how to find lattice energy of a compound

Core Concepts

In this tutorial near lattice energy, we will embrace its definition, relevant periodic table trends, factors that influence it, and how to calculate it.

Topics Covered in Other Articles

• Electronegativity
• Ionization Free energy
• Periodic Table Trends
• Electron Affinity
• What are ions
• Hess'due south Law
• Bond Enthalpy

What is Lattice Energy?

During the formation of solid ionic compounds, electropositive metals react with electronegative nonmetals. Both the generation and dissolution of such compounds involve the concept of lattice energy, a type of potential energy expressed in units of kJ/mol. Lattice energy maintains the fixed positions of cations and anions within ionic compounds. We tin can further investigate this term in two different ways, depending on our perspective.

The fundamental to understanding this concept lies in the crystalline structure of ionic compounds. Their potent, rigid composition enables interactions between each charged ion and its oppositely charged counterparts. These interactions involve large amounts of energy, explaining the loftier melting and boiling points characteristic of ionic compounds.

Lattice energy can be described equally a certain quantity of free energy is released when gaseous ions react during the germination of one mole of a solid ionic chemical compound; nonetheless, it also describes the energy that facilitates the dissociation of one mole of a solid ionic chemical compound into its constituent gaseous ions. Depending on our chosen definition, the lattice energy of a given ionic compound may either be a positive or negative value.

Exothermic versus Endothermic

Nosotros tin can view lattice energies as either endothermic or exothermic processes depending on which definition we focus on. A process is exothermic when it releases free energy. Our starting time definition, the formation of an ionic compound, involves exothermic lattice energy, respective to a negative value.

On the other hand, if we utilise the alternate definition, the dissolution of an ionic chemical compound, the nature of the lattice energy value changes. Because this process requires energy, it falls into the endothermic category, respective to a positive value.

Factors tlid affect Lattice Free energy

1. The charges held by the constituent ions (represented past the variables Q_one and Q_two)

Every bit nosotros increment the ion charge variable, lattice energy increases. This means that ions with larger charge values volition produce ionic compounds with greater lattice energies. In turn, ions possessing weaker charges decrease the lattice energies of their compounds.

ii. The distance between the constituent ions (represented by the variable R)

As nosotros increase the distance variable, lattice energy decreases. Essentially, larger ions compose ionic compounds with smaller lattice energies due to the increased distance between them. Smaller ions produce larger lattice energies in their ionic compounds.

Lattice Energy Trends

To summarize, lattice energy increases every bit nosotros increase ion charge and decrease the distance. More specifically, it increases from left to right across periods and from bottom to tiptop upwardly groups.

Nosotros can summarize lattice energy periodic table trends in the following image:

Finding Lattice Energies

When presented with multiple ionic compounds, chemists must ofttimes determine which exhibits the highest lattice free energy. To do so, they consider both the ion charge variable and the distance variable.

Calculating Lattice Energies

Although calculating exact lattice energies can prove complicated, we often simplify the process using Coulomb's Law. This law provides the following equation describing the lattice energy of a given ionic compound:

Q₁ & Q₂ = the relative charges of the constituent ions in an ionic chemical compound
R = the distance between charges
K = 2.31 x 10^^-19 J-nm.

The final answer should be written in units of Joules (J).

Steps to Solve:

1. Solve the equation for each ionic compound, inputting the accuse and distance values specific to it.
2. Compare the results; the largest quantity denotes the ionic compound with the largest lattice energy.

Approximating Lattice Energies

During comparisons, we tin can also utilise the charge and altitude variables to estimate relative lattice energies.

Steps to Solve:

1. Showtime look at the relative charges displayed past each ion in a given compound—if one compound has much college ionic charges, then information technology will likely take the higher lattice energy.

2. If the charge discrepancies between compounds exercise not seem clear, calculate Q_i x Q₂ for each compound and compare those values. For example, a calculated charge of -iii has 3 times the magnitude of a calculated charge of -ane; this would denote that the ionic compound with the accuse of -iii exhibits a much higher lattice energy than the ionic compound with the -1 charge (roughly 3 times as high).

3. If the charges of multiple compounds are the same or too similar in value to produce distinctions, consider the sizes of the ions. Juxtapose atomic size, comparing cation to cation and anion to anion between compounds. If you see a pregnant discrepancy in size either between cations or between anions, the component with the larger diminutive radius will lower the lattice free energy of its corresponding compound. Conversely, the ion with a smaller atomic radius will increase the energy value of its respective chemical compound.

