Section-C: Physical Chemistry

a) To determine the surface tension of ethyl/acetic acid Solutions

Principle: Surface tension (γ) is the force per unit length at the surface of a liquid. We measure it *relatively* using a stalagmometer, which allows a liquid to fall as drops from a capillary tube. The weight of a drop is balanced by the surface tension.

At the point of detachment: Weight of one drop ∝ Surface Tension

m·g = k·γ

For two different liquids (a reference, 'w' for water, and the test liquid, 'l'):
m_w / m_l = γ_w / γ_l

Since mass (m) = volume (V) × density (ρ), and the stalagmometer delivers the *same volume* (V) for a given number of drops (n), the mass of a single drop is m = (V_total × ρ) / n.
V_total is the volume between the two marks on the stalagmometer.

Working Formula:
γ_l / γ_w = (m_l / m_w) = [ (V_total · ρ_l) / n_l ] / [ (V_total · ρ_w) / n_w ]
γ_l = γ_w · (ρ_l / ρ_w) · (n_w / n_l)
Where:

• γ_l, γ_w = Surface tension of liquid and water
• ρ_l, ρ_w = Density of liquid and water
• n_l, n_w = Number of drops for the liquid and water (for the same volume)

Procedure

1. Clean the stalagmometer thoroughly with chromic acid, then water, then the test liquid.
2. Set up the stalagmometer vertically.
3. Suck up distilled water above the top mark (A).
4. Allow the water to fall drop by drop, and start counting when the meniscus crosses mark A and stop when it crosses mark B. Record the number of drops (n_w). Repeat for a consistent reading.
5. Rinse the stalagmometer with the first solution (e.g., 5% acetic acid).
6. Repeat step 4 for this solution to get n_l.
7. Repeat for all other concentrations (e.g., 10%, 15%, 20%).
8. (In an exam, you will likely be *given* the density values (ρ) for all solutions).
9. Calculate γ_l for each solution using the formula.
10. Construction of Graph: Plot Surface Tension (γ) (y-axis) vs. Concentration (C) (x-axis).

b) To determine the viscosity of glycerol/acetic acid Solutions

Principle: Viscosity (η) is a liquid's resistance to flow. We measure it *relatively* using an Ostwald Viscometer. Poiseuille's equation governs the flow of a liquid through a capillary tube.

For a fixed volume (V) of liquid to flow through the capillary of length (l) and radius (r):

η = (π · P · r⁴ · t) / (8 · V · l)

The pressure (P) driving the liquid is proportional to its density (P = h·g·ρ). All other terms (π, r, V, l, h, g) are constant for the viscometer.
So, η ∝ ρ · t

Working Formula:
η_l / η_w = (ρ_l · t_l) / (ρ_w · t_w)
η_l = η_w · (ρ_l / ρ_w) · (t_l / t_w)
Where:

• η_l, η_w = Viscosity of liquid and water
• ρ_l, ρ_w = Density of liquid and water
• t_l, t_w = Time of flow for liquid and water (between the two marks)

Procedure

1. Clean the Ostwald viscometer thoroughly.
2. Pipette a precise, fixed volume of distilled water into the wider bulb.
3. Place the viscometer in a thermostat (water bath) at a constant temperature.
4. Suck the water up through the capillary bulb, above the top mark (A).
5. Allow the water to flow down. Start a stopwatch when the meniscus crosses mark A and stop it when it crosses mark B. Record the time (t_w). Repeat for a consistent reading.
6. Dry the viscometer and repeat the process with the first solution (e.g., 10% glycerol), ensuring you use the *exact same volume* as the water.
7. Record the flow time (t_l). Repeat for all other concentrations.
8. (You will be given the density (ρ) and viscosity of water (η_w) at the given temperature, and the densities of all solutions).
9. Calculate η_l for each solution.
10. Construction of Graph: Plot Viscosity (η) (y-axis) vs. Concentration (C) (x-axis).

c) Determination of transition temperature of a substance

Principle: The transition temperature is the temperature at which one stable solid form (allotrope or hydrate) of a substance transitions into another.
e.g., Na2SO4·10H2O (decahydrate) ⇌ Na2SO4 (anhydrous) + 10 H2O at 32.38°C.
This transition involves an absorption or release of heat (latent heat).

