Conductometry PDF

# CONDUCTOMETRY ## Introduction - Electrolytic Conductance - resistance, conductance, Ohm's law, cell constant, specific and equivalent conductance, molar conductance, variation of specific conductance with concentrations, conductivity cell, conductivity meter - Applications: - Whetstone Bridg...

# CONDUCTOMETRY ## Introduction - Electrolytic Conductance - resistance, conductance, Ohm's law, cell constant, specific and equivalent conductance, molar conductance, variation of specific conductance with concentrations, conductivity cell, conductivity meter - Applications: - Whetstone Bridge - Determination of cell constant - Conductometric titrations (strong acid-strong base, strong acid-weak base, weak acid strong base) - Numerical problems ## Basic Concepts - **Electrolytes:** Substances that form ions in solution and conduct electricity through them (e.g. NaCl, KCl). - **Electrolysis:** The decomposition of an electrolyte by passing an electric current through its solution. - **Electrolytic cell:** The apparatus used to carry out the process of electrolysis. - **Resistance:** The property of a material that opposes the flow of charge or electric current. (Ohm-meter) - **Conductivity:** The ability of a solid or solution to pass an electrical current through it. Also known as *conductance*. (Siemens per meter (S/m)) ## Conduction in Metals and Electrolytes - Electrolytes obey Ohm's law according to which resistance is directly proportional to length (l) and inversely proportional to its area of cross section (A). - $R = \rho\frac{l}{A}$, where $\rho$ is the specific resistance. - **Specific resistance**: The resistance of a specimen of material 1m in length having 1m² as the area of cross section. (Ohm) - **Specific conductance (k):** The reciprocal of specific resistance. - $k = \frac{1}{\rho} = \frac{l}{A \times R}$ - Unit: $S cm^{-1}$, where $S = Siemen = ohm^{-1} = mho$ ## The Flow of Electricity - The flow of electricity through a solution of electrolytes is due to the migration of ions when a potential difference is applied between the two electrodes. Cations move towards the negative electrode (cathode) while anions move towards the positive electrode (anode). ## Conductivity and Conductance of Solutions - **Conductance (or conductivity) of a solution:** The ability of a solution to conduct electricity. - **Equivalent conductance (λ or Λ):** The conducting power of all the ions produced by one gram equivalent of an electrolyte in a given solution. - λ = k × V, where V = volume in cubic centimeter containing 1 gram equivalent of electrolyte at dilution V - λ = $\frac{k\times 1000}{N}$, where N = Normality of the solution - Unit: $ohm^{-1} cm^2 eqvt^{-1}$ - **Molar conductance (μ):** The conducting power of all the ions produced by 1 mole of an electrolyte in the solution. - μ = k × V; where V = volume in cubic centimeter containing 1 mole of the electrolyte - μ = $\frac{k\times 1000}{M}$, where M = number of moles of electrolytes in 1000 cc of solution (molarity). - Unit: $ohm^{-1} cm^2 mol^{-1}$ ## Variation of Equivalent and Specific Conductance with Dilution or Concentration - **Specific conductance**: The conductance of 1 cc of a solution of an electrolyte. - **Factors affecting specific conductance:** - Concentration of ions - Speed of ions - **Equivalent and molar conductance increases with dilution:** This is because these quantities are the products of specific conductance and the volume in cc of the solution containing 1 gram equivalent or 1 mole of the electrolyte solution respectively. ### Strong Electrolytes - Completely ionized at all concentrations or dilutions. - Equivalent conductance increases with dilution and attains a maximum value called the limiting value (at infinite dilution, $λ_∞$). ### Weak Electrolytes - Have low ionic concentrations and negligible interionic forces. - Equivalent conductance increases with dilution, but it is dependent on the degree of dissociation, α. - α = $\frac{Equivalent conductance at dilution V}{Equivalent conductance at infinite dilution}$ ## Cell Constant - The ratio of distance between electrodes to the cross-sectional area of each electrode. - $k_{cell} = \frac{l}{A}$ - Unit: $cm^{-1}$ or $m^{-1}$ - $k_{cell} = \frac{Specific conductance}{Observed conductance}$ ## Measurement of Electrolytic Conductance - Conductance is the reciprocal of resistance. - **How to measure:** - The solution whose conductance is to be measured is taken in a conductivity cell. - The resistance of the electrolytic solution is measured using a Wheatstone's bridge. - *Cell Diagram:* - **A:** Battery - **R:** Resistance box - **H:** Sliding contact which moves along the wire AB - **B:** Wire - **C:** Conductivity cell - **I:** Induction coil - Resistance of cell, C, is measured using the Wheatstone bridge, and specific conductance is calculated using the relationship: - $k = \frac{1}{R} \times cell constant$ - The values of equivalent conductance and molar conductance can be calculated using the following formulae: λ = $\frac{Specific conductance \times 1000}{Normality}$ μ = $\frac{Specific conductance\times 1000}{Molarity}$ ## Numerical Problems - **Example 1:** - 0.5 N solution of a salt placed between