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Chapter 8: Problem 21

(a) Define the term lattice energy. (b) Which factors govern the magnitude of the lattice energy of an ionic compound?

Short Answer

Expert verified
(a) Lattice energy is defined as the energy required to separate one mole of a solid ionic compound into its constituent gaseous ions or the energy released when these ions in the gas phase come together to form one mole of a solid ionic compound. (b) The magnitude of lattice energy in an ionic compound is governed by two main factors: (1) the charge of the ions, with higher charges leading to stronger electrostatic attraction and higher lattice energy, and (2) the size of the ions, with smaller ions having a shorter distance between them and thus resulting in stronger electrostatic attraction and higher lattice energy.

Step by step solution

01

(a) Definition of Lattice Energy

Lattice energy is the energy required to separate one mole of a solid ionic compound into its constituent gaseous ions. In other words, it is the energy released when the constituent ions in the gas phase come together to form one mole of a solid ionic compound.
02

(b) Factors Governing Lattice Energy

There are two main factors that determine the magnitude of lattice energy in an ionic compound: 1. Charge of the ions: The lattice energy is directly proportional to the product of the charges of the constituent ions. The higher the charges, the stronger the electrostatic attraction between the ions, resulting in a higher lattice energy. For example, the lattice energy of magnesium oxide (MgO) will be higher than that of sodium chloride (NaCl) because Mg has a charge of +2 and O has a charge of -2, whereas Na and Cl both have a charge of ±1. 2. Size of the ions: The lattice energy is inversely proportional to the distance between the centers of the constituent ions, or the radii of the ions. Smaller ions have a shorter distance between them, leading to stronger electrostatic attraction and higher lattice energy. As the size of the ions increases, their distance from each other also increases, which results in a lower lattice energy. In summary, the magnitude of lattice energy for an ionic compound is governed by the charges and sizes of the constituent ions. The higher the charges and the smaller the ions, the greater the lattice energy.

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Key Concepts

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

Ionic Compound
An ionic compound is formed through the chemical bonding between atoms with opposite charges called ions. These ions are created when atoms lose or gain electrons, resulting in positively charged cations and negatively charged anions. The resulting compound is a solid with a characteristic crystalline structure known as a lattice. In this lattice, cations and anions are arranged in a repetitive three-dimensional pattern stabilized by the electrostatic forces between them.

Consider common table salt, sodium chloride (NaCl), as an example of an ionic compound. Sodium (Na) donates an electron to become Na+, while chlorine (Cl) accepts an electron to become Cl-. These oppositely charged ions attract each other to form NaCl, showcasing a simple 1:1 ionic compound.
Electrostatic Attraction
Electrostatic attraction is the force that holds together the positively charged cations and negatively charged anions in an ionic compound. It's what makes the ionic bond. This force is a fundamental aspect of Coulomb's law, which describes how the attraction between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Coulomb's law can be simplified into an equation: \( F = k \frac{|q_1 q_2|}{r^2} \) where \( F \) is the force of attraction, \( q_1 \) and \( q_2 \) are the charges of the ions, \( r \) is the distance between the centers of the two ions, and \( k \) is Coulomb's constant. In our daily life, this electrostatic attraction is what provides the solidity of the materials made from ionic compounds, like kitchen salt.
Ion Charge
The ion charge refers to the electric charge an atom holds after it has lost or gained electrons during the formation of an ionic compound. In chemical terms, it indicates how many electrons an atom has compared to its neutral state. This charge is crucial because it determines the strength of the electrostatic force between ions.

The greater the charge on each ion, the stronger the force that binds the ions together. For instance, in calcium fluoride (CaF2), the calcium ion has a charge of +2, while each fluoride ion has a charge of -1. The interaction between these ions is stronger than between ions with charges of +1 and -1 because the product of their charges (2 x -1 = -2 and -1 x +1 = -1) results in a more substantial electrostatic attraction. Thus, calcium fluoride has a higher lattice energy when compared to a compound like sodium chloride.
Ionic Radius
Ionic radius is the measure of an ion's effective size, which directly impacts the distance between ions within an ionic compound. It's a factor in determining the strength of the electrostatic attraction; the smaller the ionic radii, the closer the ions can be to one another, leading to a higher lattice energy.

