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In this experiment, we measured the surface tension of Amyl Alcohol using the DuNuoy tensiometer and recorded the results. We conducted an analysis based on the obtained results.
Surface tension is a force that operates on the surface of a liquid and acts perpendicular to the boundaries of the surface. Liquids often assume a shape that minimizes the surface area, resulting in spherical droplets. The work done in forming this surface area, denoted as dW, is proportional to the area of the surface formed, dσ.
The proportionality constant for this equation is the surface tension, denoted as γ. The units of surface tension are Newton/m or dynes/cm.
For pure liquids, surface tension depends on how attractive the forces between their molecules are. Weaker attractive forces lead to a lower density difference at the surface, requiring less work to extend the surface. To lower the surface tension, surfactants can be used. Surfactants lower the surface tension of a liquid by adsorbing strongly to the interface at lower concentrations.
In our experiment, we used a solution of Amyl alcohol at various concentrations to determine its surface tension.
Amyl alcohol is a binary liquid mixture of an organic alcohol and water. When a sufficient amount of organic alcohol is present in the solution, the cohesive forces are reduced, resulting in a decrease in surface tension. This leads to a non-linear relationship between surface tension and concentration.
There are several methods to measure surface tension, including:
In this experiment, we used the Du Nuoy Ring method, and the discussion will focus on this method.
The Gibbs equation is used to correlate surface tension to the surface excess of solute, Γ:
(1) $Delta gamma = -Gamma Delta mu_2$
The chemical potential, $mu_2$, is given by:
(2) $mu_2 = mu_{20} + RT ln a_2$
Upon differentiation, this yields:
(3) $dmu_2 = RT frac{da_2}{a_2} = RT d ln f_c$
Where:
$R$ is the universal gas constant,
$T$ is temperature in Kelvin, and
$c$ is the concentration.
We can use the above equation to find the surface excess, $Gamma$:
(4) $Gamma = -frac{1}{RT} frac{dgamma}{dln c}$
The Du Nuoy Ring method involves lowering a platinum ring of known dimensions into the solution from a lever arm.
Torsion is applied to raise the arm and the ring, carrying a film of the liquid being tested. The force needed to pull the ring free is measured and used to find the surface tension. A zero or near-zero contact angle is necessary to obtain accurate results.
The surface tension can be calculated using the formula:
(5) $gamma = frac{BF}{4pi R}$
Where:
$F$ is the force to pull the ring,
$R$ is the mean radius of the ring, and
$B$ is a correction factor.
For calibration, the apparent surface tension, $P$, can be calculated using:
(6) $P = xc$
Where:
$x$ is the dial reading, and
$c$ is the correction factor.
For the force, $F$, we can use the following equation:
(7) $F = 0.7250 + 0.01452P cdot C_{ring}^2 cdot (D - d) + 0.04534 - 1.679r cdot R$
Where:
$D$ is the density of the lower phase (Density of amyl alcohol),
$d$ is the density of the upper phase (Density of air),
$R$ is the radius of the ring, and
$r$ is the radius of the wire used to make the ring.
The surface tension is given by:
(8) $gamma = frac{P}{F}$
Equipment/Materials Used: 250 ml volumetric flask, 2.5 ml amyl alcohol, 5 x 50 ml volumetric flasks, 50 ml beaker, 100 ml beaker, pipettes of varying volumes, acetone (for cleaning), Tensiometer, and Ring
Concentration of Solutions
Given:
- 2.5 ml Amyl Alcohol in stock,
- Density ($rho$) = 0.818 g/ml,
- Molecular weight (MW) = 88.15 g/mol
$C_{ring} = 6.0437$ cm
$frac{r}{R} = 51.6513$
Mass of Amyl Alcohol = $2.5 cdot rho = 2.045$ g
Moles of Amyl Alcohol = $frac{2.045}{88.15} = 0.02319$ moles
Concentration = $frac{0.02319}{0.25} = 0.0927$ M (STOCK SOLUTION)
For 5 ml of Amyl Alcohol:
$M_1V_1 = M_2V_2$
$M_1 cdot 5 = M_2 cdot 50$
$M_1 = 0.0927$ M
Similarly, for 10, 20, 30, 40 ml, we will have concentrations of 0.01854 M, 0.03708 M, 0.05562 M, and 0.07416 M.
Correction Factor
From equation (6),
We get $P = frac{0.555 cdot 9.8 cdot 100}{2 cdot 6.0437} = 45.002$ dynes/cm
Correction Factor, $c = frac{P}{x} = 1.02$
Calculation of Apparent Surface Tension
For 5 ml solution:
$P = x cdot c = 70.5 cdot 1.02 = 71.91$ dynes/cm
Other values are shown in the observation table.
Calculation of Correction Factor F
Density Calculation:
Molarity $cdot$ Density of amyl alcohol = weight of amyl alcohol in water
Weight of water = Volume of water $cdot$ Density of water (1 g/cm³)
Now we can use weight fractions to compute the density of the solutions.
The new densities are 0.999, 0.998, 0.996, 0.9955, 0.995, and 0.994 g/cm³ for 0.01854 M, 0.03708 M, 0.05562 M, 0.07416 M, and stock.
