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Chapter 2: Problem 30

(a) What is the mass in amu of a carbon-12 atom? (b) Why is the atomic weight of carbon reported as 12.011 in the table of elements and the periodic table in the front inside cover of this text?

Short Answer

Expert verified
(a) The mass of a carbon-12 atom is exactly 12 amu, as it has 12 nucleons (6 protons and 6 neutrons), and 1 amu is defined as 1/12th the mass of a carbon-12 atom. (b) The atomic weight of carbon is reported as 12.011 because it is a weighted average of the masses of its naturally occurring isotopes (carbon-12, carbon-13, and traces of carbon-14) taking into account their relative abundances. This value reflects the presence of different isotopes and their contributions to the element's overall atomic weight.

Step by step solution

01

(a) Mass of a Carbon-12 Atom in amu)

A carbon-12 atom is a specific isotope of carbon, made up of 6 protons, 6 neutrons, and 6 electrons. By definition, 1 atomic mass unit (amu) is equal to 1/12th the mass of a carbon-12 atom. Therefore, since the carbon-12 atom has 12 nucleons (protons and neutrons) and amu is defined based on the carbon-12 atom, the mass of a carbon-12 atom is exactly 12 amu.
02

(b) Explanation for Carbon's Atomic Weight of 12.011)

The atomic weight of an element is the weighted average of the masses of its naturally occurring isotopes, taking into account their relative abundances. Carbon has several natural isotopes, including the aforementioned carbon-12, as well as carbon-13 and traces of carbon-14. The majority is carbon-12 (approximately 98.89%), with carbon-13 making up most of the remaining percentage (around 1.11%), and carbon-14 being extremely rare. The atomic weight of carbon, which is \(\text{12.011}\), is calculated as follows: Atomic weight of Carbon = (relative abundance of carbon-12 脳 mass of carbon-12) + (relative abundance of carbon-13 脳 mass of carbon-13) + (relative abundance of carbon-14 脳 mass of carbon-14) Atomic weight of Carbon 鈮� (0.9889 脳 12 amu) + (0.0111 脳 13 amu) + (trace amount 脳 14 amu) Atomic weight of Carbon 鈮� 12.011 amu Due to the presence of carbon isotopes, carbon's atomic weight is not exactly 12, but 12.011. This weighted average takes into account the different isotopes and their relative abundances and is used to report the atomic weight in the periodic table.

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Most popular questions from this chapter

Mass spectrometry is more often applied to molecules than to atoms. We will see in Chapter 3 that the molecular weight of a molecule is the sum of the atomic weights of the atoms in the molecule. The mass spectrum of \(\mathrm{H}_{2}\) is taken under conditions that prevent decomposition into \(\mathrm{H}\) atoms. The two naturally occurring isotopes of hydrogen are \({ }^{1} \mathrm{H}\) (atomic mass = 1.00783 amu; abundance \(99.9885 \%\) ) and \({ }^{2} \mathrm{H}\) (atomic mass \(=\) 2.01410 amu; abundance \(0.0115 \%\) ). (a) How many peaks will the mass spectrum have? (b) Give the relative atomic masses of each of these peaks. (c) Which peak will be the largest and which the smallest?

The first atoms of seaborgium (Sg) were identified in 1974 . The longest-lived isotope of Sg has a mass number of \(266 .\) (a) How many protons, electrons, and neutrons are in an \({ }^{266} \mathrm{Sg}\) atom? (b) Atoms of Sg are very unstable, and it is therefore difficult to study this element's properties. Based on the position of Sg in the periodic table, what element should it most closely resemble in its chemical properties?

The most common charge associated with scandium in its compounds is \(3+.\) Indicate the chemical formulas you would expect for compounds formed between scandium and (a) iodine, \((\mathbf{b})\) sulfur, \((\mathbf{c})\) nitrogen.

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