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AP Chemistry Unit 2.2 Intramolecular Force and Potential Energy

Intramolecular Force and Potential Energy study notes -AP Chemistry - New Syllabus 2024-2025

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LEARNING OBJECTIVE

  • Represent the relationship between potential energy and distance between atoms, based on factors that influence the interaction strength.

Key Concepts:

  •  Potential Energy vs. Internuclear Distance: Equilibrium Bond Length and Bond Energy
  •  Influence of Atomic Size and Bond Order on Bond Length and Energy
  •  Coulomb’s Law: Ion Interaction Strength

           

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 2.2.A.1

A graph of potential energy versus the distance between atoms (internuclear distance) is a useful representation for describing the interactions between atoms. Such graphs illustrate both the equilibrium bond length (the separation between atoms at which the potential energy is lowest) and the bond energy(the energy required to separate the atoms).

 2.2.A.2

In a covalent bond, the bond length is influenced by both the size of the atom’s core and the bond order (i.e., single, double, triple). Bonds with a higher order are shorter and have larger bond energies.

 2.2.A.3

Coulomb’s law can be used to understand the strength of interactions between cations and anions. i. Because the interaction strength is proportional to the charge on each ion, larger charges lead to stronger interactions. ii. Because the interaction strength increases as the distance between the centers of the ions (nuclei) decreases, smaller ions lead to stronger interactions.

 

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 2.2.A.1 Potential Energy vs. Internuclear Distance: Equilibrium Bond Length and Bond Energy:

1.Interatomic Forces: Interatomic forces are the forces between atoms that govern how they bond and interact. These forces, including covalent, ionic, metallic, Van der Waals, and hydrogen bonds, determine the physical and chemical properties of materials. They influence the structure, stability, and behavior of substances.

i. Attractive and repulsive forces between atoms:

Interatomic forces are the attractive and repulsive forces that act between atoms, influencing how atoms bond and interact in a substance. These forces are key to understanding the behavior and properties of matter. They can be broadly classified into:

  1. Attractive Forces:

    • These forces draw atoms together, stabilizing bonds and structures. Examples include:
      • Covalent bonds (sharing of electrons)
      • Ionic bonds (electrostatic attraction between oppositely charged ions)
      • Metallic bonds (delocalized electron sea in metals)
      • Van der Waals forces (weak interactions between molecules)

  2. Repulsive Forces:

    • These forces occur when atoms are brought too close together, causing them to repel each other. This happens due to the overlap of electron clouds or the repulsion between positively charged nuclei. The Pauli exclusion principle also contributes to repulsion when electron orbitals overlap too much.

Together, these attractive and repulsive forces determine the equilibrium distance between atoms, their bonding, and the physical properties of substances. When atoms are at their optimal distance, the attractive and repulsive forces balance each other, resulting in a stable configuration.

ii. How these forces change with distance:

Interatomic forces change with distance as follows:

  • At large distances: Both attractive and repulsive forces are weak or negligible.
  • As atoms approach each other: Attractive forces increase, while repulsive forces begin to grow due to electron and nucleus interactions.
  • At very short distances: Repulsive forces dominate, pushing atoms apart as their electron clouds and nuclei repel each other.
  • At equilibrium distance: Attractive and repulsive forces balance each other, resulting in a stable bond.

2. Potential Energy Curve: The potential energy curve is a graph that illustrates how the potential energy of a system changes as the distance between interacting atoms or molecules varies. It shows the balance between attractive and repulsive forces, with the minimum point representing the most stable configuration (equilibrium distance) and higher energies at very short or long distances.

  • Potential Energy Curve shows how potential energy changes with the distance between atoms or molecules.
  • At Large Distances: High potential energy due to weak attraction, minimal interaction.
  • As Atoms Approach: Attractive forces dominate, lowering potential energy and forming bonds.
  • At Equilibrium Distance: Minimum potential energy, where attractive and repulsive forces balance, resulting in stability.
  • At Very Short Distances: Repulsive forces dominate, causing sharp increase in potential energy, representing instability.

i. Shape of the potential energy curve:

The shape of the Potential Energy Curve is typically U-shaped or bell-shaped. Here’s a breakdown of its key features:

  1. At large distances: The curve starts at a relatively high potential energy, reflecting weak attractive forces between atoms. There’s little interaction at this stage.

