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Atoms involved in bonds are usually more stable than they would be otherwise. This means that energy is released in the formation of the bond. For ionic bonds, Coulomb’s law is used to calculate this energy:
where E is energy in joules (J), k is a constant equal to 2.31×10−28 J⋅m, q1 and q2 are the charges of the two ions, and d is the distance between the nuclei of the two ions in meters (m).
Whereas the bond energy calculated by Coulomb’s law pertains to a single ionic bond, lattice energypertains to all the ionic bonding among a group of atoms arranged in a crystal lattice. Lattice energy is calculated by using the Coulomb’s law equation, but with a different constant (unique to each substance) that takes into account the crystalline structure of the substance.
By convention, lattice energy is defined as the amount required to either break an ionic solid into individual gaseous ions, or to form an ionic solid from gaseous ions.
Calculate the amount of energy released in the formation of one mole of SrO bonds (not lattice energy). The radius of the strontium ion is 1.13 Å, and the radius of the oxide ion is 1.40 Å. Note that 1Å=10−10m.
Arrange the following ionic compounds in order of decreasing amount of energy released in lattice formation: NaF, MgS, TlN, and CsI.
Which substance in each of the following pairs has the larger lattice energy?
A.) KCl or RbCl
B.) CaF2 or BaF2
C.) CaO or KI
where Z is true nuclear charge and S is the amount of shielding.
In 1930, John C. Slater devised the following set of empirical rules to estimate S for a designated ns or np electron:
- Write the electron configuration of the element, and group the subshells as follows: (1s), (2s, 2p), (3s, 3p), (3d), (4s, 4p), (4d), (4f ), (5s, 5p), and so on.
- Electrons in groups to the right of the (ns, np) group contribute nothing to the shielding constant for the designated electron.
- All the other electrons in the (ns, np) group shield the designated electron to the extent of 0.35 each.
- All electrons in the n−1 shell shield to the extent of 0.85 each.
- All electrons in the n−2 shell, or lower, shield completely—their contributions to the shielding constant are 1.00 each.
When the designated electron is in an nd or nf group, rules (i), (ii), and (iii) remain the same but rules (iv) and (v) are replaced by the following:
- Each electron in a group lying to the left of the nd or nf group contributes 1.00 to the shielding constant.
These rules are a simplified generalization based on the average behavior of different types of electrons.
A.) Calculate Z eff for a valence electron in an oxygen atom
B.) Calculate Z eff for the 4s electron in a copper atom, Cu.
C.) Calculate Z eff for a 3d electron in a copper atom, Cu.
The size of ions as measured by ionic radii varies in a systematic manner. The size of the ion can be explained in part by effective nuclear charge, Z eff, which is the net nuclear charge felt by an electron. The effective nuclear charge takes into account the actual nuclear charge and the shielding of this charge by inner electrons. When an atom loses electrons, the resulting cation is smaller both because the remaining electrons experience a larger Z eff and because these electrons are usually in orbitals closer to the nucleus than the electrons that were lost. The more electrons that are lost, the smaller the ion becomes.
Similarly, when an atom gains electrons, the resulting anion is larger owing to both increased electron-electron repulsions and a reduction in Z eff. The more electrons that are gained, the larger the ion becomes.
1.) Rank the following ions in order of decreasing radius: F− , Cl− , Br− , I− , and At− .
2.) Rank the following items in order of decreasing radius: Ca , Ca2+ , and Ca2− .
3.) Rank the following in order of decreasing ionic radii. K+, S^2-, Ca^2+, Sc^3+, Cl^-, P^3-
Which of the following are valid transitions?
During an emission, electrons move from a higher energy orbital to a lower energy orbital. Which of the following are valid transitions that produce lines in the emission spectrum of Zn?
1.) [Ar] 3d10→[Ar] 4s2, 3d10
2.) [Ar] 4s2, 3d10→[Ar] 4s1, 3d11
3.) [Ar] 4s2, 3d10→[Ar] 3d10
4.) [Ar] 4s1, 3d10, 6s1→[Ar] 4s2, 3d10
5.) [Ar] 4s2, 3d10→[Ar] 4s1, 3d10, 6s1
6.) [Ar] 4s2, 3d10→[Ar] 4s2, 3d10, 4p2
An atom consists of a small, positively charged nucleus, surrounded by negatively charged electrons. We organize the electrons in a logical manner. As the atomic number increases, electrons are added to the subshells according to their energy. Lower energy subshells fill before higher energy subshells.
The order of filling is 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p.
The periodic table can be used to help you remember the order.
Give the complete ground-state electron configuration for silicon
Give the ground-state electron configuration for silicon (Si) using noble-gas shorthand.
Give the actual ground-state electron configuration for copper (Cu) using the complete form.
Give the ground-state electron configuration for copper (Cu) using noble-gas shorthand.
Quantum numbers can be thought of as labels for an electron. Every electron in an atom has a unique set of four quantum numbers.
The principal quantum number n corresponds to the shell in which the electron is located. Thus n can therefore be any integer. For example, an electron in the 2p subshell has a principal quantum number of n=2 because 2p is in the second shell.
The azimuthal or angular momentum quantum number ℓ corresponds to the subshell in which the electron is located. s subshells are coded as 0, p subshells as 1, d as 2, and f as 3. For example, an electron in the 2p subshell has ℓ=1. As a rule, ℓ can have integer values ranging from 0 to n−1.
The magnetic quantum number mℓcorresponds to the orbital in which the electron is located. Instead of 2px, 2py, and 2pz, the three 2p orbitals can be labeled −1, 0, and 1, but not necessarily respectively. As a rule, mℓcan have integer values ranging from −ℓ to +ℓ.
The spin quantum number ms corresponds to the spin of the electron in the orbital. A value of 1/2 means an “up” spin, whereas −1/2means a “down” spin.
What is the only possible value of mℓ for an electron in an s orbital?
What are the possible values of mℓ for an electron in a d orbital?
The atomic radius of an element can be predicted based on its periodic properties. Atomic radii increase going down a group in the periodic table, because successively larger valence-shell orbitals are occupied by electrons. Atomic radii generally decrease moving from left to right across a period because the effective nuclear charge increases.
1.) Rank Ca Mg Be Sr, from largest to smallest according to their atomic radius.
2.) Rank Li, Be, B, N, from largest to smallest according to their atomic radius.