MLiquids : Viscosity of Water, Dynamic Viscosity & Kinematic Viscosity
Discover what is viscosity, master viscosity of water, dynamic viscosity, kinematic viscosity, and viscosity units. Learn dynamic viscosity of water, kinematic viscosity of water, and dynamic viscosity units with expert explanations.
What is Viscosity: Understanding Viscosity of Water
Viscosity represents one of the most important properties in liquid chemistry. This comprehensive guide explores what is viscosity, viscosity of water, dynamic viscosity, kinematic viscosity, and viscosity units. You’ll master dynamic viscosity of water, kinematic viscosity of water, and dynamic viscosity units with practical measurement methods.
Understanding viscosity is crucial for countless applications from industrial processes to biological systems. The viscosity of water serves as a fundamental reference point, while dynamic viscosity and kinematic viscosity provide different perspectives on fluid resistance to flow.
Intermolecular Forces in Liquids
🔗 Dipole-Dipole Attractions
Dipole-dipole attractions occur between polar molecules and play a crucial role in liquid behavior. These forces determine how polar molecules interact with each other and affect liquid properties.
- Permanent dipoles align to minimize energy
- Strength depends on dipole moment magnitude
- Critical for liquid structure and stability
- Influences solvent-solute interactions
⚡ London Forces
London dispersion forces exist between all molecules and significantly impact liquid properties in non-polar systems. These weak but universal forces affect molecular cohesion and liquid behavior.
- Present in all molecular interactions
- Strength increases with molecular size
- Influences non-polar liquid properties
- Affects molecular mobility in liquids
💧 Hydrogen Bonding in Liquids
Hydrogen bonding represents the strongest intermolecular force and fundamentally determines liquid properties in polar systems. Water’s hydrogen bonding network creates unique liquid characteristics and behaviors.
Liquid Structure
Tetrahedral arrangement in water
Dynamic Exchange
Continuous breaking and forming
Molecular Balance
Maintains liquid stability
🔗 Van der Waals Forces
Understanding Van der Waals Forces
Van der Waals forces are weak intermolecular forces that include dipole-dipole interactions, London dispersion forces, and dipole-induced dipole forces. These forces play a crucial role in determining liquid properties and molecular behavior.
Dipole-Dipole
Permanent dipole interactions
London Dispersion
Temporary dipole forces
Dipole-Induced
Induced dipole interactions
📐 Van der Waals Equation
The van der Waals equation of state accounts for intermolecular forces and molecular volume:
- a = intermolecular attraction parameter
- b = molecular volume parameter
- Corrects ideal gas behavior
- Important for liquid-gas transitions
⚡ Energy Relationships
Van der Waals forces follow specific energy dependencies with distance:
- Dipole-dipole: E ∝ 1/r³ (orientation averaged)
- London forces: E ∝ 1/r⁶ (always attractive)
- Dipole-induced: E ∝ 1/r⁶ (polarizability dependent)
- Total energy: Sum of all contributions
🎯 Applications in Liquid Properties
Boiling Points
Stronger forces = higher boiling points
Surface Tension
Intermolecular cohesion effects
Viscosity
Molecular friction resistance
Solubility
Like dissolves like principle
💧 Hydrogen Bonding
Characteristics of Hydrogen Bonds
Hydrogen bonding is a special type of dipole-dipole interaction that occurs when hydrogen is bonded to highly electronegative atoms (N, O, F). These bonds are stronger than typical van der Waals forces, with energies ranging from 10-40 kJ/mol.
🔋 Strength
- • 10-40 kJ/mol energy
- • Stronger than van der Waals
- • Weaker than covalent bonds
- • Temperature dependent
📐 Directionality
- • Linear arrangement preferred
- • Angle-dependent strength
- • Geometric constraints
- • Affects molecular packing
🔗 Cooperativity
- • Multiple bonds strengthen each other
- • Network formation
- • Collective behavior
- • Enhanced stability
🌊 Water’s Hydrogen Bond Network
Water molecules can form up to 4 hydrogen bonds per molecule, creating a tetrahedral arrangement that gives water its unique properties.
