EXPERIMENT: DETERMINATION OF SURFACE TENSION BY CAPILLARY RISE METHOD

1. AIM

To determine the surface tension of a given liquid using the capillary rise method.

2. APPARATUS USED

• Capillary tubes of different radii
• Traveling microscope
• Screw gauge (for measuring capillary radius)
• Glass beaker
• Test liquid (water, alcohol, etc.)
• Thermometer
• Laboratory stand with clamp
• Clean cloth/tissue paper
• Distilled water (for cleaning)
• Vernier caliper (optional)

3. DIAGRAM

4. THEORY

The phenomenon of surface tension arises from the cohesive forces between liquid molecules. At the surface, liquid molecules experience an inward pull due to the absence of liquid molecules above them. This creates a molecular pressure difference across the curved liquid surface.

When a capillary tube with a small radius is inserted into a liquid that wets it (contact angle < 90°), the liquid rises in the tube due to adhesive forces between the liquid and the glass wall. This rise continues until the upward capillary force balances the downward gravitational force on the liquid column.

For a liquid with density ρ, surface tension T, in a capillary tube of radius r, the height h of the liquid column is related to these parameters through the following relationship derived from force balance:

Where:

• T is the surface tension of the liquid
• θ is the contact angle between the liquid and the capillary tube
• r is the radius of the capillary tube
• h is the height of the liquid column in the capillary
• ρ is the density of the liquid
• g is the acceleration due to gravity

For complete wetting (θ ≈ 0° for water in clean glass), cos θ ≈ 1, and the equation simplifies to:

5. FORMULA

The surface tension (T) of the liquid is given by:

Where:

• T is the surface tension in N/m
• h is the capillary rise in meters
• r is the radius of the capillary tube in meters
• ρ is the density of the liquid in kg/m³
• g is the acceleration due to gravity (9.8 m/s²)

6. PROCEDURE

1. Clean the apparatus:
   • Clean the capillary tubes with distilled water followed by the test liquid.
   • Ensure the beaker is thoroughly cleaned and dried.
2. Measure the radius of the capillary tube:
   • Use a screw gauge to measure the outer diameter of the capillary tube at multiple points.
   • Measure the inner diameter at both ends and calculate the average radius.
3. Set up the apparatus:
   • Fill the beaker with the test liquid up to about three-fourths of its capacity.
   • Fix the capillary tube vertically in the clamp attached to the laboratory stand.
   • Lower the capillary tube into the liquid.
4. Ensure proper conditions:
   • Make sure the lower end of the capillary tube is immersed in the liquid.
   • The capillary tube should be perfectly vertical.
   • Wait for a few minutes to allow the liquid level in the capillary to stabilize.
5. Measure the capillary rise:
   • Use the traveling microscope to measure the height of the liquid in the capillary tube above the liquid surface in the beaker.
   • Take readings for the upper meniscus level in the capillary tube.
   • Take readings for the liquid level in the beaker.
   • Calculate the difference to find the capillary rise (h).
6. Repeat the experiment:
   • Repeat the procedure using different capillary tubes of varying radii.
   • Record all measurements in the observation table.
7. Record the temperature:
   • Note the room temperature using the thermometer as the density of the liquid depends on temperature.

7. OBSERVATION TABLE

Table 1: Measurement of Capillary Tube Radius

Table 2: Measurement of Capillary Rise

Table 3: Calculation of Surface Tension

Temperature of the liquid: ______ °C
Density of the liquid at the given temperature (ρ): ______ kg/m³
Acceleration due to gravity (g): 9.8 m/s²

8. CALCULATIONS

1. Calculate the inner radius of each capillary tube:
   
   $$r = \frac{\text{Corrected Outer Diameter}}{2} - \text{Wall Thickness}$$
2. Convert all measurements to SI units:
   • Convert radius from mm to m: r (m) = r (mm) × 10^-3
   • Convert height from cm to m: h (m) = h (cm) × 10^-2
3. Calculate the surface tension for each capillary tube using the formula:
   $$T = \frac{h \times r \times \rho \times g}{2}$$
4. Calculate the mean value of surface tension from all observations.
5. Sample calculation (for one reading):

   Given:

   • Capillary radius (r) = ______ m
   • Capillary rise (h) = ______ m
   • Density of liquid (ρ) = ______ kg/m³
   • Acceleration due to gravity (g) = 9.8 m/s²
   $$\begin{align*} \text{Surface tension (T)} &= \frac{h \times r \times \rho \times g}{2}\\ &= \frac{\_\_\_\_ \times \_\_\_\_ \times \_\_\_\_ \times 9.8}{2}\\ &= \_\_\_\_\_\_ \text{ N/m} \end{align*}$$

9. RESULT

The surface tension of the given liquid at ______ °C as determined by the capillary rise method is ______ N/m.

10. PRECAUTIONS

1. The capillary tube must be thoroughly cleaned to ensure proper wetting (contact angle ≈ 0°).
2. The capillary tube should be positioned perfectly vertical.
3. The inner radius of the capillary tube should be measured accurately at different points.
4. The liquid level in the beaker should be sufficient to immerse the lower end of the capillary tube.
5. Allow sufficient time for the liquid level in the capillary to stabilize before taking measurements.
6. The meniscus reading should be taken carefully using the traveling microscope.
7. Avoid parallax error while taking readings.
8. The temperature of the liquid should be constant throughout the experiment.
9. Handle the capillary tubes carefully to avoid breakage.
10. Use appropriate density values for the liquid at the experimental temperature.

11. VIVA VOCE QUESTIONS