  2. As atoms approach each other: The curve slopes downward, indicating that attractive forces dominate, pulling the atoms closer and lowering the potential energy.

  3. At equilibrium distance: The curve reaches its lowest point (the minimum), where the system is most stable. This represents the equilibrium bond length—the point where the attractive and repulsive forces balance.

  4. At very short distances: The curve rises sharply as repulsive forces (electron-electron and nucleus-nucleus repulsion) increase, pushing the atoms apart and raising the potential energy.

ii. Relationship between potential energy and distance:

  • At Large Distances: The atoms have high potential energy due to weak attractive forces, with minimal interaction.
  • As Distance Decreases: Attractive forces dominate and cause the potential energy to decrease as atoms move closer.
  • At Equilibrium Distance: The potential energy is at its minimum, where the system is most stable.
  • At Very Short Distances: Repulsive forces increase rapidly, causing the potential energy to rise steeply as atoms push apart.

iii. Steps for Analyzing the Graph:

  1. X-axis (Distance): Represents the distance between the two atoms or molecules.

    • As distance decreases, the atoms move closer.
    • As distance increases, the atoms are farther apart.

  2. Y-axis (Potential Energy): Represents the potential energy of the system at different distances.

    • Lower potential energy indicates a more stable configuration.
    • Higher potential energy indicates an unstable configuration.

3. Equilibrium Bond Length: Equilibrium Bond Length is the distance between the nuclei of two atoms in a molecule where the potential energy of the system is at its minimum. At this distance, the attractive and repulsive forces between the atoms balance each other, resulting in a stable bond.

i. What defines the equilibrium bond length:

  • Equilibrium bond length is the distance between two atoms where the net potential energy is at its minimum.
  • Attractive forces pull atoms together, lowering potential energy.
  • Repulsive forces push atoms apart, raising potential energy.
  • The equilibrium bond length occurs when attractive and repulsive forces balance, resulting in the most stable configuration.
  • It represents the lowest potential energy and the optimal bond stability.
  • Moving atoms closer or farther from this distance increases potential energy and destabilizes the bond.

ii. How the lowest potential energy corresponds to the optimal separation:

  • The lowest potential energy corresponds to the optimal separation (equilibrium bond length) because, at this distance, the forces between the atoms are perfectly balanced:
    • Attractive forces pull the atoms together, lowering the potential energy.
    • Repulsive forces push the atoms apart, increasing the potential energy.
  • The optimal separation (equilibrium bond length) occurs at the point where the total potential energy (sum of attractive and repulsive energies) is minimized.
  • If atoms are closer than the equilibrium distance, repulsive forces dominate and push them apart, increasing potential energy.
  • If atoms are farther apart, attractive forces decrease, also increasing potential energy.

4. Bond Energy: Bond Energy is the amount of energy required to break a chemical bond between two atoms in a molecule or the energy released when the bond is formed. It is a measure of the strength of the bond and is typically expressed in units of kilojoules per mole (kJ/mol).

NOTES:

  1. Breaking a Bond: To break a bond, energy must be supplied to overcome the attractive forces between the atoms. This energy is called bond dissociation energy.

  2. Forming a Bond: When a bond forms, energy is released because the atoms come together and the attractive forces stabilize the system.

  3. Relation to Bond Strength:

    • A high bond energy indicates a strong bond, meaning more energy is required to break it (e.g., the bond in O₂ has a high bond energy).
    • A low bond energy indicates a weak bond, meaning less energy is required to break it (e.g., the bond in hydrogen (H₂) is weaker than in oxygen (O₂)).

  4. Bond Length and Bond Energy: Typically, shorter bonds (like in triple bonds) have higher bond energies because the atoms are more tightly held together, while longer bonds (like in single bonds) have lower bond energies.

i. How bond energy relates to the potential energy curve and the work needed to break a bond:

  • Bond Energy is the energy required to break a bond or released when a bond is formed.
  • It corresponds to the energy difference between the lowest point (equilibrium bond length) on the potential energy curve and the energy at the point where the atoms are separated (no bond).
  • Bond energy is the work needed to break the bond, represented by the energy required to move the atoms from the equilibrium bond length to a point of higher potential energy (separation).
  • In the potential energy curve, the bond energy is the energy required to move atoms from the minimum energy point (stable bond) to the point where the bond breaks.