- Tetrahedral geometry: 109.5° bond angles
- Dynamic network: Continuous breaking/forming
- Temperature effects: Network disruption with heating
- Density anomaly: Ice less dense than water
📊 Types of Hydrogen Bonds
Intermolecular
Between different molecules (e.g., water-water)
Intramolecular
Within the same molecule (e.g., protein folding)
Network Structures
Extended 3D arrangements (e.g., ice, DNA)
🎯 Effects on Liquid Properties
🌡️ Boiling Point Elevation
Hydrogen bonding significantly increases boiling points:
- • H₂O: 100°C (vs. -80°C predicted without H-bonds)
- • NH₃: -33°C (vs. -120°C predicted)
- • HF: 20°C (vs. -140°C predicted)
💧 Viscosity and Surface Tension
Enhanced intermolecular cohesion leads to:
- • Higher viscosity values
- • Increased surface tension
- • Better wetting properties
- • Enhanced capillary action
💨 Vapour Pressure
Fundamentals of Vapour Pressure
Vapour pressure is the pressure exerted by vapor molecules in equilibrium with their liquid phase. It’s a fundamental property that depends on temperature and molecular structure, directly affecting boiling points and evaporation rates.
📊 Clausius-Clapeyron Equation
The relationship between vapour pressure and temperature follows:
Where ΔHᵥₐₚ is the enthalpy of vaporization and R is the gas constant
Determination of Vapour Pressure Methods
🔬 The Static Method
Measures vapour pressure at equilibrium without gas flow. This method provides accurate measurements for liquid characterization.
- Closed system measurement
- Equilibrium conditions maintained
- High accuracy for liquid studies
- Temperature control critical
🌪️ The Dynamic Method
Involves gas flow over the liquid surface, useful for studying liquids under dynamic conditions.
- Continuous gas flow system
- Simulates natural conditions
- Relevant for industrial applications
- Flow rate affects measurements
📊 Vapour Pressure Data for Common Liquids
| Liquid | 20°C (kPa) | 40°C (kPa) | 60°C (kPa) | 80°C (kPa) |
|---|---|---|---|---|
| Water | 2.34 | 7.38 | 19.9 | 47.4 |
| Ethanol | 5.95 | 18.7 | 47.0 | 101.3 |
| Acetone | 24.6 | 54.7 | 101.3 | 166.9 |
| Benzene | 10.0 | 24.6 | 51.3 | 101.3 |
🔥 Boiling Point
Understanding Boiling Point
The boiling point is the temperature at which a liquid’s vapour pressure equals the external pressure. At this point, vapor bubbles form throughout the liquid, causing the characteristic boiling phenomenon.
Normal Boiling Point
At 1 atm pressure (101.3 kPa)
Standard Boiling Point
At 1 bar pressure (100 kPa)
Reduced Pressure
Lower pressure = lower boiling point
📊 Boiling Points and Intermolecular Forces
| Compound | Formula | Boiling Point (°C) | Intermolecular Forces |
|---|---|---|---|
| Water | H₂O | 100.0 | Hydrogen bonding |
| Ethanol | C₂H₅OH | 78.4 | Hydrogen bonding |
| Acetone | CH₃COCH₃ | 56.1 | Dipole-dipole |
| Benzene | C₆H₆ | 80.1 | London forces |
| n-Hexane | C₆H₁₄ | 68.7 | London forces |
| Diethyl ether | C₂H₅OC₂H₅ | 34.6 | Dipole-dipole, London |
🎯 Factors Affecting Boiling Point
🔗 Molecular Structure
- • Intermolecular forces: Stronger forces = higher boiling point
- • Molecular size: Larger molecules = more London forces
- • Branching: Branched molecules have lower boiling points
- • Polarity: Polar molecules have higher boiling points
🌡️ External Conditions
- • Pressure: Higher pressure = higher boiling point
- • Altitude: Higher altitude = lower boiling point
