Chemistry: The Science in Context (Fifth Edition)
Chemistry: The Science in Context (Fifth Edition)
5th Edition
ISBN: 9780393614046
Author: Thomas R. Gilbert, Rein V. Kirss, Natalie Foster, Stacey Lowery Bretz, Geoffrey Davies
Publisher: W. W. Norton & Company
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Chapter 2, Problem 2.29QP
Interpretation Introduction

Interpretation: The exact mass of 48Ti isotope is to be calculated from the given table.

Concept introduction: The exact mass of an isotope is calculated from the formula,

Averageatomicmass=m1×x1+m2×x2+m3×x3+...+mnxn

To determine: The exact mass of 48Ti isotope from the given table.

Expert Solution & Answer
Check Mark

Answer to Problem 2.29QP

Solution

The exact mass of 48Ti isotope is 47.95amu_ .

Explanation of Solution

Explanation

The exact mass of an isotope is calculated from the formula,

Averageatomicmass=m1×x1+m2×x2+m3×x3+...+mnxn (1)

Where,

  • m is mass of an isotope.
  • x is natural abundance expressed in decimals.

The given values and natural abundance in decimals are summarized in Table 1 .

Symbol Exact mass (m) in amu Natural abundance in percentage Natural abundance in decimals (x)
46Ti 45.95263=m1 8.25% 0.0825=x1
47Ti 46.9518=m2 7.44% 0.0744=x2
48Ti m3 73.72% 0.7372=x3
49Ti 48.94787=m4 5.41% 0.0541=x4
50Ti 49.9448=m5 5.18% 0.0518=x5
Average 47.87

Table 1

In Table 1 ,

  • m1 is the exact  mass of 46Ti isotope.
  • m2 is the exact mass of 47Ti isotope.
  • m3 is the exact mass of 48Ti isotope
  • m4 is the exact mass of 49Ti isotope.
  • m5 is the exact mass of 50Ti isotope.
  • x1 is the natural abundance in decimals for 46Ti isotope.
  • x2 is the natural abundance in decimals for 47Ti isotope.
  • x3 is the natural abundance in decimals for 48Ti isotope.
  • x4 is the natural abundance in decimals for 49Ti isotope.
  • x5 is the natural abundance in decimals for 50Ti isotope.

The m3 , exact mass of 48Ti is to be calculated.

Substitute the all values of m,x and average atomic mass in equation (1) .

Averageatomicmass=m1×x1+m2×x2+m3×x3+m4×x4+m5×x547.87=((45.95263×0.0825)+(46.9518×0.0744)+(m3×0.7372)+(48.94787×0.0541)+(49.9448×0.0518))=3.7911+3.4932+0.7372m3+2.6481+2.5871

Simplifying,

47.87=12.5195+0.7372m30.7372m3=47.8712.51950.7372m3=35.3505m3=35.35050.7372

So,

m3=47.95amu

Hence, the exact mass of 48Ti isotope is 47.95amu_ .

Conclusion

The exact mass of 48Ti isotope is 47.95amu_

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Chapter 2 Solutions

Chemistry: The Science in Context (Fifth Edition)

