1
2 S1. Development and validation of the method detecting pK a
3 Selection of the detection wavelength
4
Solutions (5×10 -5
mol/L) of p -nitrophenol were prepared in 0.01 mol/L NaOH,
5 0.01 mol/L HCl and 0.01 mol/L NaHCO
3
, and a 0.1-mol/L imperialine-ethanol
6 solution was also prepared. The resulting samples were scanned using an
7 ultraviolet-visible spectrophotometer (Cary 100 Bio UV-VIS, Varian Medical Systems
8 Inc., USA) to select the optimal wavelength for analyte absorbance detection.
9 The UV-VIS spectra of p -nitrophenol and imperialine were merged, as shown in
10 Figure S1
, illustrating that at a detection wavelength (λ) of 401 nm, the p -nitrophenol
11 absorptive difference between the ionized and non-ionized forms was the most
12 significant, while imperialine did not exhibit any absorbance.
13

14 Figure S1.
The UV-VIS spectrum of o-nitrophenol and imperialine. (A) UV-VIS spectrum of
15 o-nitrophenol in different media: 1. 0.01 mol/L NaOH; 2. 0.01 mol/L NaHCO
3
; 3. 0.01 mol/L HCl.
16 (B) UV-VIS spectrum of imperialine.
17
18 Measurement of the p-nitrophenol pK a
19
Solutions (5×10 -5 mol/L) of p -nitrophenol were prepared in solutions of 0.01
20 mol/L NaOH, 0.01 mol/L HCl and PBS (with pH values of 7.0, 7.4, 7.8 and 8.5).
21 Their absorbance values were then obtained using a UV-VIS spectrophotometer at the
22 selected wavelength; meanwhile, the pH of the PBS solution was precisely
23 determined. The p K a
of p -nitrophenol was calculated using Eq. (S1) ,
24 (S1)
25 where A is the absorbance of the solution containing a certain total concentration of
26 the acid-base mixture; A
1 is the absorbance of the acid form (100 % non-ionized type);
27 A
2
is the absorbance of the base form (100 % ionized type) at the same concentration;
28 and γ is the activity coefficient.
29 The
γ was calculated according to the Debye-Huckel Formula, Eq. ( S2 ),
30 (S2)
31 where I represents the ionic strength of the solution, and Z represents the charge
32 number of the ion.
33 I was calculated using Eq. (S3) ,
34 (S3)

35 where m
B is the molality of each ion in the buffer solution, and Z
B is the charge
36 number of that ion.
37 The absorbance ( A ) of p -nitrophenol at different pH values is shown in Table S1 ,
38 as measured by the spectrophotometric indicator method with a detection wavelength
39 of 401 nm. The calculation was carried out using Eq. (S1) ; the p K a
of the chosen
40 indicator, p -nitrophenol, was calculated as 7.16, which corresponds well with the
41 reported value of 7.17
[S1] . Therefore, our proposed method was accurate and
42 reliable.
43 Table S1.
The pK a
of p -nitrophenol as determined by the spectrophotometric indicator method a pH A lg γ pK a
T （ Int ）
7.00
7.39
7.80
8.50
0.5550 ± 0.0001
0.7262 ± 0.0001
0.8339 ± 0.0001
0.8987 ± 0.0002
-0.3354
-0.3361
-0.3367
-0.3371
44
45
All results are the mean of measurements from three replicates. a A
1
= 0.0282
， A
2
= 0.9170
， λ = 401 nm
7.17
7.16
7.15
7.16