. The accurate value 18.00 kJ mol⁻¹ for the enthalpy of fusion of benzoic acid has been reported (D. C. Ginnings, G. T. Furukawa J. Am. Chem. Soc. 1953, 75, 522). Are the ΔHm,HBO values estimated from the solubility measurements in agreement with the literature value
The Correct Answer and Explanation is:
To determine if the ΔHₘ,HBO values estimated from solubility measurements agree with the literature value for the enthalpy of fusion of benzoic acid (18.00 kJ mol⁻¹), you must compare the calculated values directly with the literature reference.
The enthalpy of fusion (ΔHₘ) represents the amount of energy required to convert a solid substance into its liquid phase at its melting point without changing its temperature. For benzoic acid, this value has been accurately reported as 18.00 kJ mol⁻¹ based on precise calorimetric studies published by Ginnings and Furukawa in 1953.
When solubility measurements are used to estimate ΔHₘ,HBO (the enthalpy of fusion based on solubility data in a particular solvent), the van’t Hoff equation is often applied. This relationship connects solubility to temperature, allowing the calculation of enthalpy changes based on how solubility varies with temperature. The equation takes the form:
ln S = -ΔHₘ / (R × T) + constant
Where:
- S is the solubility of the compound
- ΔHₘ is the enthalpy of fusion
- R is the universal gas constant
- T is the temperature in Kelvin
By plotting ln S versus 1/T, the slope of the line provides -ΔHₘ / R, allowing the enthalpy of fusion to be estimated.
If the ΔHₘ,HBO values derived from solubility experiments closely match the literature value of 18.00 kJ mol⁻¹, this indicates strong agreement and suggests that the experimental approach is valid. However, small deviations may arise due to experimental uncertainties, differences in solvent interactions, or the purity of the benzoic acid sample.
In conclusion, if your estimated ΔHₘ,HBO values are approximately 18.00 kJ mol⁻¹ within acceptable experimental error (typically within 5 percent), they are considered in agreement with the literature value. If there are larger discrepancies, it suggests experimental limitations or methodological errors in the solubility-based approach.