- • Impurities: Usually increase boiling point
- • Surface area: Affects rate but not temperature
🧮 Surface Tension Numerical Problems
Practice problems to master surface tension calculations and applications
📏 Problem 1: Capillary Rise Method
Given:
- • Water rises 2.8 cm in a capillary tube
- • Tube radius = 0.5 mm
- • Contact angle θ = 0°
- • Density of water = 1000 kg/m³
- • g = 9.8 m/s²
Find: Surface tension of water
Solution:
γ = ρghr/(2cosθ)
γ = (1000)(9.8)(0.028)(0.0005)/(2×cos0°)
γ = 0.1372/2 = 0.0686 N/m
γ = 68.6 mN/m
💧 Problem 2: Drop Formation
Given:
- • 50 drops of water fall from a burette
- • Total volume = 2.5 mL
- • Burette tip radius = 1.2 mm
- • Surface tension of water = 72.8 mN/m
Find: Theoretical volume per drop
Solution:
V = 2πrγ/ρg (Tate’s law)
V = 2π(0.0012)(0.0728)/(1000×9.8)
V = 5.49×10⁻⁵/9800
V = 5.6×10⁻⁹ m³ = 0.056 mL
🫧 Problem 3: Bubble Pressure
Given:
- • Soap bubble radius = 3.0 cm
- • Surface tension of soap solution = 25 mN/m
- • Atmospheric pressure = 101.3 kPa
Find: Pressure inside the bubble
Solution:
ΔP = 4γ/r (for soap bubble)
ΔP = 4(0.025)/(0.03)
ΔP = 0.1/0.03 = 3.33 Pa
P_inside = P_atm + ΔP
P_inside = 101,303.33 Pa
⚖️ Problem 4: Ring Detachment
Given:
- • Platinum ring diameter = 4.0 cm
- • Force required to detach = 0.0182 N
- • Ring thickness negligible
Find: Surface tension of the liquid
Solution:
F = γ × L (where L = 2πr for ring)
γ = F/(2πr)
γ = 0.0182/(2π × 0.02)
γ = 0.0182/0.1257
γ = 0.145 N/m = 145 mN/m
🎯 Key Formulas for Surface Tension Calculations
Capillary Rise Method:
Drop Weight Method:
Bubble Pressure:
Ring Detachment:
Surface Tension in Liquids
Surface tension plays a crucial role in liquid behavior by affecting droplet formation, wetting properties, and interfacial phenomena. Understanding surface tension helps explain many liquid characteristics and industrial applications.
📏 Units of Surface Tension
🌊 What is Surface Tension?
Surface tension is the cohesive force between liquid molecules at the surface of a liquid. It arises because molecules at the surface experience unequal intermolecular forces compared to molecules in the bulk liquid. This creates a “skin-like” effect that allows insects to walk on water and causes droplets to form spherical shapes.
Molecular Forces
Unequal attractions at surface
Droplet Formation
Minimizes surface area
Energy Balance
Surface energy minimization
🧮 Surface Tension Formula
Surface tension (γ) is defined as the force per unit length acting perpendicular to any line on the surface:
Where F is the force in Newtons and L is the length in meters, giving units of N/m or J/m²
Determination of Surface Tension Methods
📏 Capillary Rise Method
Measures surface tension through liquid rise in narrow tubes, relevant for osmotic membrane pore analysis.
- Simple and accurate method
- Requires clean capillary tubes
- Contact angle measurement critical
💧 Drop Formation Method
Analyzes droplet formation to determine surface tension, useful for osmotic solution characterization.
- Dynamic measurement technique
- Suitable for various liquids
- Requires precise volume control
💍 Ring-detachment Method
Uses platinum ring to measure surface tension, excellent for osmotic solution studies.
- High precision measurements
- Suitable for temperature studies
- Requires calibrated equipment
🫧 Bubble Pressure Method
Measures pressure required to form bubbles, relevant for membrane pore characterization in osmosis.