5. Types of Interactions:

Type of Bond/ForceDefinitionCharacteristicsExamplesBond StrengthProperties
Covalent BondFormed by sharing electron pairs between atoms.Strong bond, shared electrons, typically between nonmetals.Water (H₂O), Methane (CH₄), Oxygen (O₂)StrongStable, directional, usually lower melting/boiling points compared to ionic bonds.
Ionic BondFormed by transfer of electrons from one atom to another, creating ions.Electrostatic attraction between cations and anions, occurs between metals and nonmetals.Sodium chloride (NaCl), Magnesium oxide (MgO)Very strongHigh melting/boiling points, conduct electricity in solution.
Van der Waals ForcesWeak intermolecular forces between molecules.Includes dispersion forces, dipole-dipole interactions, and hydrogen bonding.Nitrogen (N₂), noble gases, water (H₂O)Very weakAffects molecular interactions, responsible for gas condensation.

i. How these interactions affect the potential energy vs. distance graph:

The different types of interactions (covalent bonds, ionic bonds, and van der Waals forces) affect the potential energy vs. distance graph in distinct ways. Here’s how they influence the curve:

Type of InteractionEffect on Potential Energy vs. Distance Curve
Covalent Bonds– The potential energy curve shows a steep drop as atoms approach each other, reaching a sharp minimum at the equilibrium distance. – The bond is strong and stable, so the curve remains low and flat near equilibrium, indicating stability.
Ionic Bonds– The potential energy curve also drops significantly as atoms approach, reaching a shallow minimum (compared to covalent bonds) where the ions are stable. – The curve typically shows a steep rise as atoms get too close due to strong repulsive forces (electron-electron, nucleus-nucleus).
Van der Waals Forces– The potential energy curve shows a gentle decrease at longer distances, with a shallow minimum indicating weak interactions. – At very short distances, the potential energy increases gradually due to repulsive forces (electron-electron repulsion), but the curve rises less steeply than in ionic bonds.

Key Effects:

  1. Covalent Bonds:

    • Steep drop in potential energy as atoms approach.
    • Sharp minimum representing the strong, stable bond.

  2. Ionic Bonds:

    • Steep drop to a shallow minimum due to strong ionic attraction.
    • Sharp rise at short distances due to strong repulsion between ions.

  3. Van der Waals Forces:

    • Gentle drop in potential energy at longer distances.
    • Shallow minimum and gradual rise due to weak forces.

6. Effect of Atomic Size:

  • Bond Length:
    • Larger atomic size → Longer bond length.
    • Smaller atomic size → Shorter bond length.
  • Bond Energy:
    • Larger atomic size → Weaker bond → Lower bond energy.
    • Smaller atomic size → Stronger bond → Higher bond energy.

Atomic size significantly affects both bond length and bond energy, with larger atoms generally leading to longer and weaker bonds, while smaller atoms form shorter and stronger bonds.

7. Molecular Vibrations and Bond Strength:

  • Molecular Vibrations: The oscillatory motion of atoms within a molecule, where atoms move back and forth around their equilibrium positions. These vibrations can involve bond stretching (changing the distance between atoms) and bond bending (changing the bond angle).

  • Bond Strength: The measure of how strongly two atoms are held together in a molecule. Stronger bonds, such as covalent bonds, require more energy to break, while weaker bonds, like van der Waals forces, are easier to break. Bond strength directly affects the vibrational frequency of a bond.

i. How Atoms Vibrate Around the Equilibrium Bond Length:

  1. Equilibrium Bond Length: This is the optimal distance between two atoms where the attractive forces (pulling them together) and repulsive forces (pushing them apart) are balanced, resulting in the lowest potential energy.

  2. Vibrational Motion: Atoms continuously move around this equilibrium bond length due to thermal energy. The vibrations can be:

    • Bond Stretching: Atoms oscillate along the bond axis, either moving closer together or farther apart.
    • Bond Bending: Atoms move perpendicular to the bond axis, changing the bond angle.

    The vibrational amplitude depends on factors like temperature and the strength of the bond.

