How Does Surface Tension Relate to Phenol Concentrations in Aqueous Solutions?

In summary, to estimate the fraction of the surface covered by phenol at a given concentration range, you can use the surface excess concentration and the surface area of a phenol molecule.
  • #1
KatrinaM
2
0

Homework Statement



cphenol/mole dm−3 0.05 0.08 0.127 0.268 0.496
γ/mN m−1 67.88 64.60 60.10 51.58 44.97

Estimate the relative surface excess concentrations of phenol in the concentration
ranges of (i) 0.05 to 0.08 mole/dm3 and (ii) 0.268 to 0.496 mole/dm3 at
the surface of an aqueous solution from the following data taken at 293 K
Given that the cross section of a phenol molecule is about 0.4 nm2 estimate
what fraction of the surface is covered by phenol at the higher of the two
concentration ranges.


Homework Equations


dγ = − ΓRTd ln c, where lambda is the surface excess concentration of phenol relative to that of water, gamma is the surface tension, and c the concentration of phenol
the surface excess concentration of component phenol equals the number of moles of surface excess quantities divided by the surface area



The Attempt at a Solution


Basically I worked out the first question, getting answers of 2.8E-6 mol/m^2 and 4.41E-6 mol m^-2, but I have little idea on how to answer the last question. I tried to work backwards, I'm guessing it has something to do with working out the number of moles of phenol per m^2 of the surface and multiplying by the surface area of a phenol molecule, but I'm not sure how to calculate that, and I'd be grateful if you give a hint in the right direction.
 
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  • #2


To estimate the fraction of the surface covered by phenol at the higher concentration range, you can use the following formula:

λ = (n/N)A

Where:
λ is the surface excess concentration of phenol relative to that of water
n is the number of moles of phenol at the higher concentration range (0.496 mol/dm^3)
N is the number of moles of water at the higher concentration range (0.496 mol/dm^3)
A is the surface area of a phenol molecule (0.4 nm^2)

You can calculate N by using the ideal gas law:

N = PV/RT

Where:
P is the pressure (1 atm)
V is the volume of the solution (1 dm^3)
R is the gas constant (0.0821 L atm/mol K)
T is the temperature (293 K)

Once you have calculated λ, you can then use the following formula to estimate the fraction of the surface covered by phenol:

Fraction of surface covered = λ * A

This will give you the fraction of the surface covered by phenol at the higher concentration range. Repeat the calculations for the lower concentration range to compare the two values.
 

Related to How Does Surface Tension Relate to Phenol Concentrations in Aqueous Solutions?

1. What is surface tension?

Surface tension is a physical property of liquids that describes the force present at the surface of a liquid due to the attraction between its molecules. This force causes liquids to form droplets or gather in certain shapes, such as a water droplet on a surface.

2. How is surface tension measured?

Surface tension is typically measured in units of force per unit length, such as newtons per meter. One common method of measuring surface tension is by using a tensiometer, which measures the force required to pull a small, thin loop of wire apart from the surface of a liquid.

3. What factors affect surface tension?

The surface tension of a liquid can be affected by a number of factors, including temperature, the presence of solutes, and the nature of the liquid's molecules. Generally, surface tension decreases as temperature increases, and it can also be reduced by the presence of certain substances, such as surfactants.

4. How does surface tension play a role in everyday life?

Surface tension is responsible for many everyday phenomena, such as the ability of insects to walk on water, the formation of water droplets on surfaces, and the shape of liquid drops. It also plays a role in industrial processes, such as coating and printing, and in the function of biological systems, such as the alveoli in our lungs.

5. Can surface tension be altered or controlled?

Yes, surface tension can be altered or controlled by changing factors such as temperature, adding surfactants, or using specialized techniques such as ultrasonic vibration. This can have practical applications in fields such as medicine, where altering surface tension can aid in drug delivery, and in engineering, where surface tension can be harnessed for the creation of self-cleaning surfaces.

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