#### Electrical conductivity along the coexistence curve

We measured the electrical conductivity of three different solutions: (I-W), (I-W)+510

^{-4} M [KCL] and (I-W) +510

^{-3} M [KCL], with versus temperature above the separation temperature T

_{t} at each concentration X of the isobutyric acid along the coexistence curve .The conductivity data for these solution are shown in Fig 1.(a, b, c) . The data cover a good range of temperature above T

_{t}. The lower limit was considered adequate for the main purpose of this study. Data were taken at the higher temperature in order to establish the temperature dependence of these transport properties well away from T

_{c}, the separation temperature for the critical concentration X

_{c}, T

_{c}= T

_{t} (X=X

_{c}). The critical concentration X

_{c} and temperature T

_{c} were taken in weight percent in isobutyric acid to:

The critical temperature T

_{c} and the critical composition X

_{c} increased linearly with the salt concentration. The effect of KCl salt on the shift of the critical point of this mixture (I-W), was extensively studied in a previous work [

1].

**Figure 1.**
Temperature dependence of electrical conductivity along the coexistence curves in the single phase region of isobutyric acid–water (I-W): a)(I-W); b)(I-W) + 5 10^{-4} M [KCl]; c) (I-W) + 5 10^{-3} M [KCl].

**Figure 1.**
Temperature dependence of electrical conductivity along the coexistence curves in the single phase region of isobutyric acid–water (I-W): a)(I-W); b)(I-W) + 5 10^{-4} M [KCl]; c) (I-W) + 5 10^{-3} M [KCl].

For each composition X of the acid, the plot of electrical conductivity σ (Ω

^{-1}cm

^{-1}_{)} versus the temperature T should be a straight line of slope A

_{x} (fig.1). Accordingly, the electrical conductivity σ (Ώ

^{-1}cm

^{-1} ) is analytically represented by:

where A

_{x} and σ

_{x} are functions of the composition x in isobutyric acid along the coexistence curve. The coefficient σ

_{x} is the limit of electrical conductivity σ at the phase separation temperature T

_{t}. This result is interesting, showing the linearity of the electrical conductivity with temperature. In this case the electrical conductivity does not exhibit any critical anomaly and it presents a regular behavior. In order to fit the data according to equation (6), we used the program origin 3.5. The results of this fit are given in

Table 1.

**Table 1.**
Results of fitting of data from

figure 1 using relation (6). The parameter values of A

_{x} and σ

_{x} are expressed in Ω

^{-1}cm

^{-1}K

^{-1} and Ω

^{-1}cm

^{-1} respectively. T

_{t} is the experimental transition temperature of each composition X % in isobutyric acid.

**Table 1.**
Results of fitting of data from figure 1 using relation (6). The parameter values of A_{x} and σ_{x} are expressed in Ω^{-1}cm^{-1}K^{-1} and Ω^{-1}cm^{-1} respectively. T_{t} is the experimental transition temperature of each composition X % in isobutyric acid.
X% in acid | (I-W) | (I-W) + 5 10^{-4} M [KCl] | (I-W) + 5 10^{-3} M [KCl] |
---|

T_{t} (°C) | σ_{x} | A_{x}10^{+3} | T_{t} (°C) | σ_{x} | A_{x}10^{+3} | T_{t} (°C) | σ_{x} | A_{x}10^{+3} |
---|