Thermometric Method: We measure the rate of cooling of the substance. When a substance cools, it loses heat to the surroundings, and its temperature drops.
1. When cooling a normal liquid, the cooling curve is smooth.
2. When a liquid freezes, it releases latent heat of fusion, and the temperature stays *constant* at the freezing point.
3. When a salt hydrate (like Na2SO4·10H2O) cools, it will start to precipitate. At the transition temperature, the hydrate *decomposes* (an endothermic process) or *forms* (exothermic), which changes the rate of cooling. The cooling curve will show a break or plateau at this temperature.

Procedure (e.g., Na2SO4·10H2O)

1. Place the salt (Glauber's salt, Na2SO4·10H2O) in a test tube and heat it in a water bath until it dissolves completely in its own water of crystallization (around 35-40°C).
2. Place the test tube in an outer beaker (to ensure slow, uniform cooling).
3. Insert a sensitive thermometer (e.g., 0.1°C) and a stirrer.
4. Start stirring slowly and record the temperature at regular intervals (e.g., every 30 seconds).
5. Continue recording until the temperature is well below the transition point (e.g., 25°C).
6. Construction of Graph: Plot Temperature (T) (y-axis) vs. Time (t) (x-axis).
7. The graph will show a curve. The point where the *rate of cooling changes* (the curve becomes horizontal or changes slope) is the transition temperature.

d) To determine the solubility of Salt (NaCl, KCl, KNO3) at room temperature

Principle: Solubility is the maximum amount of solute that can dissolve in a given amount of solvent (e.g., 100 g) at a specific temperature.
To find this, we will prepare a saturated solution of the salt at room temperature. We will then take a known mass (or volume) of this saturated solution, evaporate the water, and weigh the dry salt left behind.

Procedure

1. Take about 50 mL of distilled water in a beaker. Add the given salt (e.g., KCl) while stirring continuously.
2. Keep adding salt until some undissolved solid remains at the bottom, even after 10-15 minutes of stirring. This is a saturated solution.
3. Record the temperature of the solution (room temperature).
4. Weigh a clean, dry evaporating dish (Mass 1, m1).
5. Carefully pipette a known volume (e.g., 10 mL or 20 mL) of the *clear saturated solution* into the evaporating dish. (Alternatively, weigh the dish + solution (m2)).
6. Gently heat the dish on a water bath or sand bath to evaporate all the water. Do not heat too strongly, or the salt may spatter and be lost.
7. Once completely dry, cool the dish in a desiccator and weigh it again (Mass 2, m3).

Calculation

• Mass of dry salt (solute): m_solute = m3 - m1
• Mass of solution taken: m_solution = m2 - m1 (if weighed)
• Mass of water (solvent): m_solvent = m_solution - m_solute

Solubility (in g per 100 g of water):
Solubility = (m_solute / m_solvent) × 100

e) To determine the refractive index of a given liquid

Principle: Refractive index (n) is the ratio of the speed of light in a vacuum (or air) to its speed in the liquid. It's a measure of how much the liquid bends light.
n = (sin i) / (sin r), where 'i' is the angle of incidence and 'r' is the angle of refraction.

We use an Abbe Refractometer, which measures the "critical angle" of total internal reflection, from which it directly calculates and displays the refractive index.

Procedure (using Abbe Refractometer)

1. Ensure the prisms of the refractometer are clean. Use a soft tissue and a drop of solvent (like ethanol or acetone).
2. Open the prisms and place 2-3 drops of the given liquid onto the lower prism.
3. Close the prisms and clamp them.
4. Adjust the light source (mirror) to get maximum illumination in the eyepiece.
5. You will see a light and a dark field in the eyepiece. The boundary may be colored (chromatic aberration).
6. Turn the "Dispersion Correction" knob until the boundary is a sharp, black-and-white line.
7. Turn the main "Refractive Index" knob until this sharp line is exactly on the crosshairs.
8. Read the refractive index value (n) directly from the scale.
9. Also, record the temperature, as refractive index is temperature-dependent.

Finding Specific and Molar Refraction

The refractive index (n) and density (ρ) of a liquid are related by the Lorentz-Lorenz equation.

Specific Refraction (R_s):
R_s = [ (n² - 1) / (n² + 2) ] · (1 / ρ)
(Units: cm³/g)

Molar Refraction (R_m):
R_m = R_s × Molar Mass (M)
R_m = [ (n² - 1) / (n² + 2) ] · (M / ρ)
(Units: cm³/mol)

To find R_s and R_m: You must also measure the density (ρ) of the liquid (e.g., using a pycnometer or specific gravity bottle) and know its molar mass (M).