  3. Frequency of Vibration: The frequency at which atoms vibrate depends on the bond strength and the masses of the atoms. Stronger bonds (like triple bonds) result in higher frequencies, while weaker bonds (like single bonds) vibrate at lower frequencies.

ii. Impact of Bond Energy on Molecular Stability:

  1. Higher Bond Energy:

    • Stronger Bond: A higher bond energy indicates a stronger bond, meaning the atoms are more tightly bound.
    • Vibration Characteristics: Atoms in molecules with strong bonds vibrate with higher frequency and less amplitude, making them less susceptible to breaking under normal conditions.
    • Increased Stability: Stronger bonds contribute to greater molecular stability, as more energy is required to break the bond.

  2. Lower Bond Energy:

    • Weaker Bond: A lower bond energy indicates a weaker bond, meaning the atoms are less tightly held together.
    • Vibration Characteristics: Atoms in molecules with weaker bonds vibrate with lower frequency and larger amplitude, making them more likely to break under stress or thermal motion.
    • Decreased Stability: Weaker bonds result in lower molecular stability, as less energy is required to break the bond.
 
 
 
2.2.A.2 Influence of Atomic Size and Bond Order on Bond Length and Energy:

1. Atomic Size: Atomic size (atomic radius) is the distance from the nucleus of an atom to the outermost electron shell. It is a measure of the “size” of an atom, representing how far the outermost electrons are from the nucleus. The atomic radius can vary depending on the atom’s position in the periodic table and the number of electron shells it has.

  • Atomic size and bond length: Larger atoms have longer bonds because their electron clouds extend farther out, while smaller atoms form shorter bonds.
  • Larger atoms: Greater atomic radius, leading to longer bond lengths.
  • Smaller atoms: Smaller atomic radius, resulting in shorter bond lengths.
  • Across a period: Atomic size decreases, bond length also decreases.
  • Down a group: Atomic size increases, bond length increases.

2. Bond Order: Bond order is a concept used in chemistry to describe the number of chemical bonds between two atoms in a molecule. It gives an indication of the strength and stability of a bond. Mathematical expression for bond order is: Bond Order =

12×(Number of bonding electrons−Number of antibonding electrons)\frac{1}{2} \times (\text{Number of bonding electrons} – \text{Number of antibonding electrons})

i. NOTES:

  • Higher Bond Order: Indicates a stronger, more stable bond.
  • Bond Order of 1: A single bond (e.g., in H₂).
  • Bond Order of 2: A double bond (e.g., in O₂).
  • Bond Order of 3: A triple bond (e.g., in N₂).
  • Bond Order of 0: No bond exists between the atoms (e.g., in He₂ molecule).

ii. Trends:

  • Molecular Orbitals Theory: Bond order is calculated based on the difference between the number of electrons in bonding and antibonding molecular orbitals.
  • Odd number of electrons: Molecules with odd electron counts (like NO) may have fractional bond orders.

iii. Bond Order and Stability:

  • Higher bond order = stronger and shorter bond, more stable.
  • Lower bond order = weaker and longer bond, less stable.

iv. Example:

  • O₂ (Oxygen molecule): Bond order = 2 (double bond).
  • N₂ (Nitrogen molecule): Bond order = 3 (triple bond).

3. Bond Energy: Bond energy is the amount of energy required to break a bond in one mole of molecules, turning the bonded atoms into individual atoms in the gas phase. It is an indicator of the strength of a chemical bond.

  1. Higher Bond Orders and Bond Energy:

    • Higher bond orders (such as double or triple bonds) correspond to stronger bonds. This is because there are more electron pairs shared between the atoms, resulting in a stronger attractive force.
    • Stronger attractive forces make it harder to break the bond, which means the bond energy is higher.

