Question

For each of the following, write an equation that corresponds to the energy given. a. lattice energy of \(\mathrm{NaCl}\) b. lattice energy of \(\mathrm{NH}_{4} \mathrm{Br}\) c. lattice energy of \(\mathrm{MgS}\) d. \(\mathrm{O}=\mathrm{O}\) double bond energy beginning with \(\mathrm{O}_{2}(g)\) as a reactant

Short answer

The energy equations for each case are: a. For \(\mathrm{NaCl}\): \(E_{lattice} = k \frac{(+1)(-1)}{r}\) b. For \(\mathrm{NH}_{4} \mathrm{Br}\): \(E_{lattice} = k \frac{(+1)(-1)}{r}\) c. For \(\mathrm{MgS}\): \(E_{lattice} = k \frac{(+2)(-2)}{r}\) d. For \(\mathrm{O}=\mathrm{O}\) double bond energy: \(\mathrm{O}_{2}(g) \rightarrow 2\mathrm{O}(g)\), with \(\Delta E_{\text{bond}}\) being the energy required to break the bond.

Step-by-step solution

a. lattice energy of \(\mathrm{NaCl}\)

Lattice Energy Formula: \(E_{lattice} = k \frac{Q_1Q_2}{r}\) In the case of \(\mathrm{NaCl}\), sodium (Na) has a charge of +1 and chlorine (Cl) has a charge of -1. The equation for the lattice energy of \(\mathrm{NaCl}\) is: $$E_{lattice} = k \frac{(+1)(-1)}{r}$$

b. lattice energy of \(\mathrm{NH}_{4} \mathrm{Br}\)

Lattice Energy Formula: \(E_{lattice} = k \frac{Q_1Q_2}{r}\) For \(\mathrm{NH}_{4} \mathrm{Br}\), the group \(\mathrm{NH}_{4}\) has a charge of +1, and bromine (Br) has a charge of -1. The equation for the lattice energy of \(\mathrm{NH}_{4} \mathrm{Br}\) is: $$E_{lattice} = k \frac{(+1)(-1)}{r}$$

c. lattice energy of \(\mathrm{MgS}\)

Lattice Energy Formula: \(E_{lattice} = k \frac{Q_1Q_2}{r}\) In the case of \(\mathrm{MgS}\), magnesium (Mg) has a charge of +2, and sulfur (S) has a charge of -2. The equation for the lattice energy of \(\mathrm{MgS}\) is: $$E_{lattice} = k \frac{(+2)(-2)}{r}$$

d. \(\mathrm{O}=\mathrm{O}\) double bond energy beginning with \(\mathrm{O}_{2}(g)\) as a reactant

We cannot calculate the energy using lattice energy formula as \(\mathrm{O}_{2}\) is a gaseous molecule with an \(\mathrm{O}=\mathrm{O}\) double bond, instead of an ionic compound. To find the bond energy (BE) for the double bond, we need to look into reference materials or experiments. Typically, we would look up the bond energy value for \(\mathrm{O}=\mathrm{O}\) and use it to calculate the total energy change for a given chemical reaction. So, the equation for the bond energy of \(\mathrm{O}=\mathrm{O}\) will be in the form: $$\mathrm{O}_{2}(g) \rightarrow 2\mathrm{O}(g)$$, where \(\Delta E_{\text{bond}}\) is the required energy to break the \(\mathrm{O}=\mathrm{O}\) bond.

Key concepts

Lattice Energy Formula

Understanding the concept of lattice energy is critical for students who are delving into the world of ionic compounds. Lattice energy is defined as the energy required to separate one mole of an ionic solid into its component gaseous ions.

The lattice energy formula, which forms the basis for calculating this energy, is an extension of Coulomb's Law and is given by: \[\begin{equation}E_{lattice} = k \frac{Q_1 Q_2}{r}\end{equation}\]where:

• k is the proportionality constant,
• Q_1 and Q_2 are the charges of the ions, and
• r is the distance between the ion centers.

Evaluating lattice energy involves identifying the charges on the ions that make up the lattice and considering the distances between them. This calculation is pivotal as it helps in understanding the stability of an ionic solid. For instance, a higher lattice energy suggests a more stable and tightly bound ionic compound.

In practice, the determination of actual lattice energies from experimental data requires sophisticated techniques since ionic solids don't consist solely of two ions. However, theoretical values calculated using the formula above provide an essential understanding and a good approximation for comparisons between different ionic compounds.

Ionic Bonding

Ionic bonding is a type of chemical bond where atoms with opposite charges are held together due to electrostatic forces. It typically occurs between metal atoms, which tend to lose electrons, and non-metal atoms, which tend to gain electrons.

In the creation of an ionic bond, a metal atom, having a relatively low ionization energy, will lose one or more electrons to become a positively charged ion called a cation. Simultaneously, a non-metal atom with high electron affinity will gain these electrons to become a negatively charged ion called an anion.

For example, sodium (Na), a metal, loses an electron to form Na^+, while chlorine (Cl), a non-metal, gains an electron to form Cl^-. These ions then attract each other to form sodium chloride (NaCl), an ionic compound. This transaction of electrons to form oppositely charged ions and the subsequent formation of an electrostatic bond is the essence of ionic bonding. The strength and stability of ionic bonds are directly influenced by lattice energy because it reflects the energy holding those ions together in the crystal lattice of the ionic compound. A greater difference in charge and a smaller ionic radius result in stronger ionic bonding due to higher lattice energy.

Chemical Bond Energy

Chemical bond energy is a measure of the strength of a bond between atoms in a molecule. It is defined as the amount of energy that is required to break one mole of the bond in a chemical compound, under specific conditions, such as a constant volume or pressure.

This energy is released when a bond is formed and is absorbed when a bond is broken. For covalent bonds, such as the O=O double bond in an oxygen molecule, the bond energy is a crucial parameter because it tells us about the stability of a molecule and how much energy would be involved in a chemical reaction.

Knowing the bond energies allows chemists to predict the heat of reaction, which is the total energy change during a chemical reaction. This is calculated by subtracting the sum of the bond energies for the bonds broken from the sum of the bond energies for the bonds formed. When bond energy values are not provided and cannot be calculated directly from first principles, as in the case of ionic compounds, reference materials and experimental data are invaluable in providing these figures.

In summary, while ionic compounds rely on the concept of lattice energies, covalent compounds utilize bond energies to explain the energy involved in chemical processes. The knowledge of chemical bond energy is not only fundamental in understanding chemical reactions but also in the design and synthesis of new compounds with desired properties and behaviours.