Learnt Chapters Chemical Measurements Experimental Errors Statistics Quality Assurance Chemical Equilibrium Titration Fundamentals of Electrochemistry Redox Titration SI Units Chemical Concentrations.
SI Units Solution Solute Solvent Mole Atomic mass Formula mass Molecular mass Molarity(mol/V) Molality(mol/m solvent) Chemical Concentrations Chemical Measurements Formal concentration Strong electrolyte Weak electrolyte Electrolyte Weight percent Volume percent Percent concentration Distillation Preparing Solutions Deionization Preparing solution by dillution Mconc.Vconc = Mdil.Vdil Gravimetric Analysis Volumetric Analysis Stoichiometry Calculations for Gravimetric Analysis 9.25 x 10^4 - significant figures 9.250 x 10^4 - significant figures 9.250 x10^4 - significant figures 0.000 925 - significant figures Significant Figures Express all numbers with the same exponent • Align all numbers with respect to the decimal point • Round the answer according to the number with the fewest decimal places exceed or be less than the number of significant figures in the original data Addition and Subtraction Significant Figures in Arithmetic Multiplication and Division the fewest significant figures Number of digits in mantissa of log x = number of significant figures in x Logarithms and Antilogarithms arises from a flaw in equipment or experiment design Systematic Experimental Errors Number of digits in antilog x (=10x) = number of significant figures in mantissa of x arises from uncontrolled variables in measurement Random Types of Error due to accidental but significant departures from procedure Gross (blunders) Precision and Accuracy Absolute and Relative Uncertainty Addition and subtraction: Propagation of Uncertainty from Random Error Multiplication and division Mixed operations Propagation of Uncertainty from Systematic Error Mean(average) Mean Value and Standard Deviation measures how closely data are clustered about the mean Standard deviation Gaussian Distribution Degrees of freedom Variance Relative standard deviation (coefficient of variation): Other Statistical Parameters Null hypothesis: states that two sets of data are drawn from populations with the same properties Comparison of Standard Deviations with the F Test Ftest > Fcalculated > Reject the null hypothesis Fcalculated = s1^2 / s2^2 ( s1 >= s2) Confidence Intervals Student’s t: used to compare results from different experiments The t test determines if there is a statistical difference between x1 and x2 ( x : average) ttest > tcalculated > reject the null hypothesis Comparing Measured Result with “K nown” Value Comparing Replicate Measurements When Standard Deviations Are Not Significantl y Different (2a) Comparison of Means with Student's t Three cases Comparing Replicate Measurements When Standard Deviations Are Significantly Different(2b) Statistics Paired t Test for Comparing Individual Differences One-Tailed and Two-Tailed Significance Tests t Tests with a Spreadsheet a statistical test to decide whether to discard a datum that appears discrepant (an “outlier”) Grubbs Test for an Outlier Gtest > Gcalculated > Reject the null hypothesis • Prepare a calibration curve from known standards • Work in a region where the calibration curve is linear (usually) The Method of Least Squares Calibration Curves used to draw the “best” straight line through experimental data points that contain some scatter shows the response of an analytical method to known quantities of analyte Standard solutions Blank solutions A Spreadsheet for Least Squares is what we to get the right answer Use objectives Raw data Treated data Results Type of Blanks Method blank Reagent blank Field blank Basics of Quality Assurance Matrix Spike recovery Spike(or fortification) the process of proving that an analytical method is acceptable for intended purpose extent to which an analytical method can distinguish analyte from everything else in the sample Selectivity Linearity measures how well a calibration curve follows straight line emphasize the difference between calibration data and the least-squares line Residual Plots Method Validation Instrument precision Intra-assay precision Intermediate precision Interlaboratory precision Type of precision Quality Assurance Linear range Dynamic range Range and Robustness Robustness : ability of an analytical method to be unaffected by small, deliberate changes in operating parameters known quantities of the analyte added to the unknown change in analytical sensitivity caused by something in the sample other than analyte Mattrix effect Standard Addition Graphical Procedure for Standard Addition to Single Solution Graphical Procedure for Multiple Solutions with Constant Volume Standard addition known amount of a compound—same substance as analyte—added to the unknown Internal standards known amount of a compound—different from analyte—added to the unknown Internal Standards solutions with known concentrations of analyte used to prepare a calibration curve External standards Multipoint Calibration Curve for Internal Standard Equilibrium constant, K Reaction is favored if K > Equilibrium constants are dimensionless Each quantity in the ratio is given as concentration at standard state The