Determination of Surface Tension of Mercury by Quincke's Method
1. Aim
To determine the surface tension of mercury using Quincke's method of capillary depression.
2. Apparatus Used
- Quincke's apparatus consisting of two glass tubes of different diameters (one wide and one capillary tube) connected at the bottom
- Traveling microscope with vernier scale
- Mercury
- Leveling screw
- Spirit level
- Thermometer
- Meter scale
- Magnifying glass
- Clean, dry cloth
- Distilled water (for cleaning)
3. Diagram
4. Theory
Quincke's method is based on the principle of capillary depression. When a liquid does not wet the walls of a capillary tube (as is the case with mercury), there is a depression in the level of the liquid in the capillary tube compared to its level in a wide tube.
The surface tension of a liquid is related to this depression by the following theory:
When a liquid comes in contact with a solid surface, the interaction between the molecules of the liquid and the solid determines whether the liquid will wet the surface or not. In the case of mercury, the cohesive forces between mercury molecules are stronger than the adhesive forces between mercury and glass. This causes mercury to form a convex meniscus in a glass tube.
In Quincke's apparatus, two tubes of different diameters are connected at the bottom. Mercury is filled in the apparatus, and due to the surface tension effect, the mercury level in the capillary tube is depressed below the level in the wider tube.
The pressure difference across a curved liquid surface is given by Laplace's equation:
\[ P = T\left(\frac{1}{R_1} + \frac{1}{R_2}\right) \]
where:
- \(P\) is the pressure difference
- \(T\) is the surface tension
- \(R_1\) and \(R_2\) are the principal radii of curvature of the liquid surface
For a spherical meniscus in a capillary tube, \(R_1 = R_2 = R\), and the equation simplifies to:
\[ P = \frac{2T}{R} \]
The pressure difference is also related to the height difference by the hydrostatic pressure equation:
\[ P = \rho g h \]
where:
- \(\rho\) is the density of mercury
- \(g\) is the acceleration due to gravity
- \(h\) is the depression in the capillary tube
Combining these equations and considering the geometry of the meniscus in the capillary tube, we get the formula for calculating surface tension.
5. Formula
The surface tension (T) of mercury is given by:
\[ T = \frac{1}{2}\rho g h r \]
where:
- \(T\) is the surface tension of mercury (N/m)
- \(\rho\) is the density of mercury (13.6 × 10³ kg/m³)
- \(g\) is the acceleration due to gravity (9.8 m/s²)
- \(h\) is the depression in the level of mercury in the capillary tube (m)
- \(r\) is the radius of the capillary tube (m)
6. Procedure
- Clean the Quincke's apparatus thoroughly using distilled water and dry it completely.
- Set up the apparatus vertically with the help of a spirit level and leveling screws.
- Fill the apparatus with mercury carefully until it reaches an appropriate level in both tubes.
- Allow the system to stabilize for a few minutes.
- Mount the traveling microscope on a stable stand and adjust it to clearly view the mercury levels in both tubes.
- Focus the microscope on the mercury level in the wider tube and note the reading.
- Without changing the horizontal position of the microscope, move it vertically to focus on the mercury level in the capillary tube and note the reading.
- Calculate the difference between the two readings to determine the depression (h).
- Measure the radius of the capillary tube using a suitable method (pre-calibrated or using a micrometer).
- Record the room temperature using a thermometer.
- Repeat steps 6-8 for at least five different positions of the mercury levels by adjusting the amount of mercury in the apparatus.
- Calculate the surface tension using the formula given.
