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!

 

[eljose79]

Hi there,

For part 1, to find the volume of the molecule, you can use the formula V = lwh, where l is the length of the alkyl chain (44.1 armstrong), w is the width of the molecule (which can be calculated by multiplying the number of carbon atoms in the chain by the bond length of 1.54 armstrong), and h is the height of the molecule (which can be calculated by multiplying the number of carbon atoms in the chain by the bond length of 1.54 armstrong and then dividing by the cosine of 35 degrees). Once you have the volume, you can divide it by the density (0.87 g/cm3) to get the cross sectional area.

For part 2, to calculate the surface excess, you can use the formula surface excess = (surface tension x concentration)/(RT), where R is the gas constant and T is the temperature in Kelvin. Once you have the surface excess, you can divide it by the area per molecule (calculated in part 1) to get the number of molecules at the air/water interface. To find the number of EO groups, you can divide the area per molecule of the small molecule surfactant (0.55 x 10-18 m2) by the area per EO segment (which is assumed to be the same for both surfactants) and then multiply by the number of molecules at the air/water interface. This will give you an estimate of the number of EO groups in the polymeric surfactant.

 

[charng]

To find the effective cross sectional area of a molecule in a monolayer film, we need to consider the density of the film as well as the surface tension of the solution.

For the first question, you have correctly calculated the length of the hydrocarbon chain standing upright above the film. To find the volume of the molecule, we can use the formula: Volume = length x cross sectional area. Using the density of the film, we can then calculate the mass of the molecule using the formula: Mass = density x volume. Finally, we can use the mass and the length of the alkyl chain to calculate the cross sectional area of the molecule using the formula: Cross sectional area = mass/length.

For the second question, we can use the Gibbs equation to calculate the surface excess of the surfactant at each concentration. Then, we can use the formula: Surface excess = number of molecules/area to calculate the area per molecule at the air/water interface. To estimate the number of EO groups in the polymeric surfactant, we can use the fact that the area per EO segment is the same for the two surfactants in their saturated monolayers and solve for the number of EO groups.

 

[charng]

1) To find the effective cross sectional area of a molecule in a monolayer film, you can use the formula: cross sectional area = volume/length of alkyl chain. Since you already have the length of the alkyl chain (44.1 Å), you just need to find the volume of the molecule. To do this, you can use the density of the film (0.87 g/cm3) and the molecular weight of the acid (448.7 g/mol) to calculate the volume using the formula: volume = mass/density. Once you have the volume, you can plug it into the formula to find the cross sectional area of the molecule.

2) Part 1: To calculate the surface excess of the surfactant, you can use the given values of surface tension and the Gibbs equation: surface excess = -dy/(RTdlnC). Using the given concentrations and surface tensions, you can calculate the surface excess for each concentration. Then, you can plot the surface excess versus concentration and extrapolate the graph to find the surface excess at a concentration of 0 (just below the critical micelle concentration). This value will give you the surface excess of the surfactant at the air/water interface. To calculate the area per molecule, you can use the formula: area per molecule = surface excess/number of molecules per unit area. The number of molecules per unit area can be calculated using Avogadro's number and the molar mass of the surfactant.

Part 2: To estimate the number of EO groups in the polymeric surfactant, you can use the given area per molecule (0.55 x 10-18 m2) and the area per EO segment (assuming it is the same for both surfactants). The ratio of these two areas will give you the number of EO segments in the polymeric surfactant molecule.