Equilibrium Constant •If the direction of a reaction is reversed, the new value of K is simply the reciprocal of the original value of K • If two reactions are added, the new K is the product of the two individual equilibrium constants • If n reactions are added, the overall equilibrium constant is the product of n individual equilibrium constants Manipulating Equilibrium Constants •Δ H positive, heat is absorbed and the reaction is endothermic •Δ H negative, heat is released and the reaction is exothermic The heat absorbed or released Enthalpy • If Δ S is positive, the products have greater entropy than the reactants • If Δ S is negative, the products have lower entropy than the reactants Δ S = qrev/T the dispersal of energy into molecular motions Entropy Gibbs free energy (Δ G) is the arbiter between opposing tendencies of Δ H and Δ S At constant temperature (T): Equilibrium and Thermodynamics Free energy A reaction is favored if Δ G is negative Le Châ telier’s Principle make thermodynamic predictions, not kinetic predictions Equilibrium Problems equilibrium constant for the reaction in which a solid salt dissolves to give its constituent ions in solution Saturated solution Use the solubility product to find concentration of one ion when concentration of the other is known or fixed by some means Solubility Product Chemical Equilibrium Disproportionation the process in which an element in an intermediate oxidation state, such as Hg(I), gi ves products in both higher and lower oxidation states Common Ion Effect the application of Le Châ telier’s principle Complex Formation Anions (X ) that precipitate metals (M+) are often observed to form complex ions refers to chemistry involving transfer of an H+ from one molecule to another acid is a proton donor base is a proton acceptor salt contains cations and anions Strong electrolytes dissociate nearly completely into ions in dilute aqueous solutions Brø nsted-Lowry Acids and Bases Protic Acids and Bases Conjugate Acids and Bases The Nature of H+ and OH Autoprotolysis (self-ionization) Water undergoes autoprotolysis in which it acts as both acid and base pH < > Acidic solution pH > > Basic solution pH = > Neutral pH Scale • However, these are not the limits of pH • Very high concentrations of acid can reach pH = pH Learnt Chapters • Strong acids/bases react nearly “c ompletely” to produce H+ /OH • Weak acids/bases react only “partially” to produce H+ /OH The acid dissociation constant (Ka) is the equilibrium constant for a weak acid reacti ng with water Ka is “s mall” for weak acids Weak Acids and Bases The base hydrolysis constant (Kb) is the equilibrium constant for a weak base reacting with water Kb is “s mall” for weak acids Strengths of Acids and Bases • Most carboxylic acids are weak acids • Most carboxylate anions are weak bases Common Classes of Weak Acids and Bases Polyprotic Acids and Bases (Oxalic Acid) Carbonic Acid is formed by the reaction of carbon dioxide with water Polyprotic Acid and Conjugate Base Volumetric analysis Titration quantity of added titrant is exact amount necessary for stoichiometric reaction with the analyte Equivalence point the ideal (theoretical) result based on stoichiometry actual measurement, marked by a sudden change in physical property of the solution End point Titrations Titration Error Titration error Blank titration Primary Standards Standardization • Prepare a titrant with approximately the desired concentration and use it to titrate a primary standard • Method can be used to determine the concentration of the titrant • Validity of analytical result ultimately depends on knowing the concentration of the primary standard Direct titration Back titration Gravimetric titration Types of Titrations The key step in any titration calculation is to relate moles of titrant to moles of analyte Titration Calculations Standardization of Titrant Followed by Analysis of Unknown Titration of a Mixture show how concentration of reactant varies as titrant is added Concentration varies over orders of magnitude so use p function pX = log10[X] Titration Equivalence Point of Precipitation Titration Before the Equivalence Point Precipitation Titration Curves At the Equivalence Point After the Equivalence Point Shape of the Titration Curve Ksp Affects Titration Equivalence Point Calculating Concentrations During a Precipitation Titration Titration of a Mixture If a mixture of two ions is titrated, the less soluble precipitate forms first Calculating Titration Curves with a Spreadsheet Volhard Titration End-Point Detection Fajans Titration commonly used to measure [Cl ] (can be adapted for other anions) can be applied to many systems Adsorption Indicators Electrochemistry involves transfer of electrons from one reagent to another reagent Redox Reactions • The oxidizing agent, also called the oxidant, takes electrons from the reducing agent In this process, the reducing agent is oxidized • The reducing agent, also called the reductant, gives electrons to the oxidizing agent In this process, the oxidizing agent is reduced Redox reactions involve electron transfer The electrochemical cell isolates the electrons electrochemical cell can be readily connected to instruments that measure the