Question

Silver crystallizes in fcc structure. If edge length of unit cell is 400 pm, calculate density of silver (Atomic mass of Ag = 108). Write a note on Haloform reaction.

Hint:

FCC density uses \( Z = 4 \); haloform reaction is diagnostic for compounds with \( \text{CH}_3\text{CO}- \).

Answer 1

i. Density of Silver: For FCC, number of atoms per unit cell \( Z = 4 \). Edge length \( a = 400 \, \text{pm} = 4 \times 10^{-8} \, \text{cm} \), atomic mass \( M = 108 \, \text{g mol}^{-1} \), Avogadro’s number \( N_A = 6.022 \times 10^{23} \, \text{mol}^{-1} \).
Density \( \rho = \frac{Z \cdot M}{N_A \cdot a^3} \).
\[ a^3 = (4 \times 10^{-8})^3 = 6.4 \times 10^{-23} \, \text{cm}^3. \] \[ \rho = \frac{4 \cdot 108}{6.022 \times 10^{23} \cdot 6.4 \times 10^{-23}} \approx \frac{432}{3.85408 \times 10^1} \approx 11.21 \, \text{g cm}^{-3}. \] ii. Haloform Reaction: Compounds with a methyl ketone group (\( \chemfig{CH_3-C(=O)-} \)) or acetaldehyde, when treated with halogens (e.g., I\(_2\)) and a base (e.g., NaOH), form haloforms (e.g., \( \chemfig{CHI_3} \)) and a carboxylate. Example: \[ \chemfig{CH_3-CO-CH_3} + 3\text{I}_2 + 4\text{NaOH} \to \chemfig{CHI_3} + \chemfig{CH_3COONa} + 3\text{NaI} + 3\text{H}_2\text{O}. \] Used in iodoform test to detect methyl ketones or acetaldehyde.