7. Observation Table
Table 1: Measurement of Depression (h)
| Observation | Reading of mercury level in wide tube (mm) | Reading of mercury level in capillary tube (mm) | Depression, h (mm) |
|---|---|---|---|
| 1 | |||
| 2 | |||
| 3 | |||
| 4 | |||
| 5 |
Mean value of depression (h) = ________ mm = ________ m
Table 2: Physical Constants
| Constant | Value |
|---|---|
| Radius of capillary tube (r) | ________ mm = ________ m |
| Density of mercury (ρ) | 13.6 × 10³ kg/m³ |
| Acceleration due to gravity (g) | 9.8 m/s² |
| Room temperature | ________ °C |
8. Calculations
Substituting the measured values in the formula:
\[ T = \frac{1}{2}\rho g h r \]
\[ T = \frac{1}{2} \times (13.6 \times 10^3 \text{ kg/m}^3) \times (9.8 \text{ m/s}^2) \times (h \text{ in m}) \times (r \text{ in m}) \]
\[ T = 66,640 \times h \times r \text{ N/m} \]
Sample Calculation:
If h = ________ m and r = ________ m
\[ T = 66,640 \times (\_\_\_\_\_\_) \times (\_\_\_\_\_\_) = \_\_\_\_\_\_ \text{ N/m} \]
9. Result
The surface tension of mercury at ________ °C is ________ N/m.
10. Precautions
- Handle mercury with extreme care as it is toxic. Avoid skin contact and inhalation of mercury vapor.
- Ensure the apparatus is thoroughly cleaned and dried before use.
- Set up the apparatus vertically using a spirit level to avoid parallax errors.
- Allow the mercury levels to stabilize before taking readings.
- Ensure there are no air bubbles in the mercury column.
- Take multiple readings and calculate the mean value for more accurate results.
- Record the temperature as surface tension is temperature-dependent.
- Make sure the capillary tube is uniform throughout its length.
- Handle the traveling microscope carefully to avoid disturbing the experimental setup.
- In case of a mercury spill, follow appropriate cleanup procedures and dispose of mercury waste properly.
- Clean the apparatus thoroughly after the experiment.
- Keep the laboratory well-ventilated when working with mercury.
11. Viva Voce Questions
Q: What is surface tension?
A: Surface tension is the property of a liquid surface that makes it behave like an elastic sheet or membrane under tension. It is caused by the cohesive forces between liquid molecules and is measured as force per unit length (N/m).
Q: Why does mercury form a convex meniscus in a glass tube?
A: Mercury forms a convex meniscus because the cohesive forces between mercury molecules are stronger than the adhesive forces between mercury and glass. This results in mercury not wetting the glass surface and forming a rounded or convex surface.
Q: How does temperature affect the surface tension of mercury?
A: Surface tension generally decreases with increasing temperature. As temperature rises, the kinetic energy of molecules increases, reducing the cohesive forces between them and thereby lowering the surface tension.
Q: Why is Quincke's method suitable for measuring the surface tension of mercury?
A: Quincke's method is suitable for measuring the surface tension of non-wetting liquids like mercury because it takes advantage of the capillary depression phenomenon, which is more pronounced and easier to measure for mercury compared to other methods.
Q: What is the significance of the radius of the capillary tube in this experiment?
A: The radius of the capillary tube directly affects the capillary depression. A smaller radius results in a greater depression, making the measurement more accurate. The radius is a crucial parameter in the formula for calculating surface tension.
Q: How does the density of mercury affect the measurement?
A: The density of mercury directly affects the hydrostatic pressure and thus the capillary depression. A higher density results in a greater pressure difference for the same height, which influences the surface tension calculation.
Q: What are the sources of error in Quincke's method?
A: Sources of error include parallax errors in reading the mercury levels, impurities in mercury, variations in the capillary tube radius, temperature fluctuations, vibrations, and errors in measuring the depression height.
Q: How can you improve the accuracy of this experiment?
A: Accuracy can be improved by using a clean capillary tube of uniform diameter, taking multiple readings, controlling the temperature, using a more precise measuring instrument like a cathetometer, and ensuring the apparatus is perfectly vertical.
Q: Why is mercury commonly used in scientific instruments despite its toxicity?
A: Mercury is used because of its unique properties such as being liquid at room temperature, high density, excellent electrical conductivity, uniform thermal expansion, and not wetting glass surfaces, which make it valuable for instruments like thermometers, barometers, and manometers.
Q: What safety precautions should be taken when working with mercury?
A: Safety precautions include wearing protective gloves, working in a well-ventilated area, avoiding direct skin contact, using a spill kit for cleanup, proper disposal of mercury waste, and thorough hand washing after the experiment.