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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

Carbonic acid occurs in carbonated beverages. When allowed to react with lithium hydroxide it produces lithium carbonate. Lithium carbonate is used to treat depression and bipolar disorder. Write chemical formulas for carbonic acid, lithium hydroxide, and lithium carbonate.

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Millikan determined the charge on the electron by studying the static charges on oil drops falling in an electric field (Figure 2.5). A student carried out this experiment using several oil drops for her measurements and calculated the charges on the drops. She obtained the following data: $$ \begin{array}{cc} \hline \text { Droplet } & \text { Calculated Charge (C) } \\ \hline \text { A } & 1.60 \times 10^{-19} \\ \text {B } & 3.15 \times 10^{-19} \\ \text {C } & 4.81 \times 10^{-19} \\ \text {D } & 6.31 \times 10^{-19} \end{array} $$ (a) What is the significance of the fact that the droplets carried different charges? (b) What conclusion can the student draw from these data regarding the charge of the electron? (c) What value (and to how many significant figures) should she report for the electronic charge?
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