15 | | | | 15.063 | -3.58 | 15.68 | | | |

16 | 19.992 | -3.23 | 14.27 | | | | | | |

18 | | | | 18.820 | -3.48 | 15.09 | | | |

18.5 | | | | | | | 17.125 | -5.91 | 24.82 |

20 | 22.842 | -2.78 | 12.42 | | | | | | |

22 | 23.527 | -2.85 | 11.96 | 22.710 | -3.29 | 14.18 | | | |

25 | 25.547 | -2.58 | 11.34 | | | | | | |

27.5 | | | - | | | | 26.649 | -4.93 | 20.51 |

29 | | | | 26.353 | -2.56 | 11.09 | | | |

30 | 26.930 | -2.26 | 10.9 | | | | | | |

32 | | | | 27.014 | -2.31 | 9.9 | | | |

32.5 | 27.057 | -2.46 | 10.7 | | | | 28.021 | -3.88 | 16.39 |

35 | 26.962 | -2.79 | 10.34 | | | | | | |

38 | 26.945 | -2.67 | 10.17 | 27.356 | -1.69 | 7.52 | 28.516 | -3.58 | 14.78 |

40 | 26.904 | -2.66 | 10.12 | | | | 28.091 | -3.61 | 14.1 |

42 | | | | 27.018 | -1.46 | 6.24 | | | |

43 | 26.841 | -2.72 | 10.06 | | | | | | |

46 | 26.750 | -2.71 | 10.03 | | | | | | |

47 | | | | | | | 28.012 | -3.14 | 12.37 |

50 | 26.217 | -2.88 | 10.02 | | | | | | |

55 | | | | 24.803 | -0.871 | 3.52 | 27.645 | -2.72 | 10.31 |

57 | 23.520 | -2.83 | 10.01 | | | | | | |

62.5 | | | | | | | 21.984 | -1.01 | |

65 | | | | 14.390 | -0.46 | 1.84 | | | |

-The results of the work show that in the neighbourhood of the transition temperature T

_{t}, the electrical conductivity σ does not show any anomaly, where as the transport properties of ions in binary liquids exhibit intriguing anomalies near a consolute critical point [

9].

-The coefficient A_{x} of Eq.6 shows two distinct domains for the composition X for the system (I-W). The region 1 with X ≤ 26% has a composition which is poor in acid. the average of A_{x} is around 13.51 μΩ^{-1}cm^{-1}K^{-1}.The region 2 with X ≥ 26% has a composition which is rich in acid . The coefficient of A_{x} is around 10.31 μΩ^{-1}cm^{-1}K^{-1}.

-When the KCl salt is added at the concentration 5 10^{-4} and 5 10^{-3} mol per kilogram of mixture, A_{x} is higher in the first region than in the system without ions. This increasing is due to the solvatation of ions by water. For X=22%; we have:

A

_{x} (I-W) =11.96 μΩ

^{-1}cm

^{-1}K

^{-1} and A

_{x} (I-W +510

^{-4} M [KCl] ) =14.18 μΩ

^{-1}cm

^{-1}K

^{-1} . It is obvious, the electrical conductivity depends well of solvation phenomenon in binary fluid [

10]. However, the coefficient A

_{x} can be determined by the derivation of σ, according to :

This has given us a possibility to build the two graphs of

fig. 2 and

fig. 3, presenting the behavior of the derivative ∂σ/∂T with the composition X of the acid isobutyric.

Figure 2 presents our experimental data for the derivation ∂σ/∂T as a function of X(%) in acid of the pure system (I-W) without ions (K

^{+}, Cl

^{-}). The composition X has a significant effect on ∂σ/∂T. The thermal derivative decreases rapidly as X increases. A very good fit to our experimental results is obtained (dashed line in fig. 2). The derivation ∂σ/∂T can be related to the composition X by the equation:

**Figure 2.**
Thermal derivative ∂σ/∂T vs composition X of acid for the mixture isobutyric acid – water (I-W). Dashed line represents the theoretical behavior, in the poor region of acid, ∂σ/∂T decreases rapidly.

**Figure 2.**
Thermal derivative ∂σ/∂T vs composition X of acid for the mixture isobutyric acid – water (I-W). Dashed line represents the theoretical behavior, in the poor region of acid, ∂σ/∂T decreases rapidly.

**Figure 3.**
Thermal derivative ∂σ/∂T as a function of X composition in acid, showing the influence of the concentration of (K^{+}, Cl^{-}) ions.

**Figure 3.**
Thermal derivative ∂σ/∂T as a function of X composition in acid, showing the influence of the concentration of (K^{+}, Cl^{-}) ions.

Parameters (∂σ/∂T)_{0}, A, B and Y are normalized by the fit as : (∂σ/∂T)_{0} = 9.603 Ω^{-1}cm^{-1}K^{-1}; A = 357.158 and B = 3.686 ; Y = 5.035.

Figure 3 shows the influence of the KCl salt on the thermal derivative of the electrical conductivity ∂σ/∂T which increases with the concentration of ions (K

^{+}, Cl

^{-}). For the critical composition X

_{c}, we have the following comparison:

- (i)
( ∂σ/∂T )_{(I-W) + 5 10}^{-4} _{M [KCl]} = 7.52 10^{-3} Ω^{-1}cm^{-1}K^{-1}

- (ii)
( ∂σ/∂T )_{(I-W) + 5 10}^{-3} _{M [KCl]} = 14.78 10^{-3} Ω^{-1}cm^{-1}K^{-1}

However, the dependence of ionic concentration of (K

^{+}, Cl

^{-}) on the derivative ∂σ/∂T can be seen clearly in

figure 3. Also ∂σ/∂T decreases when the composition X of the isobutyric acid is elevated.