two platinum electrodes 20 cm apart and area of cross section 4 cm² has a resistance of 25 ohm. Calculate equivalent conductance of the solution. - **Solution:** - Given: - l = 20 cm - A = 4cm² - R = 25 ohm - $Specific conductance(k) = \frac{1}{R} \times\frac{l}{A} = 0.2 ohm^{-1} cm^{-1}$ - $Equivalent conductance (λ) = \frac{Specific conductance \times 1000}{Normality} = 400 ohm^{-1} cm^2 eqvt^{-1}$ - **Example 2:** - The resistance of an N/10 solution of a salt is found to be 2.5x103ohm. Calculate the equivalent conductance of the solution. Cell constant of the cell is 1.15 cm. - **Solution:** - Given: - Normality = N/10 = 0.1 N - R = 2.5 × 103 ohm - Cell constant (1/A) = 1.15 cm²¹ - $Specific conductance (k) = \frac{1}{R} \times Resistance = 0.2 ohm^{-1} cm^{-1}$ - $Equivalent conductance (λ) = \frac{Specific conductance \times 1000}{Normality} = 4.6 ohm^{-1} cm^2 eqvt^{-1}$ ## Variation of Conductance with Temperature - Conductance of a solution of an electrolyte increases with rise in temperature. (Normally increases by 2 to 7% for 1°C rise in temperature.) - **Factors:** - **Number of ions present in the electrolyte solution** - **Speed of ions** - **Explanation:** - Increase in temperature causes ions to move faster. - Viscosity of the solvent decreases, allowing ions to move more freely. - **Weak electrolytes:** Temperature effect depends on the enthalpy change accompanying the ionization. - If ionization is endothermic, conductance increases with temperature. - If ionization is exothermic, conductance decreases with temperature. ## Variation of Molar Conductance with Dilution - Molar conductance of an electrolyte increases with dilution. - **Explanation:** - Increase in dilution increases the degree of dissociation. - More ions are present in solutions with higher dilution. - The electrolyte can furnish a larger number of ions upon dilution, increasing the conductance. ## Arrhenius Theory of Electrolyte Dissociation - **Postulates:** - When dissolved in water, neutral electrolyte molecules split into charged particles (cations and anions). - Ions in solution can constantly reunite to form neutral molecules. - Charged ions are free to move through the solution to the oppositely charged electrodes (explaining the conductivity). - The degree of dissociation determines whether the electrolyte is strong or weak - **Degree of dissociation (α):** - The fraction of the total number of molecules that dissociate into ions. - α = $\frac{Number of molecules dissociated into ions}{Total number of molecules}$ - **Limitations:** - Cannot explain conductivity of strong electrolytes in fused state. - Fails to explain the factors affecting the mobility of ions. - Only applicable to weak electrolytes. ## Ostwald Dilution Law - According to Arrhenius theory, molecules of an electrolyte undergo spontaneous dissociation into positive and negative charged ions. - **Equilibrium:** - AB ↔ A+ + B- - **Law:** - The degree of dissociation of a weak electrolyte is proportional to the square root of dilution. - α = √KcV or α = √KV ## Kohlrausch's Law - At infinite dilution, when the dissociation of an electrolyte is almost complete, each ion makes a definite contribution to the conductance of the electrolyte regardless of the associated ions. - **The equivalent conductance of the electrolyte at infinite dilution is equal to the equivalent conductance of the two ions.** - **Mathematical formula:** - λ_∞ = λ_a + λ_c - where λ_∞ = equivalent conductance at infinite dilution - λ_a = equivalent conductance of cation - λ_c = equivalent conductance of anion - **Ionic conductance is directly proportional to the ionic mobility** - λ_a α U_a and λ_c α U_c - λ_a = kU_a and λ_c = kU_c - λ_∞ = k(λ_a + λ_c) ## Applications of Kohlrausch's law - **Calculation of λ_∞ for weak electrolytes:** - λ_a = λ_∞ t_- - λ_c = λ_∞ t₊ - **Calculation of ionic mobility** - Absolute ionic mobility of an ion is the velocity of the ion in cm/sec under a potential gradient of one volt per centimeter. ## Conductometric titrations - Titrations that use conductance measurements to determine the endpoint of acid-alkali, some displacement and precipitation reactions. - **How it Works:** - Titrant is added from a burette into a definite volume of the solution. - Conductance readings are plotted against the volume of the titrant. - The intersection of two lines gives the end point of the titration. - **Advantages:** - Can be used for titrations of colored solutions (where indicators are not useful). - Can be used for titrations of weak acids and bases. - More accurate results (as the endpoint is determined graphically). - **Types:** - **Strong acid-strong base titration:** - Conductance decreases initially, then increases after complete neutralization (due to the addition of OH ions). - **Weak acid-strong base titration:** - Conductance increases slowly initially (due to common ion effect), then increases sharply after the equivalence point (as OH ions are introduced). - **Strong acid-weak base titration:** - Conductance decreases initially, then increases after the equivalence point (due to the addition of NH4+ ions). - **Weak acid-weak base titration:** - Conductance decreases initially, then increases after