Ch.2 - Atoms, Molecules, and Ions

Brown - Chemistry: The Central Science 15th Edition

Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970당신이 사용하는 게 아니라요?교과서 변경

Brown 15th Edition

Ch.2 - Atoms, Molecules, and Ions

문제 98

2장, 문제 98

The element lead (Pb) consists of four naturally occurring isotopes with atomic masses 203.97302, 205.97444, 206.97587, and 207.97663 amu. The relative abundances of these four isotopes are 1.4, 24.1, 22.1, and 52.4%, respectively. From these data, calculate the atomic weight of lead.

검증된 단계별 안내

Convert the percentage abundances of each isotope into decimal form by dividing each by 100.

Multiply the atomic mass of each isotope by its corresponding decimal abundance to find the weighted mass contribution of each isotope.

Add all the weighted mass contributions together to find the total atomic weight of lead.

Ensure that the units are consistent and the final atomic weight is expressed in atomic mass units (amu).

Review the calculation to ensure that all steps have been followed correctly and that the sum of the abundances equals 100%.

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주요 개념

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Isotopes

Isotopes are variants of a chemical element that have the same number of protons but different numbers of neutrons, resulting in different atomic masses. For lead (Pb), there are four isotopes with distinct atomic masses, which contribute to the element's average atomic weight based on their relative abundances.

Relative Abundance

Relative abundance refers to the proportion of each isotope of an element present in a sample, usually expressed as a percentage. In the case of lead, the relative abundances of its isotopes are crucial for calculating the weighted average atomic mass, as each isotope's contribution to the overall atomic weight is proportional to its abundance.

Weighted Average

The weighted average is a calculation that takes into account the different weights (or contributions) of each component in a dataset. To find the atomic weight of lead, the atomic masses of its isotopes are multiplied by their respective relative abundances, and the results are summed and divided by 100 to yield the average atomic weight.

관련 실천

교과서 질문

The element oxygen has three naturally occurring isotopes, with 8, 9, and 10 neutrons in the nucleus, respectively. a. Write the full chemical symbols for these three isotopes.

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교과서 질문

There are two different isotopes of bromine atoms. Under normal conditions, elemental bromine consists of molecules, and the mass of a molecule is the sum of the masses of the two atoms in the molecule. The mass spectrum of consists of three peaks: m/zRelative Peak Intensity157.836 0.2569 159.834 0.4999 161.832 0.2431

b. What is the mass of each isotope?

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교과서 질문

Gallium (Ga) consists of two naturally occurring isotopes with masses of 68.926 and 70.925 amu. a. How many protons and neutrons are in the nucleus of each isotope? Write the complete atomic symbol for each, showing the atomic number and mass number. b. The average atomic mass of Ga is 69.72 amu. Calculate the abundance of each isotope.

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교과서 질문

The nucleus of ⁶Li is a powerful absorber of neutrons. It exists in the naturally occurring metal to the extent of 7.5%. In the era of nuclear deterrence, large quantities of lithium were processed to remove ⁶Li for use in hydrogen bomb production. The lithium metal remaining after removal of 6Li was sold on the market. (b) The atomic masses of ⁶Li and ⁷Li are 6.015122 and 7.016004 u, respectively. A sample of lithium depleted in the lighter isotope was found on analysis to contain 1.442% ⁶Li. What is the average atomic weight of this sample of the metal?

935

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교과서 질문

a. What is the origin of each peak (of what isotopes does each consist)?

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교과서 질문

Identify the element represented by each of the following symbols and give the number of protons and neutrons in each: (b) ¹²⁷₅₃X (c) ⁸⁶₃₆X (d) ⁶⁷₃₀X

520

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