This chemistry question involves key chemical concepts and calculations. The detailed solution below walks through each step, from identifying the reaction type to computing the final answer.
ScanSolve AI Answer
Step 1: Identify the given information and the crystal structure. The compound KF has an NaCl structure. The distance between K^+ and F^- ions is 269 \, pm. For an NaCl structure, the distance between a cation and an anion (nearest neighbors) is equal to half of the unit cell edge length (a/2). So, (a)/(2) = 269 \, pm. Step 2: Calculate the unit cell edge length (a). a = 2 × 269 \, pm = 538 \, pm Step 3: Convert the unit cell edge length from picometers (pm) to centimeters (cm). 1 \, pm = 10^-10 \, cm a = 538 × 10^-10 \, cm = 5.38 × 10^-8 \, cm Step 4: Calculate the volume of the unit cell (V). V = a^3 = (5.38 × 10^-8 \, cm)^3 V = (5.38)^3 × (10^-8)^3 \, cm^3 V = 155.753512 × 10^-24 \, cm^3 Step 5: Determine the number of formula units per unit cell (Z) for an NaCl structure. For an NaCl structure, there are 4 formula units per unit cell. So, Z = 4. Step 6: Calculate the molar mass (M) of KF. Atomic mass of K ≈ 39.098 \, g/mol Atomic mass of F ≈ 18.998 \, g/mol M = 39.098 + 18.998 = 58.096 \, g/mol Step 7: Use Avogadro's number (N_A). N_A = 6.022 × 10^23 \, mol^-1 Step 8: Apply the formula for density (). = (Z × M)/(a^3 × N_A) Substitute the values: = 4 × 58.096 \, g/mol(155.753512 × 10^-24 \, cm^3) × (6.022 × 10^23 \, mol^-1) = 232.384 \, g (155.753512 × 6.022) × 10^-24+23 \, cm^3 = 232.384 \, g937.89606 × 10^-1 \, cm^3 = 232.384 \, g93.789606 \, cm^3 ≈ 2.4776 \, g/cm^3 Step 9: Compare the calculated density with the given options. The calculated density is approximately 2.4776 \, g/cm^3, which rounds to 2.48 \, g/cm^3. This matches option (d). The final answer is d) 2.48 \, g/cm^3.