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Chapter 2: Problem 94

In your own words, define or explain these terms or symbols: (a) \(\underset{\mathbf{Z}}{\mathbf{A}} \mathbf{E} ;\) (b) \(\boldsymbol{\beta}\) particle; \(\mathbf{( c )}\) isotope; \(\mathbf{( d )}^{16} \mathbf{O}\) (e) molar mass.

Short Answer

Expert verified
(a) \(\underset{\mathbf{Z}}{\mathbf{A}} \mathbf{E}\) is a symbol used to denote isotopes of an element E, where A is the mass number and Z is the atomic number. (b) A \(\boldsymbol{\beta}\) particle is a charged particle emitted in beta decay. (c) An isotope is a form of a chemical element with the same number of protons but a different number of neutrons. (d) \(^{16} \mathbf{O}\) is an isotope of oxygen with 8 protons and 8 neutrons. (e) Molar mass is the mass in grams of one mole of a substance.

Step by step solution

01

Understand \(\underset{\mathbf{Z}}{\mathbf{A}} \mathbf{E}\)

This notation is used in nuclear physics and chemistry to denote different isotopes of an element. E stands for the element under consideration. The letter A at the upper position denotes the mass number of the isotope, which is the total number of protons and neutrons in the nucleus. At the lower position, the letter Z represents the atomic number of the isotope, which is the number of protons in the nucleus.
02

Define \(\boldsymbol{\beta}\) particle

\(\boldsymbol{\beta}\) particle refers to a charged particle that is emitted in a type of radioactive decay called beta decay. There are two types of beta particles: \(\beta^-\) particles, which are electrons, and \(\beta^+\) particles, which are positrons.
03

Define isotope

An isotope is a form of a chemical element whose atomic nucleus contains a specific number of neutron(s) in addition to the number of protons that is unique to the element. Different isotopes of the same element have the same atomic number (number of protons in the nucleus) but different mass numbers due to the different numbers of neutrons.
04

Identify \(^{16} \mathbf{O}\)

The notation \(^{16} \mathbf{O}\) denotes a particular isotope of oxygen. The number 16 represents the mass number - the total amount of protons and neutrons in the nucleus of the atom. Therefore, an atom of \(^{16} \mathbf{O}\) has 8 protons (as the atomic number of oxygen is 8) and 8 neutrons.
05

Define molar mass

Molar mass is the mass in grams of one mole (6.022 x 10^23 particles) of a substance. It has the units gram per mole (g/mol). The molar mass of an element is numerically equivalent to the element's relative atomic mass.

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Key Concepts

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

Isotopes
Atoms are like special puzzles, each one made up of a unique number of protons, neutrons, and electrons. When scientists talk about isotopes, they refer to the different versions of the same element that exist. These versions all have the same number of protons in their nuclei but differ in the number of neutrons. This means isotopes of an element share the same atomic number but have different mass numbers. These mass numbers tell us the total count of protons and neutrons together.

Think of carbon, a common example. Carbon has several isotopes, like carbon-12 and carbon-14. Both have 6 protons because that's what makes them carbon, but carbon-12 has 6 neutrons, whereas carbon-14 contains 8 neutrons.
  • Same atomic number (number of protons)
  • Different number of neutrons
  • Different mass numbers
Understanding isotopes is key in fields like chemistry and physics, as they help explain things such as radioactive decay, where some isotopes can change into others.
Beta Decay
Beta decay is a fascinating process in the world of nuclear chemistry. It involves the transformation of a neutron into a proton or vice versa within an atomic nucleus. During this process, a beta particle is emitted. Beta particles come in two types: beta-minus (尾鈦�) and beta-plus (尾鈦�) particles.

In beta-minus decay, a neutron turns into a proton. As a result, an electron, which is the 尾鈦� particle, is ejected from the nucleus. This process increases the atomic number by one but keeps the mass number the same. For example, carbon-14 undergoes 尾鈦� decay to become nitrogen-14.

In beta-plus decay, a proton is converted into a neutron, releasing a positron, the 尾鈦� particle. This action decreases the atomic number by one, again without altering the mass number. An isotope like oxygen-15 can undergo 尾鈦� decay to form nitrogen-15.
  • Beta particle types: 尾鈦� (electron), 尾鈦� (positron)
  • Beta-minus increases atomic number
  • Beta-plus decreases atomic number
Beta decay is essential for understanding nuclear reactions and plays a crucial role in applications ranging from medical imaging to understanding the age of archaeological finds.
Molar Mass
In chemistry, molar mass acts as a bridge connecting the tiny atomic scale to quantities we can measure and observe. Molar mass is the mass of one mole of a substance, measured in grams per mole (g/mol). One mole is a basic unit in chemistry that represents a quantity of an element or compound鈥攕pecifically, 6.022 x 1023 particles, which is known as Avogadro's number.

Each element on the periodic table has a molar mass, which can usually be found underneath the element symbol. This mass tells us how much one mole of that element weighs in grams. For example, carbon has a molar mass of about 12.01 g/mol, according to its average atomic mass. This number helps chemists know how much of a substance is needed to react with another quantitatively.
  • Mass of one mole in g/mol
  • Uses Avogadro's number, 6.022 x 1023
  • Crucial for stoichiometry in reactions
Understanding molar mass allows scientists to work with chemical equations and predict how substances will react and in what amounts.

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Most popular questions from this chapter

In one experiment, the burning of \(0.312 \mathrm{g}\) sulfur produced 0.623 g sulfur dioxide as the sole product of the reaction. In a second experiment, \(0.842 \mathrm{g}\) sulfur dioxide was obtained. What mass of sulfur must have been burned in the second experiment?

A 5.585-kg sample of iron (Fe) contains (a) \(10.0 \mathrm{mol} \mathrm{Fe}\) (b) twice as many atoms as does \(600.6 \mathrm{g} \mathrm{C}\) (c) 10 times as many atoms as does \(52.00 \mathrm{g} \mathrm{Cr}\) (d) \(6.022 \times 10^{24}\) atoms

Before \(1961,\) the standard for atomic masses was the isotope \(^{16} \mathrm{O},\) to which physicists assigned a value of exactly \(16 .\) At the same time, chemists assigned a value of exactly 16 to the naturally occurring mixture of the isotopes \(^{16} \mathrm{O},^{17} \mathrm{O},\) and \(^{18} \mathrm{O}\). Would you expect atomic masses listed in a 60 -year-old text to be the same, generally higher, or generally lower than in this text? Explain.

Within the limits of experimental error, show that the law of conservation of mass was obeyed in the following experiment: \(10.00 \mathrm{g}\) calcium carbonate (found in limestone) was dissolved in 100.0 mL hydrochloric acid \((d=1.148 \mathrm{g} / \mathrm{mL}) .\) The products were \(120.40 \mathrm{g}\) solution (a mixture of hydrochloric acid and calcium chloride) and 2.22 L carbon dioxide gas \((d=1.9769 \mathrm{g} / \mathrm{L})\)

The two species that have the same number of electrons as \(^{3}\) th S are (a) \(^{32} \mathrm{Cl} ;\) (b) \(^{34} \mathrm{S}^{+} ;\) (c) \(^{33} \mathrm{P}^{+} ;\) (d) \(^{28} \mathrm{Si}^{2-}\) (e) \(^{35} S^{2-} ;(f)^{40} A r^{2+} ;(g)^{40} C a^{2+}\)
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