- Dynamic surface tension measurement
- Useful for surfactant solutions
- Provides time-dependent data
📊 SURFACE TENSION OF SOME LIQUIDS AT VARIOUS TEMPERATURES (dynes cm⁻¹)
Surface tension values decrease with increasing temperature due to reduced intermolecular forces
| Liquid | 0°C | 10°C | 20°C | 30°C | 40°C | 50°C | 60°C |
|---|---|---|---|---|---|---|---|
| Water (H₂O) | 75.6 | 74.2 | 72.8 | 71.2 | 69.6 | 67.9 | 66.2 |
| Ethanol (C₂H₅OH) | 24.0 | 23.2 | 22.3 | 21.4 | 20.5 | 19.6 | 18.7 |
| Benzene (C₆H₆) | 31.6 | 30.2 | 28.9 | 27.5 | 26.2 | 24.8 | 23.5 |
| Acetone (CH₃COCH₃) | 26.2 | 25.0 | 23.7 | 22.4 | 21.2 | 19.9 | 18.6 |
| Chloroform (CHCl₃) | 29.2 | 28.1 | 27.1 | 26.0 | 25.0 | 23.9 | 22.8 |
| Carbon Tetrachloride (CCl₄) | 28.4 | 27.3 | 26.2 | 25.1 | 24.0 | 22.9 | 21.8 |
| Diethyl Ether (C₂H₅OC₂H₅) | 18.2 | 17.4 | 16.6 | 15.8 | 15.0 | 14.2 | 13.4 |
| Glycerol (C₃H₈O₃) | 65.4 | 64.2 | 63.0 | 61.8 | 60.6 | 59.4 | 58.2 |
| n-Hexane (C₆H₁₄) | 20.4 | 19.8 | 18.4 | 17.0 | 15.6 | 14.2 | 12.8 |
| Mercury (Hg) | 486.5 | 485.2 | 483.9 | 482.6 | 481.3 | 480.0 | 478.7 |
Temperature Effect
Surface tension decreases linearly with temperature
Molecular Forces
Stronger intermolecular forces = higher surface tension
Unit Conversion
1 dyne/cm = 1 mN/m = 0.001 N/m
Water Reference
Water has highest surface tension among common liquids
What is Viscosity: Dynamic & Kinematic Viscosity of Water
Viscosity is the measure of a fluid’s resistance to flow and deformation. Understanding what is viscosity, particularly the viscosity of water, is fundamental to chemistry and physics. This section covers dynamic viscosity, kinematic viscosity, viscosity units, and specifically focuses on dynamic viscosity of water and kinematic viscosity of water.
📊 Viscosity Units: Dynamic Viscosity Units & Kinematic Viscosity Units
Understanding viscosity units is crucial for measuring dynamic viscosity and kinematic viscosity. Dynamic viscosity units measure absolute viscosity, while kinematic viscosity units account for fluid density.
Dynamic Viscosity Units
Kinematic Viscosity Units
🌊 Dynamic Viscosity of Water
Dynamic viscosity (absolute viscosity) measures a fluid’s internal resistance to flow. The dynamic viscosity of water at 20°C is approximately 1.002 mPa·s (millipascal-seconds).
- Temperature dependent property
- Decreases with increasing temperature
- Measured in dynamic viscosity units
- Independent of fluid density
💨 Kinematic Viscosity of Water
Kinematic viscosity is the ratio of dynamic viscosity to fluid density. The kinematic viscosity of water at 20°C is approximately 1.004 mm²/s (square millimeters per second).
- Accounts for fluid density effects
- Used in fluid mechanics calculations
- Measured in kinematic viscosity units
- Important for Reynolds number
Measurement of Viscosity
🧪 Ostwald’s Method for Viscosity Measurement
Ostwald’s method is a precise technique for measuring the relative viscosity of liquids using a capillary viscometer. This method compares the flow times of different liquids through the same capillary under identical conditions.
🔬 Principle of Ostwald’s Method
Based on Poiseuille’s law for viscous flow through capillaries. The method measures the time required for a fixed volume of liquid to flow through a capillary of known dimensions.