Applications of Lattice Energy

The Built-in-Haber Cycle

Lattice free energy is implicated in the Built-in-Haber Bike, which helps chemists analyze reaction energies. This cycle typically informs investigations of ionic chemical compound formation from dissimilar elements. It clarifies the overall reaction process past breaking it downwardly into a series of steps. This arroyo to chemical reaction analysis stems from Hess's Police, which states that overarching energy changes can be determined by exploring private steps, then combining their furnishings.

Every bit lattice energy forms part of the Built-in-Haber Cycle equation, nosotros can solve for it when the other factors are plugged in. The equation reads equally follows:

Heat of formation= lattice energy + heat of atomization + dissociation free energy + (sum of Ionization energies) + (sum of electron affinities)

The Born-Haber Cycle applies Hess's law to calculate lattice energies by juxtaposing a given ionic compound's enthalpy change of formation to the enthalpy required to form gaseous ions from its components.

Other Applications of Lattice Energies

Scientists utilize lattice energies more broadly to evaluate electron relationships and fluoride relationships. The factors, in turn, inform investigations about the relative strengths of dissimilar ionic solids as well as predictions near ionic chemical compound identities, components, and properties.

Further Examples of Computing Lattice Energies

Instance s: Using Approximation Techniques

First, we will practice solving for the charge variable.

Problem 1: Given the chemical compound MgO, determine its combined charge.

Steps to Solve:

one. Write out the charges of its ions: Mg⁺² and O^-two

2. Multiply these charges: (2) x (-ii) = -4

Trouble two: Given the compound KCl, determine its combined accuse.

1. Write out the charges of its ions: K⁺¹ and Cl^-one

ii. Multiply these charges: (i) x (-i) = -i

We can compare the -4 charge of MgO to the -ane charge of KCl as discussed. Equally the former is 4 times the quantity of the latter, nosotros can predict that its lattice energy would be approximately four times greater as well.

At present, we will practise solving for the size variable.

Problem 3: Given the chemical compound CaO, decide the sizes of its ions.

Steps to Solve:

ane. Determine the ionic radii of its cation: Ca⁺² has an ionic radius of 0.100 nm.

2. Determine the ionic radii of its anion: O^-ii has an ionic radius of 0.140nm.

We can compare these values to those of some other ionic compound as discussed. This provides insight into which exhibits larger lattice energy.

Built-in-Haber Cycle Examples

Now, we volition practice solving for exact lattice energy using the Born-Haber Wheel.

Trouble 1: Given the compound NaCl, determine its lattice free energy.

Steps to Solve:

1. Write the reaction describing the formation of NaCl under normal weather:

Na(s)+12Cl₂(g)→NaCl(s)

2. Change the reactants into their ionic gas components.

Na(s)→Na(one thousand)
Na(g)→Na+(g)+e−

12Cl2(chiliad)→Cl(1000)
Cl(g)+e−→Cl−(1000)

Na+(m)+Cl−(g)→NaCl(south)

This final transformation shows the creation of the "lattice" compound itself.

3.  In accordance with Hess's law, carve up the parts of the reaction and consider them in isolation.

NaCl(s)→Na(due south)+12Cl₂
−ΔH_f,NaCl(s)=+411 kJ

Na, Δ=107 kJ

Na(g)→Na+(k)+eastward−
IE_one,Na(g)=502 kJ

12Cl₂(g)→Cl(1000)
12ΔH_bond,Cl2(thousand)= 12×242 kJ

Cl(yard)+e−→Cl−(g)
EA1,Cl(grand)=−355 kJ

Na+(m)+Cl−(g)→NaCl(s), ΔH_lattice=?

4. Re-combine these parts to give the final Born-Habor Cycle equation:

0=ΔHcycle=ΔHf,NaCl(s)+ΔHsub,Na+IE1,Na(one thousand)+12ΔHbond,Cl2(yard)−EA1,Cl(g)−ΔHlattice

And then, solve for lattice variable: ΔHlattice,NaCl(south)

=−[411+107+502+12(242)−355]kJ

Lattice free energy of NaCl=−786 kJ

Source: https://chemistrytalk.org/what-is-lattice-energy/

Posted by: hillneho1973.blogspot.com

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