The trend in ionic radii across the periodic table shows that cations are smaller than their parent atoms because they lose their outermost electrons, while anions are larger due to the addition of electrons to the outer shell. This decrease and increase in size, respectively, plays a vital role in the packing of ions in the lattice structure and thus affects their overall stability and the corresponding lattice energy. For example, the smaller radius of Mg2+ compared to Na+ means that in their respective compounds, magnesium will typically form stronger ionic bonds than sodium.

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Most popular questions from this chapter

(a) Write the electron configuration for the element titanium, Ti. How many valence electrons does this atom possess? (b) Hafnium, Hf, is also found in group \(4 \mathrm{~B}\). Write the electron configuration for Hf. (c) Ti and Hf behave as though they possess the same number of valence electrons. Which of the subshells in the electron configuration of Hf behave as valence orbitals? Which behave as core orbitals?

Write Lewis structures that obey the octet rule for each of the following, and assign oxidation numbers and formal charges to each atom: (a) \(\mathrm{OCS},(\mathrm{b}) \mathrm{SOCl}_{2}(\mathrm{~S}\) is bonded to the two \(\mathrm{Cl}\) (d) \(\mathrm{HClO}_{2}(\mathrm{H}\) is bonded to \(\mathrm{O})\). atoms and to the \(\mathrm{O}\) ), (c) \(\mathrm{BrO}_{3}^{-}\),

Under special conditions, sulfur reacts with anhydrous liquid ammonia to form a binary compound of sulfur and nitrogen. The compound is found to consist of \(69.6 \% \mathrm{~S}\) and \(30.4 \% \mathrm{~N}\). Measurements of its molecular mass yield a value of \(184.3 \mathrm{~g} \mathrm{~mol}^{-1}\). The compound occasionally detonates on being struck or when heated rapidly. The sulfur and nitrogen atoms of the molecule are joined in a ring. All the bonds in the ring are of the same length. (a) Calculate the empirical and molecular formulas for the substance. (b) Write Lewis structures for the molecule, based on the information you are given. (Hint: You should find a relatively small number of dominant Lewis structures.) (c) Predict the bond distances between the atoms in the ring. (Note: The \(\mathrm{S}-\mathrm{S}\) distance in the \(\mathrm{S}_{8}\) ring is \(2.05 \AA\). \()\) (d) The enthalpy of formation of the compound is estimated to be \(480 \mathrm{~kJ} \mathrm{~mol}^{-1} . \Delta H_{f}^{\circ}\) of \(\mathrm{S}(g)\) is \(222.8 \mathrm{~kJ} \mathrm{~mol}^{-1}\). Estimate the average bond enthalpy in the compound.

The substance chlorine monoxide, \(\mathrm{ClO}(g)\), is important in atmospheric processes that lead to depletion of the ozone layer. The ClO molecule has a dipole moment of \(1.24 \mathrm{D}\) and the (a) Determine the magnitude of \(\mathrm{Cl}-\mathrm{O}\) bond length is \(1.60 \mathrm{~A}\). the charges on the \(\mathrm{Cl}\) and \(\mathrm{O}\) atoms in units of the electronic charge, e. (b) Based on the electronegativities of the elements, which atom would you expect to have a negative charge in the ClO molecule? (c) By using formal charges as a guide, propose the dominant Lewis structure for the molecule. Are the formal charges consistent with your answers to parts (a) and (b)? Can you reconcile any differences you find?

In the vapor phase, \(\mathrm{BeCl}_{2}\) exists as a discrete molecule. (a) Draw the Lewis structure of this molecule, using onlysingle bonds. Does this Lewis structure satisfy the octet rule? (b) What other resonance structures are possible that satisfy the octet rule? (c) On the basis of the formal charges, which Lewis structure is expected to be dominant for \(\mathrm{BeCl}_{2} ?\)
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