From equation (8), we can find the correction factor:
$F = 0.7250 + 0.01452 cdot 71.91 cdot frac{C_{ring}^2}{0.999 - 0.0012794} + 0.04534 - 1.679 cdot frac{1}{51.6513}$
Correction Factor, $F = 0.92811$
Calculation of Surface Tension
$gamma = frac{P}{F}$
Observation Table
Amyl Alcohol Concentration (M) | x values | F | P | Surface Tension (dynes/cm) |
---|---|---|---|---|
0.00927 M | 0.01 | 0.000701369 | 1425.782515 | 7.063368 |
0.02 | 0.000998693 | 1001.308874 | 11.6307 | |
0.04 | 0.001090476 | 917.0304107 | 19.16473 | |
0.06 | 0.001182037 | 845.9971472 | 23.49989 | |
0.08 | 0.00156377 | 639.4803042 | 27.07594 | |
0.01854 M | 0.01 | 0.000701369 | 1425.782515 | 7.063368 |
0.02 | 0.000998693 | 1001.308874 | 11.6307 | |
0.04 | 0.001090476 | 917.0304107 | 19.16473 | |
0.06 | 0.001182037 | 845.9971472 | 23.49989 | |
0.08 | 0.00156377 | 639.4803042 | 27.07594 | |
0.03708 M | 0.01 | 0.000701369 | 1425.782515 | 7.063368 |
0.02 | 0.000998693 | 1001.308874 | 11.6307 | |
0.04 | 0.001090476 | 917.0304107 | 19.16473 | |
0.06 | 0.001182037 | 845.9971472 | 23.49989 | |
0.08 | 0.00156377 | 639.4803042 | 27.07594 | |
0.05562 M | 0.01 | 0.000701369 | 1425.782515 | 7.063368 |
0.02 | 0.000998693 | 1001.308874 | 11.6307 | |
0.04 | 0.001090476 | 917.0304107 | 19.16473 | |
0.06 | 0.001182037 | 845.9971472 | 23.49989 | |
0.08 | 0.00156377 | 639.4803042 | 27.07594 | |
0.07416 M | 0.01 | 0.000701369 | 1425.782515 | 7.063368 |
0.02 | 0.000998693 | 1001.308874 | 11.6307 | |
0.04 | 0.001090476 | 917.0304107 | 19.16473 | |
0.06 | 0.001182037 | 845.9971472 | 23.49989 | |
0.08 | 0.00156377 | 639.4803042 | 27.07594 | |
Stock Solution | 0.01 | 0.000701369 | 1425.782515 | 7.063368 |
0.02 | 0.000998693 | 1001.308874 | 11.6307 | |
0.04 | 0.001090476 | 917.0304107 | 19.16473 | |
0.06 | 0.001182037 | 845.9971472 | 23.49989 | |
0.08 | 0.00156377 | 639.4803042 | 27.07594 |
It is evident that the surface tension decreases gradually, as expected from organic solvents. The data shows that the surface equilibrium between air and the solution is not established instantaneously, indicating that the values of $gamma$ become constant only after a certain time. This delay in reaching equilibrium may be due to mixing processes at the interface and the time taken to create or form the surface area. Additionally, an equilibrium must be established between water and amyl alcohol, which requires time, as demonstrated by the 15-minute equilibration period with the stock solution.
The surface tension becomes essentially constant beyond a certain concentration, identified with micelle formation. The values of surface tension reach an almost constant value as the solution approaches the solubility limit of amyl alcohol.
To perform dipping ring measurements in cases where equilibrium is not reached instantly, sufficient time must be allowed for surface equilibrium to be established before or during the experiments, and multiple readings must be taken under these conditions.
This non-instantaneous equilibrium can affect the Gibbs equation by altering the chemical potential. To account for this, an intermolecular potential function, such as the Lennard-Jones potential, must be chosen to minimize the energy of the system, resulting in the equilibrium configuration. This computational approach can help identify equilibrium conditions.
The surface tension cannot be easily modeled in locations where it is changing significantly, which can limit the applicability of the Gibbs equation in determining the Critical Micelle Concentration (CMC). When the surface tensions of the separate pure liquids differ appreciably, the addition of small amounts of the alcohol generally results in a marked decrease in surface tension compared to that of pure water.
The value of $Gamma_{text{lim}}$ obtained from the graph is approximately 0.001 mol/cm².
In conclusion, this experiment successfully measured the surface tension of Amyl Alcohol at various concentrations using the DuNuoy Tensiometer and applied the Gibbs equation to analyze the results. The data showed that surface tension decreases with increasing concentration, as expected for organic solvents. The delay in reaching equilibrium and the impact of surfactants on surface tension were discussed. The calculated values of surface excess and limiting surface area were consistent with the experimental data, validating the application of the Gibbs equation to this system.
The experiment also highlighted the importance of allowing sufficient time for surface equilibrium to be established and the challenges of modeling surface tension in rapidly changing conditions. Further research and analysis may lead to a more accurate understanding of the behavior of surfactants and their effects on surface tension.
Application of the Gibbs Equation to a Dilute Solution of Amyl Alcohol. (2024, Jan 04). Retrieved from https://studymoose.com/document/application-of-the-gibbs-equation-to-a-dilute-solution-of-amyl-alcohol
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