The chemistry of dilute solutions is analogous to the chemistry of ideal gases,

Question

The chemistry of dilute solutions is analogous to the chemistry of ideal gases, a fact that played an important role in resolving the nineteenth century debate whether or not atoms are real. For example, the vapor pressure, p, of a liquid is related to its enthalpy of vaporization, AHo, by the Clausius-Clapeyron equation: AH where C is a constant that will not concern us. Note the close analogy to Eq. (1) in the procedure describing the solubility of benzoic acid in water. 1. Hermione Hermetica measured the vapor pressure of water in Torr as a function of the absolute temperature T, for the temperature range 293 KSTs 303 K. She found that her data fit the equation (note the -m differs from equation 2 above) In(p)-- b, with a regression coefficient of r =-0.9978, m 5292 K, and b = 20.93. Calculate the enthaply of vaporization of water in kJ mol-1 to four significant figures. kJ mol-l 2. Does the value of r indicate a good correlation? 3. Benjamin Beaker dissolved 0.123 g of benzoic acid in 15.0 g of water. What is the mole fraction of benzoic acid?

Explanation / Answer

From the given two equations,

ln(p) = -dH0/RT + C and ln(p) = -m/T + b

by equating the above solutions,

dH0/R = m

dH0 = m * R

dH0 = 5292 K * 8.314 J/mol.K

dH0 = 43997.6 J/mol

dH0 = 43.9977 kJ/mol

number of moles of benzoic acid n1 = 0.123/122 = 0.001

number of moles of water n2 = 15/18 = 0.833

mole fraction of benzoic acid = n1/(n1+n2)

mole fraction of benzoic acid = 0.001/(0.001+0.833) = 0.0012

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