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Surface Tension–Concentration Relationship for Solutions (Gibbs Equation)
EXPERIMENT
73
Surface Tension-Concentration Relationship for Solutions (Gibbs Equation) Discussion The positive adsorption of a solute by a suitable adsorbent decreases the surface (or interfacial) tension; negatively adsorbed solutes (e.g. salts) causing an increase. For the special case of a very dilute solution of a non-ionic surface-active substance, the quantitative relationship between concentration, adsorption, and change of surface tension is given by the Gibbs adsorption equation: Γ =
— a dy - ^ RTda
— c dy BTdc
(1)
where Γ is the mass of solute adsorbed per unit area of surface from a solution of concentration c (activity a) and surface tension y. Hence if the surface tension of a liquid is measured at constant temperature for various concentrations dy/dc may be obtained for any concentration from the tangents to the graph of y vs. c. The various Γ values may then be calculated from equation (1). The value of Γ tends to a limit at the higher concentrations and this limiting value Yu can be estimated. The reciprocal value IfYu can be calculated, hence the area A, in the surface per molecule of adsorbed solute may be calculated from 1 A = (2) NYLt where N is Avogadro's number. The surface tension may be measured with a du Nouy tensiometer with which the pull on a platinum ring due to surface tension is measured with a torsion balance. The detachment force is related to the surface (or interfacial) tension by the expression y = -—
(3)
477T
where / is the pull (in dynes) on the ring, r is the mean radius of the ring and ß is a correction factor. The factor ß allows for the nonvertical direction of the tension forces and for the complex shape of 198
Surface Tension-Concentration Relationship for Solutions (Gibbs Equation)
199
the liquid supported by the ring at the point of detachment. It thus depends on the dimensions of the ring and the nature of the interface. For simplicity in this experiment ß may be assumed to have the value unity. Apparatus and Chemicals Du Nouy tensiometer, amyl alcohol. Method A 0-1 M solution of n-amyl alcohol is made containing 1-08 ml of alcohol per 100 ml of solution and from this solution 0-08 M, 0-04 M, 0-02 M and 0-01 M solutions are prepared by dilution. The surface tensions of pure n-amyl alcohol, water and the solutions are measured. The temperature is recorded. A graph is then plotted of surface tension γ vs. concentration c, and a smooth curve drawn through these points. Tangents are then con structed at concentrations 0-01, 0-02, 0*04, 0-06 and 0-08 M, and the values of dy/dc determined at these points. Values of Γ are then calculated from equation (1) and a graph of these Γ values plotted against the appropriate concentrations of the amyl alcohol solutions. The limiting value Yu can then be estimated and the reciprocal 1/ΓΖΛ calculated. The value of l/Γ is calculated for each experimental concentration and hence the area per molecule A is found. A graph of Π against A is plotted where Π is the surface pressure (yH 2 o—y solution)· If ^ e results fit the equation Y[{A-A0) the value of AQ should be calculated.
= kT
73
Surface Tension-Concentration Relationship for Solutions (Gibbs Equation) Discussion The positive adsorption of a solute by a suitable adsorbent decreases the surface (or interfacial) tension; negatively adsorbed solutes (e.g. salts) causing an increase. For the special case of a very dilute solution of a non-ionic surface-active substance, the quantitative relationship between concentration, adsorption, and change of surface tension is given by the Gibbs adsorption equation: Γ =
— a dy - ^ RTda
— c dy BTdc
(1)
where Γ is the mass of solute adsorbed per unit area of surface from a solution of concentration c (activity a) and surface tension y. Hence if the surface tension of a liquid is measured at constant temperature for various concentrations dy/dc may be obtained for any concentration from the tangents to the graph of y vs. c. The various Γ values may then be calculated from equation (1). The value of Γ tends to a limit at the higher concentrations and this limiting value Yu can be estimated. The reciprocal value IfYu can be calculated, hence the area A, in the surface per molecule of adsorbed solute may be calculated from 1 A = (2) NYLt where N is Avogadro's number. The surface tension may be measured with a du Nouy tensiometer with which the pull on a platinum ring due to surface tension is measured with a torsion balance. The detachment force is related to the surface (or interfacial) tension by the expression y = -—
(3)
477T
where / is the pull (in dynes) on the ring, r is the mean radius of the ring and ß is a correction factor. The factor ß allows for the nonvertical direction of the tension forces and for the complex shape of 198
Surface Tension-Concentration Relationship for Solutions (Gibbs Equation)
199
the liquid supported by the ring at the point of detachment. It thus depends on the dimensions of the ring and the nature of the interface. For simplicity in this experiment ß may be assumed to have the value unity. Apparatus and Chemicals Du Nouy tensiometer, amyl alcohol. Method A 0-1 M solution of n-amyl alcohol is made containing 1-08 ml of alcohol per 100 ml of solution and from this solution 0-08 M, 0-04 M, 0-02 M and 0-01 M solutions are prepared by dilution. The surface tensions of pure n-amyl alcohol, water and the solutions are measured. The temperature is recorded. A graph is then plotted of surface tension γ vs. concentration c, and a smooth curve drawn through these points. Tangents are then con structed at concentrations 0-01, 0-02, 0*04, 0-06 and 0-08 M, and the values of dy/dc determined at these points. Values of Γ are then calculated from equation (1) and a graph of these Γ values plotted against the appropriate concentrations of the amyl alcohol solutions. The limiting value Yu can then be estimated and the reciprocal 1/ΓΖΛ calculated. The value of l/Γ is calculated for each experimental concentration and hence the area per molecule A is found. A graph of Π against A is plotted where Π is the surface pressure (yH 2 o—y solution)· If ^ e results fit the equation Y[{A-A0) the value of AQ should be calculated.
= kT