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Chapter 3: Problem 25

The atomic masses in the periodic table are relative masses and average masses. Explain.

Short Answer

Expert verified
The atomic masses in the periodic table are both relative and average masses. They are relative because they are compared to the mass of the reference element, carbon-12, with an atomic mass unit (amu) defined as 1/12 of the mass of a carbon-12 atom. This allows for convenient expression and comparison of atomic masses. They are average masses because they represent the weighted average of the masses of all isotopes of an element, factoring in the relative abundance of each isotope. This provides a single atomic mass value for each element, rather than masses for individual isotopes.

Step by step solution

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1. Overview of Atomic Structure

Atoms are the basic building blocks of matter. They consist of a nucleus, which contains protons and neutrons, and electrons that orbit the nucleus. Protons and electrons have a charge, with protons being positively charged and electrons being negatively charged. Neutrons have no charge. The number of protons in the nucleus determines the element to which the atom belongs.
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2. Understanding Isotopes and Their Masses

Isotopes are atoms of the same element that have different numbers of neutrons in their nucleus. This means they have the same number of protons and electrons, but different masses because the number of neutrons varies. Each isotope has a specific mass, and the atomic mass for a given element is generally different for varying isotopes.
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3. Averaging Isotope Masses to Determine Atomic Mass

Atomic mass in the periodic table is an average of the masses of all isotopes of an element, weighted by the relative abundance of each isotope. The abundant isotopes have a higher contribution to the average mass, while the less abundant isotopes contribute less to the average. As a result, the atomic mass listed for an element in the periodic table represents an average value and not the mass of a single isotope.
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4. Atomic Masses are Relative Masses

Atomic masses measured in atomic mass units (amu) are relative, meaning they are compared to the mass of a reference element. The reference element used is carbon-12, with a mass of exactly 12 amu. An atomic mass unit is defined as 1/12 of the mass of a carbon-12 atom. Relative masses are used because the actual masses of atoms are extremely small, making it difficult to work with them directly. By comparing them to a reference element, it becomes more convenient to express and compare the atomic masses of different elements. In summary, atomic masses in the periodic table are relative masses because they are compared to the mass of a reference element, carbon-12, and they are average masses because they represent the weighted average of the masses of all isotopes for a given element, taking into account the relative abundance of each isotope.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isotopes
Atoms can sometimes be a little different from one another, even if they belong to the same element. How is this possible? It鈥檚 all thanks to isotopes! Isotopes are variations of a single element that have the same number of protons but a different number of neutrons.
This difference in neutron count gives each isotope a unique mass. For example, carbon 鈥� a commonly discussed element 鈥� has several isotopes such as carbon-12 and carbon-14. Both isotopes have 6 protons, which makes them carbon atoms, but carbon-12 has 6 neutrons, and carbon-14 has 8 neutrons.
  • Same number of protons = same element
  • Different number of neutrons = different isotopes
Isotopes play a pivotal role in determining an element's atomic mass as these differences in mass need to be taken into account.
Relative Masses
When you look at atomic masses, you'll often hear that they are 'relative'. But what does this mean? Essentially, atomic masses are not the actual weights of the atoms, but rather values compared to a standard. This standard is the carbon-12 isotope, which is defined as having a mass of exactly 12 atomic mass units (amu). One atomic mass unit is therefore set as 1/12 of the mass of a carbon-12 atom. This reference helps in expressing the masses of other atoms as fractions or multiples of the mass of carbon-12.
  • Relative to the carbon-12 isotope
  • Helpful for comparing different elements
Thus, when we see an atomic mass on the periodic table, it is a comparative figure that makes measuring extremely tiny masses much more manageable.
Periodic Table
The periodic table presents a wealth of information in a tidy, organized manner. One of the critical pieces of information it provides is the atomic mass of elements, which is often an average mass. This average atomic mass takes into account the existence of isotopes. Since isotopes of an element can vary, the periodic table lists an average mass based on how often each isotope occurs in nature.
More abundant isotopes will influence the atomic mass more heavily than those less common.
  • Weighted averages are used
  • Reflects isotope abundance
The periodic table is invaluable because it provides a quick reference to these average atomic masses, helping scientists easily recognize and work with different elements based on their atomic structure.

