′-((2-methoxy-naphthalene-1-yl)methylene) pyrimidine-5-carbohydrazide (H5) and

Compound	Concentration (M)	C.R. (mg cm^−2 min^−1)	θ
% IE
	Blank	0.082 ± 0.0017	—	—
H4	1 × 10^−6	0.040 ± 0.0022	0.512	51.2
	2 × 10^−6	0.037 ± 0.0020	0.551	55.1
	5 × 10^−6	0.033 ± 0.0018	0.603	60.3
	10 × 10^−6	0.021 ± 0.0023	0.738	73.8
	15 × 10^−6	0.015 ± 0.0012	0.815	81.5
	20 × 10^−6	0.010 ± 0.00024	0.883	88.3
H5	1 × 10^−6	0.054 ± 0.0022	0.342	34.2
	2 × 10^−6	0.042 ± 0.0015	0.486	48.6
	5 × 10^−6	0.036 ± 0.0019	0.567	56.7
	10 × 10^−6	0.026 ± 0.00210	0.683	68.3
	15 × 10^−6	0.023 ± 0.00240	0.719	71.9
	20 × 10^−6	0.012 ± 0.00028	0.853	85.3
H6	1 × 10^−6	0.051 ± 0.00230	0.384	38.4
	2 × 10^−6	0.042 ± 0.00200	0.482	48.2
	5 × 10^−6	0.036 ± 0.00180	0.561	56.1
	10 × 10^−6	0.024 ± 0.00120	0.703	70.3
	15 × 10^−6	0.010 ± 0.00110	0.875	87.5
	20 × 10^−6	0.004 ± 0.00016	0.952	95.2

As shown from Fig. 1, the curves in inhibitors presence were found below that of its absence. Also, the curves are approximately straight lines due to the absence of oxide film or any corrosion product on the steel surface.
3.1.1 Adsorption isotherms.(H4 & H5 & H6) inhibitors has shown protection from oxidation of carbon steel in the corrosive medium by adsorption on its surface because the binding energy between the H₂O molecules and the outer surface is lower than that between the molecules of the inhibitor and the surface of the metal²⁴ as determined in eqn (12):

xH2Oads + Orgsol ↔ Orgads + xH2O	(12)

where x is the amount of single organic molecules substituted for H₂O molecules. The molecules on the outer surface of a metal can be physiosorbed or chemisorbed. By minimizing the cathodic response, the physiosorbed molecules face metal corrosion, while chemisorbed molecules impede the anodic response by decreasing the possible reaction of the corroding metal at the sites of adsorption.²⁵ After examination of all adsorption isotherms we conclude that the best isotherm that fits our results is Temkin isotherm²⁶ as determined in eqn (13):

aθ = ln KC	(13)

where C is the concentration (M) of (H4 & H5 & H6); K is the adsorption equilibrium constant, (a) is a molecular interaction parameter. A graph of θ against log C gives straight lines as appeared in Fig. 2, note: slope = 2.303/a, intercept = 2.303/a log K_ads. Thermodynamic parameters of adsorption were calculated and tabulated in Table 3. The essential parameters were calculated are  ,  and  after assessment of K_ads at various temperatures (Fig. 2).²⁷ The change in free energy can be calculated from eqn (14):

	(14)

where 55.5 is the amount of H₂O in mol L⁻¹, T is the temperature and R is the universal gas constant.  ,  can be determined from eqn (15):

	(15)

	Fig. 2 Temkin adsorption isotherm of compound (H4) on carbon steel surface in 1.0 M HCl at various temperatures.

Table 3 Thermodynamic parameters for the adsorption of (H4 & H5 & H6) derivatives on carbon steel surface in 1 M HCl at different temperatures

Compound	T (°C)	Kads (M^−1)
H4	25	5.67	14.25	48.81	171
	30	6.29	14.75	48.81
	35	8.21	15.68	48.81
	40	11.33	16.77	48.81
	45	20.03	18.55	48.81
H5	25	5.67	14.25	48.82	180
	30	6.29	14.75	48.82
	35	8.21	15.68	48.82
	40	11.33	16.77	48.82
	45	20.03	18.55	48.82
H6	25	5.67	14.25	48.81	193
	30	6.29	14.75	48.81
	35	8.21	15.68	48.81
	40	11.33	16.77	48.81
	45	20.03	18.55	48.81

By plotting  vs. T, (Fig. 3), the obtained curve is straight and the slope is equal to  and the intercept is equal to  .

	Fig. 3   plotted against T (K) for H4 derivative.

Table 3 represents the calculated thermodynamic parameters and clarifies that the values of  were negative which indicates that (H4 & H5 & H6) is adsorbed spontaneously. As stated, before by different researches, the type of adsorption was ascribed as physisorption if  values were −20 kJ mol⁻¹ or lower, the reaction is happened because of the electrostatic attraction between oppositely charged (inhibitor and metal), whereas the values of about −40 kJ mol⁻¹ or more were ascribed as chemisorption because of sharing of the charge or transferring of charge between inhibitor and carbon steel.^28–30 The estimated values of  were noticed from −18.55 kJ mol⁻¹ and −14.25 kJ mol⁻¹ that belong to (physical adsorption). The minus values of  were related to the adsorption form of inhibitor molecules is an exothermic reaction. Exothermic reaction corresponded to either physisorption or chemisorption but an endothermic reaction is corresponded to as chemisorption.³¹ Also, enthalpy values are around 41.9 kJ mol⁻¹ which related to physisorption and those up to 100 kJ mol⁻¹ or larger are related to chemisorption. The determined  assessments are negative and ranged from 40.3 to 48.8 kJ mol⁻¹ demonstrating that (H4 & H5 & H6) could be physiosorbed. The  calculations are minus that corresponding to the presence of the adsorbed molecules on carbon steel surface. In addition, Fig. 3 shows  against various T (K) for H4 inhibitor.
The activation factors for the dissolution procedure were calculated according to Arrhenius eqn (16):

	(16)

where k_corr is the corrosion ratio, A is the Arrhenius constant,  is the activation energy, R is the universal gas constant, and T is the temperature. Estimations of  of carbon steel corrosion in the presence of measured amounts of (H4 & H5 & H6) were obtained from the relation of log k_corr against 1000/T graphs as appeared in Fig. 4, the transition state relation is obtained from eqn (17):

kcorr = (RT/Nh)exp(ΔS*/R)exp(−ΔH*/RT)	(17)

where N is the Avogadro's factor, h is referred to Planck's parameter, ΔS* is the activated entropy and ΔH* represents the activated enthalpy. A diagram of log(k_corr/T) versus (1000/T) give straight lines as shown in Fig. 5, with slopes is (ΔH*/2.303R) and intercepts is log(R/Nh) + ΔS*/2.303R. All calculations are listed in Table 4, the increase in  values demonstrated that (H4 & H5 & H6) is physiosorbed on the carbon steel surface.³² The positive indications of ΔH* values give the endothermic idea of the carbon steel dissolution procedure. The negative indications of ΔS* demonstrated that in the rate determine step, the association of unstable coordinated molecules is larger than the dissociation.^24,33

	Fig. 4 Arrhenius plots for carbon steel corrosion rates (kcorr) against 1000/T after 120 minutes of immersion in 1.0 M HCl with and without altered concentrations of compound (H4).

	Fig. 5 Plots of (log kcorr/T) vs. 1000/T for corrosion of carbon steel in 1.0 M HCl with and without altered concentrations of compound (H4).

Table 4 Activation parameters for the dissolution of carbon steel with and without altered concentrations of derivatives in 1.0 M HCl