  2. Bond Energy and Bond Length:

    • Shorter bonds typically have higher bond energies. This is because in shorter bonds, the nuclei of the atoms are closer together, and the electron clouds overlap more efficiently. As a result, the attractive force between the atoms is stronger.
    • The increased overlap of atomic orbitals in shorter bonds results in greater bond strength, and therefore higher bond energy.

i. Why Higher Bond Energies Result from Shorter Bonds:

  • More Electron Density: In shorter bonds (such as in double or triple bonds), there is more electron density between the atoms, which increases the attractive force, making the bond stronger.
  • Increased Stability: Stronger bonds are generally more stable because the atoms are held more tightly together. Thus, more energy is required to break the bond.

ii. Example:

  • Triple bonds (e.g., in N₂) have the highest bond energy because they have the highest bond order (3) and are the shortest bonds.
  • Single bonds (e.g., in H₂) have lower bond energy because they have the lowest bond order (1) and are longer than double or triple bonds.

iii. Points to Keep in Mind:

  • Higher bond order = More bonding electrons = Stronger bonds = Higher bond energy.
  • Shorter bond lengths generally lead to higher bond energies because the atoms are held more tightly together, increasing bond strength and stability.
  • Units: Typically measured in kJ/mol (kilojoules per mole).
  • Bond Length: Shorter bonds generally have higher bond energy.
  • Bond Order: Higher bond order (e.g., triple bonds) usually means higher bond energy.
  • Atomic Size: Larger atoms tend to form weaker bonds (lower bond energy).
  • Electronegativity: A greater difference in electronegativity between two atoms often leads to stronger bonds and higher bond energy.
  • Single bonds have the lowest bond energy (e.g., in H₂).
  • Double bonds have a higher bond energy (e.g., in O₂).
  • Triple bonds have the highest bond energy (e.g., in N₂).

iv. Formula:

Bond energy is often used in Hess’s Law to calculate the total energy change in a reaction:

ΔH=∑(Bond energies of bonds broken)−∑(Bond energies of bonds formed)\Delta H = \sum \text{(Bond energies of bonds broken)} – \sum \text{(Bond energies of bonds formed)}

Where:

  • ΔH is the enthalpy change of the reaction.
  • Bond energies of bonds broken are the energies required to break bonds in reactants.
  • Bond energies of bonds formed are the energies released when new bonds are formed in products.

4. Electronegativity: Electronegativity is the ability of an atom to attract shared electrons in a chemical bond towards itself.

  • Electronegativity Difference: A larger difference in electronegativity between two atoms leads to a more polar bond.
  • Electron Distribution: The more electronegative atom pulls shared electrons closer, creating an uneven electron distribution.
  • Bond Length: This unequal electron pull typically results in a shorter bond because the atoms are drawn closer together.
  • Bond Strength: The stronger attraction between the atoms increases the bond strength, making the bond harder to break.
  • Bond Stability: Greater electronegativity differences often lead to greater bond stability due to enhanced electrostatic attraction.

5. Orbital Overlap: Orbital overlap refers to the interaction of atomic orbitals when atoms form chemical bonds. The extent of this overlap directly influences both the strength and length of the bond. The more the atomic orbitals overlap, the stronger and shorter the bond tends to be.

i. What is Orbital Overlap?

  • When two atoms form a bond, their atomic orbitals (regions of space where electrons are likely to be found) interact or overlap. This overlap allows electrons to be shared between the atoms, forming a covalent bond.
  • The extent of overlap is crucial: the larger the overlap, the more electron density is shared between the atoms, making the bond stronger.

ii. Bond Order and Orbital Overlap:

  • Single Bonds (Bond Order = 1): In a single bond (like in H₂), the overlap occurs between one s orbital of one atom and one s orbital of the other. This results in a bond that is relatively weak and long.
  • Double Bonds (Bond Order = 2): In double bonds (like in O₂), there is one sigma bond (formed by head-on overlap of orbitals) and one pi bond (formed by side-by-side overlap of unhybridized p orbitals). The increased overlap from the pi bond leads to a stronger, shorter bond compared to a single bond.
  • Triple Bonds (Bond Order = 3): In triple bonds (like in N₂), there is one sigma bond and two pi bonds. The additional pi bonds result in even more overlap, making the bond even stronger and shorter.

iii. Why Greater Orbital Overlap Leads to Shorter, Stronger Bonds:

  • Stronger Bonds: As the amount of overlap increases, the electron density between the two atoms becomes higher, leading to a stronger attraction between the nuclei and the shared electrons. This makes it harder to break the bond, thus increasing bond strength.
  • Shorter Bonds: Greater overlap pulls the atoms closer together, reducing the bond length. In higher-order bonds, where there is more overlap (due to additional pi bonds), the atoms are pulled closer to each other, resulting in shorter bond lengths.

