Surface Tension of Solutions

1. Surface Tension of Solutions Capillary Rise Method

2. Surface Tension • Molecules at surface are in an asymmetrical environment • No intermolecular forces above the surface to balance those below • Attractive intermolecular forces pull molecules to interior • Work must be done to increase the surface area

3. The mechanical work needed to increase the area of a film may be equated to the Gibbs free energy: dG = γdA Where γ is the surface tension, and therefore:

4. Separate the free energy into bulk and surface terms: GT = Gono+ GSA GT – total free energy G0 – molal free energy GS – surface free energy no - moles of liquid A – surface area Any heat associated with the expansion of the film is: dqrev = T dSS = TSSdA Where SS is the surface entropy/area. This leads to the temperature dependence of the surface tension:

5. Effect of Composition on γ At equilibrium the Gibbs-Duhem equation is applicable for both bulk and surface phases: n1 dμ1 + n2dμ2 = 0 n1’dμ1’ + n2’ dμ2’ + A dγ = 0 ni – moles of component i primes refer to surface phase At equilibrium the μ for each component must be the same in both phases: μ1 = μ1’ dμ1 = dμ1’ μ2 = μ2’ dμ2 = dμ2’

6. Thus: n1’dμ1 + n2’ dμ2 + A dγ = 0 and with appropriate substitution: n1’(n2/n1)dμ1 + n2’ dμ2 + A dγ = 0 And: RHS: number of moles of component 2 in excess in the surface phase compared to the bulk. This excess amount may be regarded as the amount absorbed in the surface phase, Γ2.

7. The chemical potential,at constant temperature, is related to the activity: μ2 = μeo + RT ln a2 dμ2 = RT dln a2 Thus: Define Γ2’ as the excess amount/unit surface area of component 2 in the surface phase over the bulk.

8. Thus: Γ2’ = Γ2/A And: In dilute solutions: a2C2 So:

9. Electrolytes usually increase the surface tension because of Coulombic attraction that draws the ions together and away from the surface. In dilute solution γ increases linearly with concentration. model assumes a ionic concentration of zero at the surface which increases linearly until it reaches a distance, xo, where bulk concentration, Co, is equaled. This length is xo = - Γ2’/Co Taking the activity to be equal to the concentration, the equation for the length becomes - Γ2’/2C’ for a 1:1 electrolyte with bulk concentration C’. The factor of two accounts for the fact that there are two moles of particles produced in solution for every one mole of NaCl.

10. Capillary Rise Method For a liquid that adheres to glass, the energy is lowest when a thin film covers as much glass as possible. This leads to curvature of the liquid inside. Curvature means pressure beneath the meniscus is less than atmospheric pressure by about 2γ/r where r is the radius of the tube.

11. Pressure exerted by the liquid column of height, h p = ρgh = 2γ/r Thus: Or: And for the case of a contact angle, θ The amount of liquid above the meniscus can be corrected for:

12. The contact angle arises from a balance of forces at the line of contact between the liquid and the solid. γsg = γsl + γlg cos θ And so: Liquid wets the surface if 0 < θc < 90o and “beads up” if θc = 180o

13. Procedure • A clean capillary is essential to the success of the experiment. It kept in distilled water. • Cleaning can be effected by soaking in hot nitric acid for several minutes and then thoroughly washing with distilled water. • The apparatus should be assembled according to the following figure:

15. Obtain the radius of the capillary by calibration with pure water. • Calculate r from known surface tension • Or use the equation • h is the height of the column of liquid in the capillary, and ρ is the density of the liquid. The reference liquid is designated by ref.

16. Measure the capillary rise. Assume a zero contact angle. • Take at least four readings, alternately allowing meniscus to approach the final position from above and below. • Be sure you have measured relative to the outside level. • If agreement is poor, clean the apparatus and repeat the experiment. • Repeat measurements using 0.8 M n-butanol solution.

17. Dilute to ¾ with distilled water and repeat. • Continue ¾ dilutions until you have made eight sets of measurments. Your last concentration should be 0.11 M. • Rinse the apparatus and capillary with fresh solution before beginning each new dilution measurement. • Repeat the experiments with NaCl solutions of approximately 4, 3, 2 and 1 M. • Thoroughly clean capillary and store under distilled water.

18. Data Analysis • There are several sources of error: • Major difficulty is absorption of surface active substances ( e.g. oil from skin ). • A 1 Co change in temperature will alter the value of γ by about 0.5% • Capillary radius may not be uniform along its length and would be about 3% for an uncalibrated tube.

19. Calculate capillary radius or calibration factor. If calculating r then use the equation that accounts for the amount of liquid above the meniscus. • Butanol solutions may be assumed to have the same density as water but the salt solutions densities should use Table XI-1. • Plot γ of the solution(s) vs. log C and find slope. • Calculate the surface concentration. • Calculate the “effective cross-sectional area” of the molecule.

20. For the NaCl solutions plot γ vs. the bulk concentration in mol/cm3. The slope will give the value of Γ2’/2C’. • Then calculate the “empty layer thickness”, xo. Note on cathetometer: