To Determine the Surface Tension of Water by Capillary Rise Method
1. Aim
To determine the surface tension of water by observing the capillary rise in glass tubes of different diameters.
2. Apparatus Used
- Capillary tubes of different internal diameters
- Traveling microscope
- Glass trough or beaker
- Distilled water
- Thermometer
- Screw gauge (to measure the diameter of capillary tubes)
- Clamp stand
- Clean cloth or tissue paper
- Spirit level
3. Diagram
Fig. 1: Experimental setup showing capillary tubes immersed in water with traveling microscope
4. Theory
Surface tension is a property of liquid surfaces that causes them to behave like elastic sheets. It is due to the cohesive forces among liquid molecules. Molecules at the surface experience a net inward force, which tries to minimize the surface area of the liquid.
When a capillary tube with a small internal diameter is placed in water, the water rises in the tube due to adhesive forces between the water and glass molecules. This phenomenon is known as capillary rise.
The adhesive forces cause the liquid to form a concave meniscus at the interface. The surface tension of the liquid creates an upward force that balances the weight of the liquid column in the capillary tube.
At equilibrium, the force due to surface tension balances the weight of the liquid column:
Force due to surface tension = Weight of liquid column
$ 2\pi r T\cos\theta = \pi r^2 h\rho g $
Where:
- $T$ = Surface tension of the liquid
- $r$ = Internal radius of the capillary tube
- $\theta$ = Contact angle between liquid and glass (for water and clean glass, $\theta \approx 0°$, so $\cos\theta \approx 1$)
- $h$ = Height of the liquid column in the capillary tube
- $\rho$ = Density of the liquid
- $g$ = Acceleration due to gravity
5. Formula
Rearranging the equation from the theory section, we get:
$ T = \frac{\rho g h r}{2\cos\theta} $
For water in a clean glass capillary tube, $\theta \approx 0°$, so $\cos\theta \approx 1$. Therefore:
$ T = \frac{\rho g h r}{2} $
Where:
- $T$ = Surface tension (N/m)
- $\rho$ = Density of water (kg/m³)
- $g$ = Acceleration due to gravity (9.8 m/s²)
- $h$ = Height of the water column (m)
- $r$ = Internal radius of the capillary tube (m)
We can also verify that the product $h·r$ is approximately constant for different capillary tubes.
6. Procedure
- Clean the capillary tubes thoroughly with soap solution followed by distilled water, and dry them completely.
- Measure the internal diameter of each capillary tube using a traveling microscope or screw gauge.
- Fill the glass trough or beaker with distilled water.
- Record the temperature of the water using a thermometer.
- Fix the capillary tubes vertically in a clamp stand so that their lower ends are immersed in water.
- Ensure that the tubes are perfectly vertical using a spirit level.
- Allow some time for the water to rise in the capillary tubes and reach equilibrium.
- Using a traveling microscope, measure the height of the water column from the water level in the trough to the lowest point of the meniscus.
- Repeat the measurements for each capillary tube.
- Repeat all measurements at least three times to minimize random errors.
7. Observation Table
| Capillary Tube No. | Internal Diameter (2r) (mm) | Internal Radius (r) (m) | Height of Water Column (h) (mm) | Height of Water Column (h) (m) | Product (h·r) (m²) |
|---|---|---|---|---|---|
| 1 | |||||
| 2 | |||||
| 3 | |||||
| 4 |
Temperature of water = ______ °C
Density of water at this temperature (ρ) = ______ kg/m³
Acceleration due to gravity (g) = 9.8 m/s²
8. Calculations
For each capillary tube, calculate the surface tension using:
$ T = \frac{\rho g h r}{2} $
Sample calculation for Tube 1:
$ T_1 = \frac{\rho g h_1 r_1}{2} $
$ T_1 = \frac{(____\text{ kg/m}^3) \times (9.8\text{ m/s}^2) \times (____\text{ m}) \times (____\text{ m})}{2} $
$ T_1 = ____\text{ N/m} $
Similarly, calculate $T_2$, $T_3$, and $T_4$ for other tubes.