iv. Example:

  • Single Bond (H-H): In a single bond, there is only one pair of electrons shared, and the orbitals overlap minimally, leading to a weaker and longer bond.
  • Double Bond (O=O): In a double bond, the additional pi bond increases orbital overlap, making the bond both stronger and shorter than a single bond.
  • Triple Bond (N≡N): In a triple bond, two pi bonds and one sigma bond result in even greater orbital overlap, making the bond stronger and shorter than both single and double bonds.

v. Orbital Overlap and Bond Length:

  • The greater the overlap of orbitals, the closer the atoms are pulled together. This results in a shorter bond length.
  • In higher-order bonds (like double and triple bonds), the additional orbitals involved in the overlap allow the atoms to be even more tightly bound, resulting in shorter bond lengths compared to single bonds.

vi. Points to Keep in Mind:

  • Orbital overlap increases with higher bond orders (single < double < triple).
  • Greater overlap means a stronger bond because of higher electron density between atoms.
  • Greater overlap also results in a shorter bond, as the atoms are drawn closer together by the stronger attractive forces.

 2.2.A.3 Coulomb’s Law: Ion Interaction Strength:

1. Coulomb’s Law:

i. Statement: Coulomb’s Law explains the electrostatic force between charged particles. The force is proportional to the product of the charges and inversely proportional to the square of the distance between them.

ii. Formula:

F=k×∣q1q2∣r2F = k \times \frac{|q_1 q_2|}{r^2}

2. Ionization and Ionic Bonds: When atoms gain or lose electrons, they form ions. This process is called ionization. In ionic compounds, ions of opposite charges attract each other, forming ionic bonds. The strength of these bonds is influenced by two key factors:

i. Charge on the Ions: The stronger the charge on the ions, the stronger the electrostatic attraction between them. For example, a Mg²⁺ ion, which has a +2 charge, will experience a stronger attraction to an Cl⁻ ion (with a -1 charge) compared to a Na⁺ ion, which has only a +1 charge. This is because the larger charge creates a stronger force according to Coulomb’s law.

ii. Distance Between Ions: The distance between the centers of the ions also plays a role. Smaller ions can pack closer together, increasing the electrostatic force between them. For example, Mg²⁺ is smaller than Na⁺, so it can come closer to the anion (e.g., Cl⁻), creating a stronger bond.

As a result, ionic compounds with higher charges on the ions, like MgCl₂, tend to have stronger ionic bonds and higher melting points compared to those with lower charges, like NaCl. The stronger the electrostatic force, the more energy is required to break the bond.

3. Lattice Energy: Lattice energy is the energy required to separate an ionic solid into its individual ions. It depends on the charges of the ions and the distance between them.

i. Charge of Ions: Larger charges result in stronger electrostatic attraction between ions, leading to higher lattice energy (e.g., Mg²⁺ and O²⁻ have higher lattice energy than Na⁺ and Cl⁻).

ii. Ion Size: Smaller ions can pack more closely, increasing attraction and lattice energy.

Formula:

U∝Q1Q2rU \propto \frac{Q₁Q₂}{r}

Where:

  • Q₁ and Q₂ are the charges on the ions.
  • r is the distance between them.

Higher lattice energy means stronger, more stable ionic bonds. Smaller ions and higher charges result in stronger lattice energy.

4. Electrostatic Potential Energy: Electrostatic potential energy refers to the energy stored due to the interaction between two charged particles. This energy is influenced by both the magnitude of the charges and the distance between them.

  • Charges and Stability: When two charged particles (such as ions) are brought together, their potential energy depends on the product of their charges. The greater the charges, the more negative the electrostatic potential energy becomes. A more negative value indicates a more stable system because the particles are more strongly attracted to each other.
  • Distance Between Charges: The potential energy also depends on the distance between the particles. As the distance between the ions decreases, the potential energy becomes more negative, reflecting a stronger attraction between them. In ionic compounds, smaller ions (with smaller radii) can get closer together, increasing the magnitude of the negative potential energy, which results in a more stable ionic bond.

