How to find out the effective cross area of a molecule in a monolayer film?

[lovegood]

hi guys, i need some help with the following questions relating to cross sectional area. thanks in advance!

1) when n-hexatriacontanoic acid, CH3(CH2)34COOH was placed in water, a complete monomolecular film was formed. if the length of a carbon-carbon single bond in the chain is 1.54 amstrong, and each bond makes an angle of 35degrees with the vertical, calculate the effective cross sectional area of a molecule of the acid in the film. density of the film is 0.87g/cm3.

for this question, i managed to find out the length of each carbon-carbon single bond via trigo formula, and from there, i calculated the length of the hydrocarbon chain standing upright above the film, which was found to be 44.1 armstrong. however, I am not sure how to make use of the density to find out the volume, as i would like to use the formula, vol/area=length of alkyl chain to obtain the cross sectional area.

2) part 1)
the adsorption of a non-ionic surface-active agent at the air surface of an aqueous solution obeys the gibbs equation, surface excess=-dy/(RTdlnc)

the values of the surface tension of an aqueous solution of a soluble polymeric surfactant at concentrations just below its critical micelle concentrations (10-3M) at 300K is are given as below.

Concentration/M Surface tension/mNm-1
5x10-5 37.4
1x10-4 36.5
5x10-4 34.4
1x10-3 33.9

use these data to calculate the surface excess of the surfactant and hence calculate the area per molecule at the air/water interface.

part 2) the hydrophilic part of polymeric surfactant in part 1 consists of a number of ethylene oxide (EO) segments. The area per molecule occupied by the small molecule surfactant C12H25(OC2H4)6OH just below its critical micelle concentration is 0.55 x 10-18 m2. Assuming that the area per EO segment is the same for the two surfactants in their saturated monolayers, estimate the number of EO groups in the polymeric surfactant.

Thanks!

 

[Jhero]

I'm happy to assist you with your questions regarding cross sectional area.

1) To calculate the effective cross sectional area of the molecule, we need to first calculate the volume of the molecule. This can be done by multiplying the length of the hydrocarbon chain (44.1 armstrong) by the cross sectional area of the molecule. The density of the film (0.87 g/cm3) can then be used to convert the volume to mass. From there, we can use the formula you mentioned, vol/area = length of alkyl chain, to calculate the cross sectional area.

2) For part 1, we can use the given data to plot a graph of surface tension vs. concentration. The slope of this graph will give us the surface excess of the surfactant. From there, we can use the Gibbs equation to calculate the area per molecule at the air/water interface.

For part 2, we can use the given area per molecule of the small molecule surfactant to estimate the number of ethylene oxide (EO) segments in the polymeric surfactant. We can assume that the area per EO segment is the same for both surfactants in their saturated monolayers, and use this to calculate the number of segments in the polymeric surfactant.

I hope this helps you with your questions. Let me know if you need any further clarification. Best of luck!