Acidic dissociation constant and related thermodynamic quantities for diethanolammonium ion in water from 0 to 50 °C

The dissociation constants of diethanolamine (2:2′-dihydroxydiethylamine) and its conjugate acid were determined by electromotive force measurements of the cell $\text{Pt};{\mathrm{H}}_2\left(\mathrm{g},1\text{atm}\right),{\left({\text{HOC}}_2{\mathrm{H}}_4\right)}_2{\text{NH}}_2\text{Cl}\left(m_1\right),{\left({\text{HOC}}_2{\mathrm{H}}_4\right)}_2\text{NH}\left(m_2\right),\text{AgCl}\left(\mathrm{s}\right);\text{Ag}$in the temperature range 0 to 50 °C. The acidic dissociation constant (K_bh) of the diethanolammonium ion is given by $-\log K_{bh}=\frac{1830.15}{T}+4.0302-0.0043261T,$where T, the temperature on the Kelvin scale, lies between 273.15 and 323.15°. From this equation were calculated ΔG°, the change in free energy; ΔH°, the change in heat content; ΔS° the change in entropy; and $\mathrm{\Delta }{C}_p^{°}$, the change in heat capacity that accompany the dissociation of 1 mole of diethanolammonium ion in the standard state. At 25 °C, −log K_bh= 8.883; ΔG°=50,682 joule mole⁻¹; ΔH°=42,400 joule mole⁻¹; ΔS°=−27.8 joule deg⁻¹mole⁻¹; and $\mathrm{\Delta }{C}_p^{°}=49$ joule deg⁻¹mole⁻¹.