Electronic Supplementary Material for

Spectroscopic Study of Acid-base Equilibria and Ion Pairing

in Supercritical Methanol

Y. Takebayashi (*) · K. Sue · S. Yoda · T. Furuya

Nanotechnology Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), Higashi 1-1-1, Tsukuba, Ibaraki 305-8565, Japan

e-mail:

H. Hotta · A. Shono · K. Otake

Graduate School of Engineering, Tokyo University of Science, Kagurazaka 1-3, Shinjyuku-ku, Tokyo 162-8601, Japan

Contents

1 Test of the Concentration of the Solutions Mixed by Two HPLC Pumps

2 Derivation of Eq. 1 and Approximations Involved


1 Test of the Concentration of the Solutions Mixed by Two HPLC Pumps

In the present work, sample solutions at various concentrations of KOH were prepared by mixing two solutions fed by the HPLC pumps B and C as shown in Fig. 2. The concentrations of the sample solution were adjusted by controlling the flow rates of the pumps. Here we confirm that the concentrations of the mixed solution were properly adjusted to the desired values.

A methanol solution of N-methylaniline (NMA) was prepared at a concentration of 50 mmol·L–1. This NMA solution was fed by pump B, and was then mixed with pure methanol fed by pump C at a pressure of 25.0 MPa. The relative flow rates of pumps B and C were varied at ratios from 0.1:0.9 to 0.9:0.1. The total flow rate was fixed at 1.00 or 0.50 cm3·min–1. Concentrations of DMA in the mixed solution were measured by GC–FID (Agilent, 6890) at least four times.

Concentrations of NMA in the mixed solutions divided by that of the corresponding feed solution B (50 mmol·L–1) are listed in Table S1 as a function of the flow rates of the pumps. At each total flow rate, the concentration of NMA was proportional to the flow rate of pump B within a deviation of ± 1%. It is thus confirmed that the concentrations of the mixed solutions were adjusted to the desired values within ± 1%, relative to the concentration of the feed solution.


Table S1 Concentrations of NMA in the mixed solutions as a function of the flow rates of the pumps. The error limits indicate the standard deviation from the GC analysis

Total flow rate = 1.00 cm3·min–1

Pump B flow rate
(cm3·min–1) / Pump C flow rate
(cm3·min–1) / Concentration of NMA in the mixed solution
divided by that of the feed solution B (%)
0.10 / 0.90 / 9.6 ± 0.4
0.30 / 0.70 / 29.9 ± 0.5
0.50 / 0.50 / 50.0 ± 0.4
0.70 / 0.30 / 69.9 ± 0.2
0.90 / 0.10 / 90.2 ± 0.3

Total flow rate = 0.50 cm3·min–1

Pump B flow rate
(cm3·min–1) / Pump C flow rate
(cm3·min–1) / Concentration of NMA in the mixed solution
divided by that of the feed solution B (%)
0.05 / 0.45 / 10.3 ± 0.4
0.15 / 0.35 / 30.2 ± 0.3
0.25 / 0.25 / 49.7 ± 0.4
0.35 / 0.15 / 70.1 ± 0.3
0.45 / 0.05 / 90.2 ± 0.4


2 Derivation of Eq. 1 and Approximations Involved

Let us consider a methanol solution containing the acidic (HA) and basic (A–) forms of 2,5-dichlorophenol (DCP) at a total molality of (mol·kg–1). According to the Beer-Lambert law, the absorbance at each wavelength, , is expressed by

, (S1)

where and are the molar absorption coefficients of HA and A–, respectively; is the degree of dissociation of DCP, i.e., the mole fraction of DCP in its basic form; is the optical path length; and is the solution density (kg·L–1).

The molar absorption coefficient of HA, , can be obtained from the absorption spectrum measured under extremely acidic conditions, , as

, (S2)

where is the solution density under acidic conditions. In a similar way, the absorption coefficient of A–, , can be determined by using the absorption spectrum measured under extremely basic conditions, , as

, (S3)

where is the solution density under basic conditions. Substitution of Eqs. S2 and S3 into Eq. S1 then gives the following equation:

. (S4)

When all the solutions are very dilute, it is reasonable to assume that the solution densities are approximately equal to each other (). Under this assumption, Eq. S4 can be rewritten as

, (S5)

indicating that the spectrum is a linear combination of and .

ESM for “Spectroscopic Study of Acid-base Equilibrium in Supercritical Methanol” 5/5