η = (πr⁴Pt)/(8VL)
⚖️ Relative Viscosity Formula
For comparative measurements, the absolute viscosity cancels out, giving the relative viscosity formula:
🛠️ Ostwald Viscometer Components
Capillary Tube
Precise bore diameter
Bulb Reservoir
Fixed volume chamber
Timing Marks
Precise volume markers
Temperature Bath
Constant temperature
📋 Detailed Procedure
- Cleaning: Thoroughly clean viscometer with appropriate solvents
- Calibration: Use standard liquid (usually water) as reference
- Temperature Control: Maintain constant temperature (±0.1°C)
- Sample Loading: Fill viscometer with precise volume
- Flow Time Measurement: Record time between timing marks
- Repetition: Take multiple readings for accuracy
- Calculation: Apply relative viscosity formula
🎯 Applications & Advantages
- High Precision: Accurate to ±0.1% for careful work
- Simple Operation: No complex instrumentation required
- Wide Range: Suitable for various liquid viscosities
- Temperature Studies: Easy temperature variation
- Quality Control: Industrial and research applications
- Comparative Analysis: Ideal for relative measurements
⚠️ Precautions and Sources of Error
Temperature Control
- • Maintain constant temperature
- • Allow thermal equilibration
- • Use thermostat bath
Timing Accuracy
- • Use precise stopwatch
- • Consistent timing marks
- • Multiple measurements
Sample Purity
- • Clean, dry samples
- • No air bubbles
- • Proper viscometer cleaning
🌡️ Temperature Effects on Viscosity of Water
Temperature dramatically affects the viscosity of water and other liquids. Both dynamic viscosity of water and kinematic viscosity of water decrease exponentially with increasing temperature, following the Arrhenius relationship.
Viscosity of Water at Different Temperatures:
🧮 Surface Tension Numerical Problems
Practice problems to master surface tension calculations and applications
📏 Problem 1: Capillary Rise Method
Given:
- • Water rises 2.8 cm in a capillary tube
- • Tube radius = 0.5 mm
- • Contact angle θ = 0°
- • Density of water = 1000 kg/m³
- • g = 9.8 m/s²
Find: Surface tension of water
Solution:
γ = ρghr/(2cosθ)
γ = (1000)(9.8)(0.028)(0.0005)/(2×cos0°)
γ = 0.1372/2 = 0.0686 N/m
γ = 68.6 mN/m
💧 Problem 2: Drop Formation
Given:
- • 50 drops of water fall from a burette
- • Total volume = 2.5 mL
- • Burette tip radius = 1.2 mm
- • Surface tension of water = 72.8 mN/m
Find: Theoretical volume per drop
Solution:
V = 2πrγ/ρg (Tate’s law)
V = 2π(0.0012)(0.0728)/(1000×9.8)
V = 5.49×10⁻⁵/9800
V = 5.6×10⁻⁹ m³ = 0.056 mL
🫧 Problem 3: Bubble Pressure
Given:
- • Soap bubble radius = 3.0 cm
- • Surface tension of soap solution = 25 mN/m
- • Atmospheric pressure = 101.3 kPa
Find: Pressure inside the bubble
Solution:
ΔP = 4γ/r (for soap bubble)
ΔP = 4(0.025)/(0.03)
ΔP = 0.1/0.03 = 3.33 Pa
P_inside = P_atm + ΔP
P_inside = 101,303.33 Pa
⚖️ Problem 4: Ring Detachment
Given:
- • Platinum ring diameter = 4.0 cm
- • Force required to detach = 0.0182 N
- • Ring thickness negligible
Find: Surface tension of the liquid
Solution:
F = γ × L (where L = 2πr for ring)
γ = F/(2πr)
γ = 0.0182/(2π × 0.02)
γ = 0.0182/0.1257
γ = 0.145 N/m = 145 mN/m
🎯 Key Formulas for Surface Tension Calculations
Capillary Rise Method:
Drop Weight Method:
Bubble Pressure:
Ring Detachment:
Refractive Index and Optical Properties
🔍 Refractive Index
The refractive index is a fundamental optical property that measures how much light bends when passing from one medium to another. It provides valuable information about molecular density, purity, and composition of liquids.
📐 Definition and Formula
Refractive index (n) is defined as the ratio of the speed of light in vacuum to its speed in the medium:
- • c = speed of light in vacuum
- • v = speed of light in medium
- • θ₁, θ₂ = angles of incidence and refraction
🌡️ Factors Affecting Refractive Index
- • Temperature: Generally decreases with increasing temperature
- • Wavelength: Varies with light wavelength (dispersion)
- • Pressure: Slight increase with pressure for liquids
- • Concentration: Changes with solute concentration
- • Molecular structure: Depends on electronic polarizability
📊 Refractive Index Values for Common Liquids (at 20°C, 589 nm)
📏 Specific Refraction
Specific refraction is an intensive property that relates refractive index to density, providing insights into molecular structure and intermolecular interactions independent of physical conditions.