Formula:

U=k⋅q1⋅q2rU = \frac{k \cdot q_1 \cdot q_2}{r}

Where:

  • U is the electrostatic potential energy.
  • k is Coulomb’s constant.
  • q₁ and q₂ are the charges of the particles.
  • r is the distance between the charges.

i. Relevance:

  • Larger Charges: The larger the charges (q₁ and q₂), the stronger the electrostatic attraction, leading to a more negative (and thus more stable) potential energy.
  • Smaller Ions: Smaller ions can approach each other more closely, which also increases the negative potential energy, enhancing stability in ionic compounds.

5. Ion Size and Charge Density: Ion Size and Charge Density are crucial factors in determining the strength of interactions between ions in ionic compounds.

  • Ion Size: Smaller ions have a higher charge density, meaning their charge is concentrated over a smaller volume. This leads to stronger electrostatic interactions with other ions because the ions can get closer to each other. Larger ions, on the other hand, have a lower charge density, reducing the strength of these interactions.
  • Charge Density: Charge density is the ratio of the charge of an ion to its size (radius). Ions with higher charge and smaller size (like Mg²⁺ or Al³⁺) have higher charge densities, resulting in stronger electrostatic attraction with oppositely charged ions. This leads to stronger ionic bonds and higher lattice energies.

i. Impact:

  • Smaller Ions and Higher Charge Density: Lead to stronger attractions and more stable ionic compounds (e.g., Mg²⁺ and O²⁻ in MgO).
  • Larger Ions and Lower Charge Density: Lead to weaker attractions and less stable compounds (e.g., Na⁺ and Cl⁻ in NaCl).

6. Electrostatic Potential Energy: Electrostatic potential energy is the energy stored due to the interaction between charged particles, like ions in ionic compounds. It is more negative (more stable) when the charges are larger and the distance between ions is smaller.

Formula:

U=k⋅q1⋅q2rU = \frac{k \cdot q_1 \cdot q_2}{r}

Where:

  • U is the electrostatic potential energy.
  • q₁ and q₂ are the charges.
  • r is the distance between ions.

i. Points to Keep in Mind:

  • Larger Charges: Lead to stronger, more stable ionic bonds (more negative potential energy).
  • Smaller Ions: Pack closer, increasing attraction and stability.

Chemical Bonds

  • Bonds: forces that hold groups of atoms together and make them act as one unit; attraction between the nucleus of one atom and the electron of another
    • Bonds occur so atoms can achieve noble gas electron configuration
    • As the number of bonds between two atoms increases, the bond grows both shorter and stronger
      • *Number of bonds is also called bond order
    • Single Bond:
      • 1 pair e- shared
      • Weaker attraction between nucleus of one atom and the bonding e-
      • Weaker and shorter bond
    • Triple Bond
      • 3 pair e- shared
      • Stronger attraction between nucleus of one atom and the bonding e-
      • Stronger and shorter bond
    • What conditions will favor bond formation (Ex: H2 molecules over separate H atoms)
      • In order to achieve lowest possible energy → energy of aggregate is lower than that of the separated atoms
      • System will act to balance positive (repulsive) and the negative (attractive) forces
      • The likelihood that two elements will form a chemical bond by the interaction between valence electrons
    • Bond energy: the energy required to break a bond → tells us about the strength of a bond
      • If (+) → endothermic; if (-) = exothermic
      • Bond energies depend on the number of shared electrons between two atoms → greater bond energy suggests that a stronger double or triple bond forms
    • Forces of attraction: electron in each atom are attracted to the nucleus of the other
    • Forces of repulsion: electron-electron, proton-proton, nuclei-nuclei
    • Bond length: the distance where energy of interaction between the atoms is at a minimum
      • Balance between attractive and repulsive force

 

Internuclear Distance Graphs

    • Shape formed because at left of dip have forces of repulsion, at right of dip have forces of attraction, and at minimum is where the forces balance themselves out, PE is lowest; stable arrangement

Coulomb’s Law:

  • States that “the strength of attraction is proportional to the magnitude of the particle charges and inversely proportional to the distance between them”
  • Opposite charges = force of attraction = (-) value; same charges = repulsion = (+) value
  • Charges are the same = force of repulsion → positive value
  • The attraction will be greater in the charged particle with the largest charge and smallest size (largest charge-size ratio)
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