Question

1. list the following atoms in order of lattice energy (lowest to highest)

srs, nacl, cacl₂, na₂o, rbbr

for each property, check yes if the property is characteristic of most metals, or no if it is not. on
the lines below explain how metallic bonding accounts for the properties listed.

1. malleable
2. brittle
3. lustrous
4. high melting point
5. low boiling point
6. ductile
7. poor conduction of heat
8. good conduction of electricity

yes no

Explanation:

Problem 82 (Lattice Energy Ordering)

Step 1: Recall Lattice Energy Factors

Lattice energy ($U$) depends on ion charge ($Q$) and ionic radius ($r$), with $U \propto \frac{|Q_+ Q_-|}{r_+ + r_-}$. Higher charge magnitude and smaller ionic radii increase lattice energy.

Step 2: Analyze Each Compound

• RbBr: $Rb^+$ (large radius), $Br^-$ (large radius), charges $\pm1$.
• NaCl: $Na^+$, $Cl^-$, charges $\pm1$; $Na^+$ smaller than $Rb^+$, $Cl^-$ smaller than $Br^-$.
• CaCl₂: $Ca^{2+}$ (charge +2), $Cl^-$ (charge -1); $Ca^{2+}$ smaller than $Na^+$, $Rb^+$.
• Na₂O: $Na^+$ (charge +1), $O^{2-}$ (charge -2); $O^{2-}$ smaller than $Cl^-$, $Br^-$.
• SrS: $Sr^{2+}$ (charge +2), $S^{2-}$ (charge -2); $Sr^{2+}$ and $S^{2-}$ have smaller radii than $Ca^{2+}$ and $O^{2-}$? Wait, $Sr$ is below $Ca$, so $Sr^{2+}$ radius > $Ca^{2+}$; $S^{2-}$ radius > $O^{2-}$ but < $Cl^-$, $Br^-$. Wait, re-evaluate charges and radii:

• Charge magnitude: $SrS$ ($2\times2=4$), $Na₂O$ ($1\times2=2$), $CaCl₂$ ($2\times1=2$), $NaCl$ ($1\times1=1$), $RbBr$ ($1\times1=1$).
• Ionic radii: $Rb^+ > Na^+$, $Br^- > Cl^- > O^{2-}$, $Sr^{2+} > Ca^{2+}$, $S^{2-} > O^{2-}$ but < $Cl^-$, $Br^-$.

Step 3: Order by Lattice Energy

1. RbBr: Lowest (large radii, charge 1×1).
2. NaCl: Next (smaller radii than RbBr, charge 1×1).
3. CaCl₂ or Na₂O? $CaCl₂$: $Ca^{2+}$ (charge +2) with $Cl^-$ (charge -1); $Na₂O$: $Na^+$ (charge +1) with $O^{2-}$ (charge -2). Let’s calculate effective charge: $CaCl₂$: $2\times1=2$; $Na₂O$: $1\times2=2$. Now radii: $Ca^{2+}$ radius ~ 100 pm, $Na^+$ ~ 102 pm (close), $Cl^-$ ~ 181 pm, $O^{2-}$ ~ 140 pm. So $r_+ + r_-$ for $CaCl₂$: ~100 + 181 = 281; $Na₂O$: ~102 + 140 = 242. Smaller sum → higher lattice energy. So $Na₂O$ > $CaCl₂$.
4. Na₂O: Higher than CaCl₂ (smaller $r_+ + r_-$).
5. SrS: Highest (charge 2×2=4, radii: $Sr^{2+}$ ~ 118 pm, $S^{2-}$ ~ 184 pm; $r_+ + r_- = 302$? Wait, no—wait $SrS$: $Sr^{2+}$ (118 pm) and $S^{2-}$ (184 pm) → sum 302. But charge is 4, which is higher than $Na₂O$ (charge 2). So even with larger radii, higher charge dominates. Wait, maybe I messed up. Let’s re-rank:

• Charge priority: higher charge (2×2) > (2×1 or 1×2) > (1×1).
• Within same charge: smaller radii.

So:

• Charge 1×1: RbBr (large radii) < NaCl (smaller radii).
• Charge 2×1 or 1×2: CaCl₂ (2×1) vs Na₂O (1×2). Na₂O has smaller anion (O²⁻ < Cl⁻) and similar cation radius (Na⁺ ~ Ca²⁺? No, Ca²⁺ is smaller than Na⁺? Wait, Ca²⁺ (100 pm) < Na⁺ (102 pm). Wait, $Ca^{2+}$ is smaller than $Na^+$ (since Ca is in period 4, Na in 3, but Ca²⁺ loses 2 electrons, Na⁺ loses 1. Ionic radii: $Na^+$ ~ 102 pm, $Ca^{2+}$ ~ 100 pm. So $CaCl₂$: $Ca^{2+}$ (100) + $Cl^-$ (181) = 281; $Na₂O$: $Na^+$ (102) + $O^{2-}$ (140) = 242. So $Na₂O$ has smaller sum, so higher lattice energy than CaCl₂.
• Charge 2×2: SrS (Sr²⁺ + S²⁻). Sr²⁺ (118) + S²⁻ (184) = 302. But charge is 4, which is higher than 2, so SrS > Na₂O.

Final order (lowest to highest): RbBr, NaCl, CaCl₂, Na₂O, SrS.

Problems 83–90 (Metallic Properties)

(for each):

• 83. Malleable: Yes. Metallic bonding: delocalized electrons allow metal ions to slide past each other without breaking bonds.
• 84. Brittle: No. Metals are malleable/ductile, not brittle (brittle is for ionic/covalent solids).
• 85. Lustrous: Yes. Delocalized electrons reflect light.
• 86. High melting point: Yes (most metals; metallic bonds are strong, require high energy to break).
• 87. Low boiling point: No. Most metals have high boiling points (strong metallic bonds).
• 88. Ductile: Yes. Delocalized electrons allow metal ions to stretch without breaking bonds.
• 89. Poor conduction of heat: No. Delocalized electrons transfer heat efficiently.
• 90. Good conduction of electricity: Yes. Delocalized electrons move freely to conduct current.

Answer:

s:

Problem 82:

Order (lowest to highest): $\boldsymbol{\text{RbBr, NaCl, CaCl}_2\text{, Na}_2\text{O, SrS}}$

Problem 83–90 (Yes/No):

1. Malleable: $\boldsymbol{\text{Yes}}$
2. Brittle: $\boldsymbol{\text{No}}$
3. Lustrous: $\boldsymbol{\text{Yes}}$
4. High melting point: $\boldsymbol{\text{Yes}}$
5. Low boiling point: $\boldsymbol{\text{No}}$
6. Ductile: $\boldsymbol{\text{Yes}}$
7. Poor conduction of heat: $\boldsymbol{\text{No}}$
8. Good conduction of electricity: $\boldsymbol{\text{Yes}}$