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Most popular questions from this chapter

Balance each of the following chemical equations. a. \(\mathrm{KO}_{2}(s)+\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{KOH}(a q)+\mathrm{O}_{2}(g)+\mathrm{H}_{2} \mathrm{O}_{2}(a q)\) b. \(\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+\mathrm{HNO}_{3}(a q) \rightarrow \mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\) c. \(\mathrm{NH}_{3}(g)+\mathrm{O}_{2}(g) \rightarrow \mathrm{NO}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) d. \(\mathrm{PCl}_{5}(l)+\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{H}_{3} \mathrm{PO}_{4}(a q)+\mathrm{HCl}(g)\) e. \(\mathrm{CaO}(s)+\mathrm{C}(s) \rightarrow \mathrm{CaC}_{2}(s)+\mathrm{CO}_{2}(g)\) f. \(\operatorname{MoS}_{2}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{MoO}_{3}(s)+\mathrm{SO}_{2}(g)\) g. \(\mathrm{FeCO}_{3}(s)+\mathrm{H}_{2} \mathrm{CO}_{3}(a q) \rightarrow \mathrm{Fe}\left(\mathrm{HCO}_{3}\right)_{2}(a q)\)

With the advent of techniques such as scanning tunneling microscopy, it is now possible to "write" with individual atoms by manipulating and arranging atoms on an atomic surface. a. If an image is prepared by manipulating iron atoms and their total mass is \(1.05 \times 10^{-20} \mathrm{g},\) what number of iron atoms were used? b. If the image is prepared on a platinum surface that is exactly 20 platinum atoms high and 14 platinum atoms wide, what is the mass (grams) of the atomic surface? c. If the atomic surface were changed to ruthenium atoms and the same surface mass as determined in part b is used, what number of ruthenium atoms is needed to construct the surface?

Tetrodotoxin is a toxic chemical found in fugu pufferfish, a popular but rare delicacy in Japan. This compound has an LD_s0 (the amount of substance that is lethal to \(50 . \%\) of a population sample) of \(10 . \mu \mathrm{g}\) per kg of body mass. Tetrodotoxin is 41.38\(\%\) carbon by mass, 13.16\(\%\) nitrogen by mass, and 5.37\(\%\) hydrogen by mass, with the remaining amount consisting of oxygen. What is the empirical formula of tetrodotoxin? If three molecules of tetrodotoxin have a mass of \(1.59 \times 10^{-21}\) g, what is the molecular formula of tetrodotoxin? What number of molecules of tetrodotoxin would be the LD_so dosage for a person weighing 165 \(\mathrm{lb}\) ?

A 0.755 -g sample of hydrated copper(II) sulfate $$ \mathrm{CuSO}_{4} \cdot x \mathrm{H}_{2} \mathrm{O} $$ was heated carefully until it had changed completely to anhydrous copper(II) sulfate \(\left(\mathrm{CuSO}_{4}\right)\) with a mass of 0.483 g. Determine the value of \(x .[\text { This number is called the number of waters }\) of hydration of copper(Il) sulfate. It specifies the number of water molecules per formula unit of \(\mathrm{CuSO}_{4}\) in the hydrated crystal. \(]\)

Which of the following statements about chemical equations is(are) true? a. When balancing a chemical equation, you can never change the coefficient in front of any chemical formula. b. The coefficients in a balanced chemical equation refer to the number of grams of reactants and products. c. In a chemical equation, the reactants are on the right and the products are on the left. d. When balancing a chemical equation, you can never change the subscripts of any chemical formula. e. In chemical reactions, matter is neither created nor destroyed so a chemical equation must have the same number of atoms on both sides of the equation.
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