Calculate the average value of surface tension:
$ T_{avg} = \frac{T_1 + T_2 + T_3 + T_4}{4} = ____\text{ N/m} $
Also, calculate the average value of the product h·r:
$ (h \cdot r)_{avg} = \frac{h_1r_1 + h_2r_2 + h_3r_3 + h_4r_4}{4} = ____\text{ m}^2 $
9. Result
The surface tension of water at ______ °C is found to be ______ N/m.
The average value of the product h·r is ______ m².
Standard value of surface tension of water at this temperature is ______ N/m.
Percentage error = ______%
10. Precautions
- Clean the capillary tubes thoroughly before the experiment to ensure proper wetting.
- Ensure that the capillary tubes are perfectly vertical when taking measurements.
- Measure the internal diameter of the capillary tubes accurately.
- Allow sufficient time for the water to reach equilibrium in the capillary tubes.
- Take readings from the lowest point of the meniscus for accurate measurements.
- Maintain a constant temperature throughout the experiment.
- Use distilled water to avoid impurities that might affect surface tension.
- Avoid touching the inside of the capillary tubes with fingers.
- Take multiple readings and find the average to minimize random errors.
11. Sources of Error
- Inaccurate measurement of the internal diameter of the capillary tubes.
- Non-vertical positioning of the capillary tubes.
- Presence of impurities in water or on the surface of capillary tubes.
- Parallax error while taking readings.
- Temperature fluctuations during the experiment.
- Non-zero contact angle between water and glass due to improper cleaning.
- Errors in determining the exact position of the meniscus.
- Variations in the circular cross-section of the capillary tubes.
- Human errors in taking measurements.
12. Viva Voice Questions
Q1: What is surface tension? Explain its molecular origin.
Surface tension is the property of a liquid surface to behave like an elastic sheet, minimizing its surface area. At the molecular level, it arises because molecules at the surface are not surrounded by similar molecules on all sides. They experience a net inward pull from the molecules below, creating tension along the surface.
Q2: Why does the liquid rise in a capillary tube?
The liquid rises in a capillary tube due to adhesive forces between the liquid and the glass molecules, which are stronger than the cohesive forces within the liquid for liquids that wet glass (like water). This creates a concave meniscus, and the resultant upward force causes the liquid to rise until it is balanced by the weight of the liquid column.
Q3: How does the height of the liquid column vary with the radius of the capillary tube?
The height of the liquid column is inversely proportional to the radius of the capillary tube. Mathematically, $h \propto \frac{1}{r}$ or $h \cdot r = \text{constant}$.
Q4: How does temperature affect the surface tension of a liquid?
Surface tension generally decreases with increasing temperature. This is because the increased thermal energy of the molecules reduces the cohesive forces between them, thereby decreasing the surface tension.
Q5: What is the effect of adding soap to water on its surface tension?
Adding soap to water decreases its surface tension significantly. Soap molecules are surfactants with hydrophilic and hydrophobic ends, which disrupt the cohesive forces between water molecules at the surface, thus reducing the surface tension.
Q6: Why is the meniscus concave for water in a glass capillary?
The meniscus is concave for water in a glass capillary because the adhesive forces between water and glass molecules are stronger than the cohesive forces within water. This causes the water to "climb" up the glass surface, creating a concave shape.
Q7: How would you explain the phenomenon of capillary action in everyday life?
Capillary action can be observed in many everyday phenomena, such as the absorption of water by paper towels, the rise of water in plant stems and roots, the wicking of ink in fountain pens, and the absorption of water by soil.
Q8: Why do we assume that the contact angle between water and clean glass is approximately zero?
For water on clean glass, the adhesive forces between water and glass molecules are so strong compared to the cohesive forces within water that the water tries to maximize its contact with the glass surface. This results in a contact angle that is very close to zero.
Q9: How would the capillary rise be affected if we used a different liquid like mercury instead of water?
Mercury has a high surface tension but does not wet glass (i.e., the cohesive forces within mercury are stronger than the adhesive forces between mercury and glass). This results in a convex meniscus and a depression (rather than a rise) of mercury in a glass capillary tube.
Q10: If the capillary tube has a non-circular cross-section, how would it affect the calculation of surface tension?
For a non-circular cross-section, the formula $T = \frac{\rho g h r}{2}$ would not be directly applicable. Instead, we would need to consider the shape factor and wetted perimeter. The general formula would involve the ratio of the cross-sectional area to the wetted perimeter.