🧮 Lorentz-Lorenz Equation
The most commonly used formula for specific refraction:
- • r = specific refraction
- • n = refractive index
- • ρ = density of the liquid
🎯 Applications of Specific Refraction
- • Molecular characterization: Independent of temperature and pressure
- • Purity analysis: Detects impurities in liquids
- • Mixture analysis: Additive property for solutions
- • Quality control: Industrial applications
- • Research: Fundamental molecular studies
📈 Temperature Independence
Specific refraction remains relatively constant with temperature changes, making it valuable for:
🧬 Molar Refraction
Molar refraction relates refractive index to molecular structure and provides insights into electronic polarizability and molecular volume. It’s an additive property useful for predicting refractive indices of compounds.
🔬 Molar Refraction Formula
Molar refraction combines refractive index with molar volume:
- • R = molar refraction (cm³/mol)
- • M = molar mass (g/mol)
- • ρ = density (g/cm³)
🎯 Properties of Molar Refraction
- • Additive property: Sum of atomic/group contributions
- • Temperature independent: Relatively constant with T
- • Pressure independent: Unaffected by moderate pressure changes
- • Structural information: Related to molecular polarizability
- • Predictive tool: Estimate refractive indices
📊 Atomic and Group Contributions to Molar Refraction
Atoms
Bonds
Applications
🧮 Calculation Example
For ethanol (C₂H₅OH): R = 2×2.418 + 6×1.100 + 1×1.525 = 13.961 cm³/mol
Compare with experimental value: 13.01 cm³/mol
🔬 Determination of Refractive Index
Accurate refractive index measurement is essential for liquid characterization, quality control, and research applications.
Abbe Refractometer
- • High precision (±0.0001)
- • Temperature controlled
- • Wide measurement range
- • Most common laboratory instrument
Digital Refractometer
- • Automatic temperature compensation
- • Rapid measurements
- • Digital display
- • Ideal for routine analysis
Critical Angle Method
- • Fundamental principle
- • High accuracy potential
- • Research applications
- • Requires skilled operation
🌀 Optical Activity
Optical activity is the ability of certain substances to rotate the plane of polarized light. This property is exhibited by chiral molecules and provides valuable information about molecular structure and concentration.
🔍 Fundamentals of Optical Activity
- • Chirality requirement: Molecules must lack mirror symmetry
- • Polarized light rotation: Clockwise (dextrorotatory, +) or counterclockwise (levorotatory, -)
- • Concentration dependent: Rotation angle proportional to concentration
- • Path length dependent: Longer path = greater rotation
- • Wavelength dependent: Optical rotatory dispersion
🎯 Applications of Optical Activity
- • Pharmaceutical analysis: Drug purity and enantiomer ratio
- • Sugar analysis: Concentration determination
- • Protein studies: Structural analysis
- • Quality control: Industrial applications
- • Research: Stereochemistry studies
📐 Measurement of Optical Activity
Optical activity is measured using a polarimeter, which determines the angle of rotation of polarized light:
📊 Specific Rotation
Specific rotation is an intensive property that characterizes the optical activity of a substance independent of concentration and path length. It’s a fundamental constant for optically active compounds.
