Table 7 Results of values of the two thermodynamic parameters (ΔH°) and (ΔS°) obtained for linear regression by Eqs. 33 and 45 and nonlinear regression (Eqs. 44–49).

T	T	ΔG°	Linear Regression		Non Linear Regression
T	T	ΔG°	ΔH°	ΔS°	ΔH°	ΔS°
°C	K	kJ mol⁻¹	kJ mol⁻¹	J K⁻¹ mol⁻¹	kJ mol⁻¹	J K⁻¹mol⁻¹
HCl
20	293.15	− 70.626	55.649	432.815	80.850	516.72
30	303.15	− 75.822			71.176	484.90
40	313.15	− 80.440			62.120	455.25
47.55^a	320.70^a	− 83.766^c			55.649^b	432.815^b
60	333.15	− 88.837			45.638	403.65
80	353.15	− 96.685			31.023	361.63
			R² = 0.98279^d		σ = 0.0277^e	σ = 0.0213^e
H₂SO₄
20	293.15	− 70.238	85.959	534.55	108.00	608.02
30	303.15	− 76.294			99.542	580.03
40	313.15	− 81.890			91.620	554.08
47.55^a	320.70^a	− 86.007^c			85.959^b	534.55^b
60	333.15	− 92.440			77.203	509.21
80	353.15	− 102.34			64.419	472.21
			R² = 0.99458^d		σ = 0.0120^e	σ = 0.0265^e
H₃PO₄
20	293.15	− 69.240	104.941	594.307	119.61	644.21
30	303.15	− 74.907			113.98	623.08
40	313.15	− 81.320			108.71	606.82
47.55^a	320.70^a	− 86.037^c			104.941^b	594.307^b
60	333.15	− 93.817			99.113	579.11
80	353.15	− 104.37			90.606	552.11
			R² = 0.99786^d		σ = 0.0057^e	σ = 0.0287^e

(a): Crossover temperature T_cr (Fig. 11a and b). (b); current thermodynamic parameters ΔH°(T) and ΔS°(T) calculated with Eqs. 48 and 49, respectively. (c): Gibbs free energy of activation (ΔG°) estimated with Eq. 44. (d): from²². (e): Standard deviation σ.

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