob. 19.120QPCh. 19 - Prob. 19.121QPCh. 19 - Prob. 19.122QPCh. 19 - Consider the following potential energy profile...Ch. 19 - Prob. 19.124QPCh. 19 - Prob. 19.125QPCh. 19 - Prob. 19.126QPCh. 19 - Prob. 19.127QPCh. 19 - Prob. 19.128QPCh. 19 - The following expression shows the dependence of...Ch. 19 - Prob. 19.130QPCh. 19 - The rale constant for the gaseous reaction H2(g) +...Ch. 19 - Prob. 19.132QPCh. 19 - Prob. 19.133QPCh. 19 - At a certain elevated temperature, ammonia...Ch. 19 - Prob. 19.135QPCh. 19 - The rate of a reaction was followed by the...Ch. 19 - Prob. 19.137QPCh. 19 - Prob. 19.138QPCh. 19 - Prob. 19.1KSPCh. 19 - Prob. 19.2KSPCh. 19 - Prob. 19.3KSPCh. 19 - Prob. 19.4KSP
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