Ch. 2.7 - Prob. 11PECh. 2 - Prob. 2.1VPCh. 2 - Prob. 2.2VPCh. 2 - Prob. 2.3VPCh. 2 - Prob. 2.4VPCh. 2 - Prob. 2.5VPCh. 2 - Prob. 2.6VPCh. 2 - Prob. 2.7VPCh. 2 - Prob. 2.8VPCh. 2 - Prob. 2.9VPCh. 2 - Prob. 2.10VPCh. 2 - Prob. 2.11QPCh. 2 - Prob. 2.12QPCh. 2 - Prob. 2.13QPCh. 2 - Prob. 2.14QPCh. 2 - Prob. 2.15QPCh. 2 - Prob. 2.16QPCh. 2 - Prob. 2.17QPCh. 2 - Prob. 2.18QPCh. 2 - Prob. 2.19QPCh. 2 - Prob. 2.20QPCh. 2 - Prob. 2.21QPCh. 2 - Prob. 2.22QPCh. 2 - Prob. 2.23QPCh. 2 - Prob. 2.24QPCh. 2 - Prob. 2.25QPCh. 2 - Prob. 2.26QPCh. 2 - Prob. 2.27QPCh. 2 - Prob. 2.28QPCh. 2 - Prob. 2.29QPCh. 2 - Prob. 2.30QPCh. 2 - Prob. 2.31QPCh. 2 - Prob. 2.32QPCh. 2 - Prob. 2.33QPCh. 2 - Prob. 2.34QPCh. 2 - Prob. 2.35QPCh. 2 - Prob. 2.36QPCh. 2 - Prob. 2.37QPCh. 2 - Prob. 2.38QPCh. 2 - Prob. 2.39QPCh. 2 - Prob. 2.40QPCh. 2 - Prob. 2.41QPCh. 2 - Prob. 2.42QPCh. 2 - Prob. 2.43QPCh. 2 - Prob. 2.44QPCh. 2 - Prob. 2.45QPCh. 2 - Prob. 2.46QPCh. 2 - Prob. 2.47QPCh. 2 - Prob. 2.48QPCh. 2 - Prob. 2.49QPCh. 2 - Prob. 2.50QPCh. 2 - Prob. 2.51QPCh. 2 - Prob. 2.52QPCh. 2 - Prob. 2.53QPCh. 2 - Prob. 2.54QPCh. 2 - Prob. 2.55QPCh. 2 - Prob. 2.56QPCh. 2 - Prob. 2.57QPCh. 2 - Prob. 2.58QPCh. 2 - Prob. 2.59QPCh. 2 - Prob. 2.60QPCh. 2 - Prob. 2.61QPCh. 2 - Prob. 2.62QPCh. 2 - Prob. 2.63QPCh. 2 - Prob. 2.64QPCh. 2 - Prob. 2.65QPCh. 2 - Prob. 2.66QPCh. 2 - Prob. 2.67QPCh. 2 - Prob. 2.68QPCh. 2 - Prob. 2.69QPCh. 2 - Prob. 2.70QPCh. 2 - Prob. 2.71QPCh. 2 - Prob. 2.72QPCh. 2 - Prob. 2.73QPCh. 2 - Prob. 2.74QPCh. 2 - Prob. 2.75QPCh. 2 - Prob. 2.76QPCh. 2 - Prob. 2.77QPCh. 2 - Prob. 2.78QPCh. 2 - Prob. 2.79QPCh. 2 - Prob. 2.80QPCh. 2 - Prob. 2.81QPCh. 2 - Prob. 2.82QPCh. 2 - Prob. 2.83QPCh. 2 - Prob. 2.84QPCh. 2 - Prob. 2.85QPCh. 2 - Prob. 2.86QPCh. 2 - Prob. 2.87QPCh. 2 - Prob. 2.88QPCh. 2 - Prob. 2.89QPCh. 2 - Prob. 2.90QPCh. 2 - Prob. 2.91QPCh. 2 - Prob. 2.92QPCh. 2 - Prob. 2.93QPCh. 2 - Prob. 2.94QPCh. 2 - Prob. 2.95QPCh. 2 - Prob. 2.96QPCh. 2 - Prob. 2.97QPCh. 2 - Prob. 2.98QPCh. 2 - Prob. 2.99QPCh. 2 - Prob. 2.100QPCh. 2 - Prob. 2.101QPCh. 2 - Prob. 2.102QPCh. 2 - Prob. 2.103QPCh. 2 - Prob. 2.104QPCh. 2 - Prob. 2.105QPCh. 2 - Prob. 2.106QPCh. 2 - Prob. 2.107APCh. 2 - Prob. 2.108APCh. 2 - Prob. 2.109APCh. 2 - Prob. 2.110APCh. 2 - Prob. 2.111APCh. 2 - Prob. 2.112APCh. 2 - Prob. 2.113APCh. 2 - Prob. 2.114APCh. 2 - Prob. 2.115APCh. 2 - Prob. 2.116APCh. 2 - Prob. 2.117APCh. 2 - Prob. 2.118APCh. 2 - Prob. 2.119APCh. 2 - Prob. 2.120APCh. 2 - Prob. 2.121APCh. 2 - Prob. 2.122APCh. 2 - Prob. 2.123APCh. 2 - Prob. 2.124APCh. 2 - Prob. 2.125APCh. 2 - Prob. 2.126APCh. 2 - Prob. 2.127APCh. 2 - Prob. 2.128AP
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