the equivalence point (due to the addition of the weak conjugate base ions). ## Differences Between Conductometric and Volumetric Titrations **Conductometric titration** | **Volumetric titration** ----------------------------------------------------------------------|---------------------------------------------------------------------- - Conductance of the solution is measured to determine endpoint. | - Volume measurements are used to determine endpoint. - Can be carried out even with colored solutions. | - Titrations fail with colored solutions. - More accurate. | - Less accurate. - Endpoint is determined graphically. | - Endpoint is determined by color change of indicator. - Successful even with weak acids and bases. | - Volumetric titrations fail for weak acids against weak bases. ## Questions 1. Explain the conduction of electric current in electrolytes. 2. Explain the following: - Specific conductance - Molar conductance - Cell constant - Equivalent conductance 3. State and explain Kohlrausch's law; discuss its applications. 4. Explain the Wheatstone bridge method for the measurement of conductance of electrolyte solutions. 5. Write a note on conductometric titrations. 6. Explain the variation of specific conductance with dilution and temperature. 7. The conductance of a 0.1 N solution of NaCl at 25°C is measured to be 2.5x10³ ohm. Calculate the equivalent conductance if the electrodes are 2 cm apart and each having an area of 4.0 cm². ## Multiple Choice Questions 1. What is conductometry primarily used to measure? - Temperature - Electrical conductivity - Chemical reactivity - pH levels 2. Which unit is commonly used to express electrical conductivity? - Celsius - Siemens per meter (S/m) - Grams - Moles 3. In a conductometric titration, what is the endpoint determined by? - Color change - pH change - Conductivity change - Mass change 4. What does the term "specific conductance" refer to in conductometry? - The conductivity of a substance at a specific temperature and concentration - The conductivity of a substance with impurities - The conductance of a specific type of material - The conductivity of a substance at a specific pressure 5. What happens to the electrical conductivity of a solution as the concentration of ions in the solution increases? - It decreases - It remains constant - It increases - It becomes zero 6. Which type of solution would have the highest electrical conductivity? - A dilute solution of a strong acid - A concentrated solution of a weak base - A dilute solution of a weak electrolyte - A concentrated solution of a non-electrolyte 7. What is the relationship between conductivity and resistance? - They are inversely proportional - They are directly proportional - There is no relationship between them - They are logarithmically related 8. Which of the following factors can affect the electrical conductivity of a solution? - Temperature - Pressure - pH - All of the above 9. What is the SI unit of electrical conductivity? - Ohm - Volt - Siemens per meter (S/m) - Ampere 10. In conductometry, which type of cell is commonly used to measure the conductivity of a solution? - Voltaic cell - Electrolytic cell - Conductance cell - Galvanic cell 11. In conductometric titrations, what is the primary variable being measured? - pH - Volume - Electrical conductivity - Color change 12. Which type of titration involves the use of electrical conductivity to determine the endpoint? - Acid-base titration - Redox titration - Complexometric titration - Precipitation titration 13. What happens to the electrical conductivity of the solution during a conductometric titration as the titrant is added to the analyte? - It remains constant - It decreases - It increases - It fluctuates randomly 14. The equivalence point in a conductometric titration is typically indicated by: - A sudden change in color - A sudden drop in pH - A maximum change in electrical conductivity - A change in temperature 15. Which type of solution is most suitable for conductometric titrations? - Non-conductive solutions - Solutions with high conductivity - Solutions with low conductivity - Solutions with constant pH 16. What is the advantage of using conductometric titration over other titration methods? - Is faster - Requires fewer reagents - Is less sensitive - Does not require any equipment 17. In conductometric titrations, what does the equivalence point represent? - The point where the reaction is complete - The point where the indicator changes color - The point where the pH is neutral - The point where the titrant is added drop by drop 18. Which of the following titrations is best suited for conductometric titration? - Titration of a strong acid with a strong base - Titration of a weak acid with a strong base - Titration of a weak acid with a weak base - Titration of a gas with a liquid 19. What type of curve is typically obtained in a conductometric titration plot? - A straight line - A bell-shaped curve - A step-wise curve - An exponential curve 20. What is the role of the conductance cell in conductometric titrations? - It holds the titrant - It measures the electrical conductivity of the solution - It provides heat to the reaction - It determines the pH of the solution