6.03 Calorimetry

In order to describe the molar volume of pure water the equation V_3=M_3⁄ρ_(3 ) is used, whereas those of sodium nitrate and the polyether compound poly(ethylene glycol) (PEG) are shown by V_1=V_(∅_1)^∞and V_1=V_(∅_2)^∞. In these two equations, V_(∅_1)^∞ and V_(∅_2)^∞ which are the apparent molar volumes at infinite dilution of sodium nitrate and poly(ethylene glycol), must be computed on the basis of data on apparent molal volume (V_∅). The following equation shows the relation of the V_∅ of a binary solution with density,
Equation 1
The notations which are used in Equation 1 are as follows: mi: Molality of solute i,
F: Density of the binary solution, ρ_w: Density of water.

In general,
In order to yield apparent molal volumes at infinite dilutionV_∅^∞, the apparent molar volumes V_∅ of aqueous electrolyte solutions are extrapolated to zero concentration employing the Conway et al. [11, 16] equation:
Equation 2
In Equation 3, there are two parameters b and c which are experimental and k is the limiting theoretical slope which is equal to 1.868 〖cm〗^(-3) L^(1⁄2) 〖mol〗^((-3)⁄2)at 298.15 K, respectively.17 Table 4 as shown the empirical data on the solutions of sodium nitrate in order to achieve values for〖 V〗_∅.
To obtain the values for V_∅^∞ given in Table 6, they were fitted to equation 7. Note that prior measurements of density on poly(ethylene glycol) + water should perform to calculate the values of V_∅^∞ for the polymer. Table 3 has shown these empirical values for different molalities of poly(ethylene glycol). Some of the researchers 11, 18, 20 have proposed that the dependency of〖 V〗_∅ on the molality of the polymer is a linear function specified
by
Equation 3
In Equation 3, h is a constant which is experimental. Applying equation 6 and densities in Table 2, we can obtain the values of〖 V〗_∅ for the polymer. As mentioned before, these values were fitted to equation 8. We demonstrated the values of V_∅^∞ obtained using this fit for poly(ethylene glycol) in Table 6.