🧮 Specific Rotation Formula
Specific rotation normalizes observed rotation for concentration and path length:
- • [α] = specific rotation (deg·mL·g⁻¹·dm⁻¹)
- • α = observed rotation (degrees)
- • l = path length (dm)
- • c = concentration (g/mL)
- • T = temperature, λ = wavelength
🌡️ Factors Affecting Specific Rotation
- • Temperature: Usually decreases with increasing temperature
- • Wavelength: Varies significantly (optical rotatory dispersion)
- • Solvent: Can affect rotation magnitude and sign
- • Concentration: May show non-linear effects at high concentrations
- • pH: Important for ionizable compounds
📊 Specific Rotation Values for Common Compounds
| Compound | [α]²⁰ᴅ | Solvent | Application |
|---|---|---|---|
| Sucrose | +66.5° | Water | Sugar analysis |
| D-Glucose | +52.7° | Water | Biochemical analysis |
| L-Tartaric acid | +12.0° | Water | Food industry |
| Quinine | -165° | Ethanol | Pharmaceutical |
🎯 Applications of Specific Rotation
Pharmaceutical
Drug purity and enantiomer analysis
Food Industry
Sugar concentration determination
Research
Stereochemistry and structure studies
🧮 Surface Tension Numerical Problems
Practice problems to master surface tension calculations and applications
📏 Problem 1: Capillary Rise Method
Given:
- • Water rises 2.8 cm in a capillary tube
- • Tube radius = 0.5 mm
- • Contact angle θ = 0°
- • Density of water = 1000 kg/m³
- • g = 9.8 m/s²
Find: Surface tension of water
Solution:
γ = ρghr/(2cosθ)
γ = (1000)(9.8)(0.028)(0.0005)/(2×cos0°)
γ = 0.1372/2 = 0.0686 N/m
γ = 68.6 mN/m
💧 Problem 2: Drop Formation
Given:
- • 50 drops of water fall from a burette
- • Total volume = 2.5 mL
- • Burette tip radius = 1.2 mm
- • Surface tension of water = 72.8 mN/m
Find: Theoretical volume per drop
Solution:
V = 2πrγ/ρg (Tate’s law)
V = 2π(0.0012)(0.0728)/(1000×9.8)
V = 5.49×10⁻⁵/9800
V = 5.6×10⁻⁹ m³ = 0.056 mL
🫧 Problem 3: Bubble Pressure
Given:
- • Soap bubble radius = 3.0 cm
- • Surface tension of soap solution = 25 mN/m
- • Atmospheric pressure = 101.3 kPa
Find: Pressure inside the bubble
Solution:
ΔP = 4γ/r (for soap bubble)
ΔP = 4(0.025)/(0.03)
ΔP = 0.1/0.03 = 3.33 Pa
P_inside = P_atm + ΔP
P_inside = 101,303.33 Pa
⚖️ Problem 4: Ring Detachment
Given:
- • Platinum ring diameter = 4.0 cm
- • Force required to detach = 0.0182 N
- • Ring thickness negligible
Find: Surface tension of the liquid
Solution:
F = γ × L (where L = 2πr for ring)
γ = F/(2πr)
γ = 0.0182/(2π × 0.02)
γ = 0.0182/0.1257
γ = 0.145 N/m = 145 mN/m
🎯 Key Formulas for Surface Tension Calculations
Capillary Rise Method:
Drop Weight Method:
Bubble Pressure:
Ring Detachment:
Osmosis: The Complete Scientific Guide
🌊 What is Osmosis?
Osmosis represents the spontaneous movement of water molecules across a selectively permeable membrane from a region of lower solute concentration to higher solute concentration. This fundamental process drives countless biological and industrial applications.
Water Movement
Selective transport across membranes
Concentration Gradient
Drives the osmotic process
Selective Membrane
Controls molecular passage
🔬 Osmotic Pressure
Osmotic pressure quantifies the driving force behind osmosis, calculated using the van ‘t Hoff equation.
- i = van ‘t Hoff factor
- M = molar concentration
- R = gas constant
- T = absolute temperature
🏭 Industrial Applications
Osmosis powers numerous industrial processes, from water purification to pharmaceutical manufacturing.
