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Difficulty: HardPure and Impure Substances and Criteria of Purity

An analyst examined a sample of benzoic acid synthesized in a laboratory. During paper chromatography, the solvent front migrated 12.0 cm12.0\text{ cm} from the origin line, while the primary spot migrated 4.8 cm4.8\text{ cm} and a faint secondary spot appeared at 9.6 cm9.6\text{ cm}. Subsequent thermal analysis showed that the sample melted over a range of 115.0∘C115.0^\circ\text{C} to 120.5∘C120.5^\circ\text{C}, whereas pure benzoic acid has a sharp literature melting point of 122.3∘C122.3^\circ\text{C}.

What is the retention factor (RfR_f) of the primary component, and what does the data reveal regarding the sample's purity?

  1. Rf=0.40R_f = 0.40; the sample is impure because it exhibits a broad melting range below the literature value and forms multiple chromatographic spots.Answer
  2. B
    Rf=2.50R_f = 2.50; the sample is impure because the presence of impurities inverts the solvent-to-solute ratio during retention factor calculations.
  3. C
    Rf=0.40R_f = 0.40; the sample is pure because non-volatile impurities elevate boiling points while leaving solid melting ranges unaffected.
  4. D
    Rf=2.50R_f = 2.50; the sample is pure because the secondary spot represents a solvent artifact and the primary spot moved faster than the solvent front.

Answer

The retention factor (RfR_f) of the primary component is 0.400.40, and the sample is impure because it exhibits a depressed, broad melting point range and multiple spots on the chromatogram.
The retention factor is given by Rf=4.8 cm12.0 cm=0.40R_f = \frac{4.8\text{ cm}}{12.0\text{ cm}} = 0.40. The criteria of purity state that a pure solid melts sharply at a single characteristic temperature. A melting range (115.0∘C−120.5∘C115.0^\circ\text{C} - 120.5^\circ\text{C}) lower and wider than the literature value (122.3∘C122.3^\circ\text{C}), combined with multiple chromatographic spots, conclusively proves the sample is impure.

Step-by-Step Solution

1
Calculate the retention factor (RfR_f) of the primary component.
Rf=Distance moved by solute spotDistance moved by solvent front=4.8 cm12.0 cm=0.40R_f = \frac{\text{Distance moved by solute spot}}{\text{Distance moved by solvent front}} = \frac{4.8\text{ cm}}{12.0\text{ cm}} = 0.40
By definition, RfR_f is the ratio of solute distance to solvent front distance from the origin line.
2
Analyze the chromatography spot evidence for chemical purity.
The presence of two distinct spots (at 4.8 cm4.8\text{ cm} and 9.6 cm9.6\text{ cm}) indicates at least two components in the mixture.
A pure chemical compound produces exactly one spot on a developed chromatogram under uniform conditions.
3
Evaluate the melting point behavior against purity criteria.
The sample melts gradually over a 5.5∘C5.5^\circ\text{C} temperature span (115.0∘C−120.5∘C115.0^\circ\text{C} - 120.5^\circ\text{C}) below the pure literature value (122.3∘C122.3^\circ\text{C}).
Impure solids melt over a broad temperature range and at temperatures lower than the pure compound's sharp melting point.

Key Concept

Criteria of Purity: Sharp melting point / boiling point, fixed physical constants, and single-spot chromatogram.
Estimated Time:1m 30s
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Topics

Pure and Impure Substances and Criteria of Purity