Table 3 The experimental (\(x_{1}^{\exp }\))^a and calculated (\(x_{1}^{cal}\)) solubilities of acetaminophen (ACE) in the aqueous protic ionic liquid (PIL) solutions at different temperatures (T), PIL mass fraction in the aqueous mixture (w3), and pressure (dp = 866 hPa), as predicted by the Wilson and e-NRTL models, are presented

w₃ = 0.0000

298.15

1.839

1.840

− 0.04

1.847

− 0.46

303.15

2.239

2.243

− 0.16

2.253

− 0.61

308.15

2.545

2.548

− 0.10

2.556

− 0.44

313.15

3.009

3.013

− 0.13

3.021

− 0.41

w₃ = 0.0200

298.15

2.750

2.744

0.20

2.712

1.35

303.15

3.417

3.410

0.19

3.397

0.57

308.15

3.802

3.790

0.33

3.774

0.75

313.15

4.007

4.001

0.17

3.999

0.22

w₃ = 0.0500

298.15

3.256

3.261

− 0.18

3.233

0.70

303.15

3.861

3.868

− 0.17

3.835

0.68

308.15

4.055

4.060

− 0.13

4.024

0.75

313.15

4.320

4.327

− 0.16

4.293

0.63

w₃ = 0.0700

298.15

3.884

3.881

0.07

3.888

− 0.11

303.15

4.588

4.585

0.07

4.642

− 1.17

308.15

4.675

4.676

− 0.03

4.677

− 0.06

313.15

5.025

5.025

0.01

5.037

− 0.23

w₃ = 0.1000

298.15

4.380

4.381

− 0.03

4.401

− 0.49

303.15

4.807

4.817

− 0.20

4.827

− 0.41

308.15

5.407

5.403

0.06

5.454

− 0.88

313.15

5.600

5.603

− 0.06

5.625

− 0.44

w₃ = 0.1500

298.15

4.962

4.969

− 0.14

4.975

− 0.27

303.15

5.658

5.659

− 0.02

5.712

− 0.97

308.15

6.128

6.129

− 0.01

6.158

− 0.48

313.15

6.665

6.664

0.02

6.716

− 0.76

w₃ = 0.2000

298.15

5.589

5.587

0.04

5.557

0.58

303.15

6.123

6.123

0.01

6.096

0.43

308.15

6.695

6.697

− 0.03

6.641

0.80

313.15

7.337

7.339

− 0.03

7.308

0.40

ACP (1) + water (2) + ([DEA]La) (3)

w₃ = 0.0000

298.15

1.839

1.839

− 0.46

1.849

− 0.52

303.15

2.239

2.240

− 0.61

2.241

− 0.08

308.15

2.545

2.545

− 0.44

2.547

− 0.09

313.15

3.009

3.010

− 0.41

3.014

− 0.16

w₃ = 0.0200

298.15

2.492

2.490

1.35

2.462

1.19

303.15

3.159

3.152

0.57

3.135

0.76

308.15

3.555

3.549

0.75

3.534

0.58

313.15

3.722

3.718

0.22

3.693

0.77

w₃ = 0.0500

298.15

3.181

3.179

0.70

3.161

0.64

303.15

3.576

3.576

0.68

3.581

− 0.13

308.15

3.917

3.919

0.75

3.903

0.36

313.15

4.227

4.227

0.63

4.217

0.24

w₃ = 0.0700

298.15

3.452

3.457

− 0.11

3.443

0.27

303.15

3.977

3.974

− 1.17

3.976

0.03

308.15

4.167

4.171

− 0.06

4.159

0.19

313.15

4.514

4.516

− 0.23

4.517

− 0.09

w₃ = 0.1000

298.15

3.849

3.852

− 0.49

3.856

− 0.17

303.15

4.220

4.222

− 0.41

4.236

− 0.39

308.15

4.793

4.788

− 0.88

4.829

− 0.75

313.15

5.266

5.258

− 0.44

5.271

− 0.10

w₃ = 0.1500

298.15

4.290

4.292

− 0.27

4.301

− 0.27

303.15

4.611

4.615

− 0.97

4.638

− 0.59

308.15

5.038

5.043

− 0.48

5.030

0.15

313.15

5.633

5.634

− 0.76

5.642

− 0.17

w₃ = 0.2000

298.15

4.669

4.664

0.58

4.666

0.07

303.15

5.223

5.214

0.43

5.175

0.92

308.15

5.710

5.708

0.80

5.689

0.37

313.15

6.188

6.185

0.40

6.158

0.48

ACP (1) + water (2) + ([TEA]La) (3)

w₃ = 0.0000

298.15

1.839

1.844

− 0.29

1.860

− 1.15

303.15

2.239

2.247

− 0.36

2.553

− 14.04

308.15

2.545

2.548

− 0.13

2.248

11.67

313.15

3.009

3.012

− 0.09

3.015

− 0.21

w₃ = 0.0200

298.15

2.161

2.163

− 0.05

2.165

− 0.16

303.15

2.632

2.634

− 0.07

2.926

− 11.16

308.15

2.940

2.939

0.04

2.624

10.73

313.15

3.334

3.333

0.01

3.325

0.26

w₃ = 0.0500

298.15

2.597

2.593

0.16

2.592

0.18

303.15

2.944

2.944

0.00

3.205

− 8.88

308.15

3.210

3.213

− 0.09

2.942

8.34

313.15

3.521

3.523

− 0.05

3.520

0.03

w₃ = 0.0700

298.15

2.908

2.907

0.02

2.917

− 0.31

303.15

3.461

3.462

− 0.02

3.576

− 3.32

308.15

3.584

3.583

0.03

3.462

3.40

313.15

3.929

3.930

− 0.01

3.924

0.12

w₃ = 0.1000

298.15

3.094

3.093

0.06

3.051

1.40

303.15

3.834

3.817

0.44

4.206

− 9.70

308.15

4.208

4.208

0.00

3.845

8.63

313.15

4.349

4.355

− 0.13

4.348

0.02

w₃ = 0.1500

298.15

3.958

3.941

0.43

4.026

− 1.73

303.15

4.151

4.151

− 0.01

4.951

− 19.28

308.15

4.940

4.921

0.40

4.154

15.91

313.15

5.167

5.157

0.19

5.171

− 0.08

w₃ = 0.2000

298.15

4.309

4.319

− 0.23

4.336

− 0.62

303.15

4.778

4.787

− 0.19

5.355

− 12.08

308.15

5.362

5.372

− 0.20

4.745

11.49

313.15

5.751

5.758

− 0.12

5.755

− 0.07