- Reverse osmosis water treatment
- Food preservation and processing
- Pharmaceutical drug delivery
- Desalination technologies
- Biological membrane studies
⚡ Factors Affecting Osmosis Rate
Temperature
Higher temperature increases osmotic rate
Concentration
Greater gradient drives faster osmosis
Membrane
Permeability affects transport rate
Pressure
External pressure influences flow
🧮 Surface Tension Numerical Problems
Practice problems to master surface tension calculations and applications
📏 Problem 1: Capillary Rise Method
Given:
- • Water rises 2.8 cm in a capillary tube
- • Tube radius = 0.5 mm
- • Contact angle θ = 0°
- • Density of water = 1000 kg/m³
- • g = 9.8 m/s²
Find: Surface tension of water
Solution:
γ = ρghr/(2cosθ)
γ = (1000)(9.8)(0.028)(0.0005)/(2×cos0°)
γ = 0.1372/2 = 0.0686 N/m
γ = 68.6 mN/m
💧 Problem 2: Drop Formation
Given:
- • 50 drops of water fall from a burette
- • Total volume = 2.5 mL
- • Burette tip radius = 1.2 mm
- • Surface tension of water = 72.8 mN/m
Find: Theoretical volume per drop
Solution:
V = 2πrγ/ρg (Tate’s law)
V = 2π(0.0012)(0.0728)/(1000×9.8)
V = 5.49×10⁻⁵/9800
V = 5.6×10⁻⁹ m³ = 0.056 mL
🫧 Problem 3: Bubble Pressure
Given:
- • Soap bubble radius = 3.0 cm
- • Surface tension of soap solution = 25 mN/m
- • Atmospheric pressure = 101.3 kPa
Find: Pressure inside the bubble
Solution:
ΔP = 4γ/r (for soap bubble)
ΔP = 4(0.025)/(0.03)
ΔP = 0.1/0.03 = 3.33 Pa
P_inside = P_atm + ΔP
P_inside = 101,303.33 Pa
⚖️ Problem 4: Ring Detachment
Given:
- • Platinum ring diameter = 4.0 cm
- • Force required to detach = 0.0182 N
- • Ring thickness negligible
Find: Surface tension of the liquid
Solution:
F = γ × L (where L = 2πr for ring)
γ = F/(2πr)
γ = 0.0182/(2π × 0.02)
γ = 0.0182/0.1257
γ = 0.145 N/m = 145 mN/m
🎯 Key Formulas for Surface Tension Calculations
Capillary Rise Method:
Drop Weight Method:
Bubble Pressure:
Ring Detachment:
Frequently Asked Questions About Osmosis
What is the difference between osmosis and diffusion?
Osmosis specifically involves water movement across a selectively permeable membrane, while diffusion refers to the general movement of any particles from high to low concentration. Osmosis requires a membrane barrier, whereas diffusion can occur in open systems.
How does temperature affect osmosis rate?
Higher temperatures increase molecular kinetic energy, leading to faster water molecule movement and increased osmosis rates. However, extremely high temperatures can damage biological membranes and disrupt the osmotic process.
Why is osmosis important in biological systems?
Osmosis maintains cell shape, regulates water balance, enables nutrient transport, and controls blood pressure. Without osmosis, cells would either shrivel or burst, making it essential for all life processes.
What factors determine osmotic pressure?
Osmotic pressure depends on solute concentration, temperature, and the van ‘t Hoff factor (number of particles formed when a solute dissolves). The relationship follows the equation π = iMRT.
How is osmosis used in water purification?
Reverse osmosis applies pressure to force water through a membrane against its natural osmotic gradient, removing contaminants and producing pure water. This process is widely used in desalination and drinking water treatment.
How to Measure Osmotic Properties: Step-by-Step Guide
🧪 Measuring Osmotic Pressure
- Prepare solutions of known concentrations
- Set up osmometer with selectively permeable membrane
- Fill compartments with test and reference solutions
- Monitor height difference over time
- Calculate osmotic pressure using π = ρgh
- Verify results using van ‘t Hoff equation
📊 Analyzing Osmotic Data
- Record temperature and concentration data
- Plot osmotic pressure vs. concentration
- Calculate van ‘t Hoff factor from slope
- Determine membrane selectivity coefficient
- Assess temperature dependence
- Compare with theoretical predictions
Explore More Chemistry Topics
Scientific References
Atkins, P., & de Paula, J. (2018). Physical Chemistry: Thermodynamics, Structure, and Change. Oxford University Press. View Source
Castellan, G. W. (1983). Physical Chemistry. Addison-Wesley. View Source
Nobel Prize Committee. (1901). The Nobel Prize in Chemistry 1901: Jacobus Henricus van ‘t Hoff. View Source