electric current and potential associated with the redox reaction is a measurable property of the electrons that are transferred in a redox reaction Electric Charge Calculating the total charge of an ion is the quantity of charge flowing each second through a circuit Electric Current The unit of current is the ampere, abbreviated A Basic Concepts Any electric charge creates an electric potential • Electric potentials of opposite sign are attractive • Positive and negative charges attract each other • Electric potentials of the same sign are repulsive • Positive charges repel other positive charges; negative charges repel other negativ e charges Voltage, Work, and Free Energy • Potential difference is measured in units of volts (V) Relation between work, voltage, and charge W = E.q Sign conventions for heat and work Calculating Δ G: Gibbs Free Energy of Reaction states that current, I, is directly proportional to the potential difference, E, across a circuit and inversely proportional to the resistance, R, of the circuit Ohm’s Law Power A battery gives off its energy as either heat or work is the work done per unit time The SI unit of power is the watt (W) uses a spontaneous redox reaction to generate electricity The potentiometer in the circuit measures the difference in electric potential (voltage) between the two metal electrodes A Cell in Action Emeasured = E+ - EThe net reaction is composed of a reduction and an oxidation, each of which is called a half-reaction Galvanic Cells The two half-reactions are written with equal numbers of electrons before adding to obtain the net reaction Half-Reactions and Net Reactions A single-vessel Galvanic cell does not always work is a U-shaped tube filled with a gel containing KNO3 or other electrolyte not involved in the reaction Divided cell with a salt bridge The design of a galvanic cell can be summarized using line notation Line Notation for Galvanic cells Potentiometer The instrument that is used to measure the voltage of a galvanic cell Fundamentals of Electrochemistry Practical application of galvanic cells: pH meters When a pH probe is dipped into a solution to measure pH, a galvanic cell is created • The pH probe constitutes one half-cell with a saltbridge • The solution whose pH is measured constitutes the second half-cell • The pH meter is the potentiometer (voltmeter) • The center wire of the BNC socket is the positive input • The outer connection of the BNC socket is the negative input Measured cell potential Standard Potentials Standard conditions for galvanic cells When all components of both half-cells are present at standard concentrations, pressures, and temperatures, then the measured cell potential Standard cell potential o E+ is the standard reduction potential of the electrode attached to the positive terminal o E • is the standard reduction potential of the electrode attached to the negative terminal Predicting standard cell potential The standard hydrogen electrode (S.H.E.) is a half-reaction whose standard reductio n potential is defined to be at 25° C The S.H.E is used as a reference half-reaction to measure other standard half-reaction potentials How are standard half-reaction potentials measured? • The cell voltage for standard cells can be readily predicted using the tabulated halfreaction standard reduction potentials How is a nonstandard potential calculated? Nernst Equation The Nernst Equation is used to calculate the reduction potential for each half-cell (E+ or E under nonstandard conditions ) The simplified Nernst equation at 298.15 K The net reaction Nernst equation E° and the Equilibrium Constant E° and the Equilibrium Constant • Galvanic cells produce electricity when they are not at equilibrium • The voltage of a good battery can be predicted by the Nernst equation • When a battery has died, the chemicals inside have reached equilibrium (Q = K) and the battery voltage has dropped to zero (E = V) Finding K for Net Reactions That Are not Redox Reactions Biochemists Use E° ′ Redox Titration Curve: Before Titrant Is Added The initial potential of the analyte solution (before any titrant is added) is highly sensitive to impurities and cannot ordinarily be accurately calculated Redox Titration Curve: Before the Equivalence Point Redox Titration Curve: Half Equivalence Point The Shape of a Redox Titration Curve Redox Titration Curve: At the Equivalence Point Redox Titration Curve: After the Equivalence Point Redox Titration Curve: Twice the Equivalence Point Titration Curve Symmetry Near Equivalence Point is a compound that changes colors when going from its oxidized to reduced state Redox Indicators Finding the End Point Gran Plot uses data from well before Ve to locate Ve Starch-Iodine Complex Redox Titration Oxidation state adjustment is especially useful for analytes that contain an element i n multiple oxidation states Preadjustment of Analyte Oxidation State must be quantitative Excess preadjustment reagent must be eliminated so that it does not interfere in the subsequent titration Preoxidation Prereduction An important prereduction technique uses a packed column with a solid reducing agent Adjustment of the Analyte Oxidation State Prereduction Columns Jones reductor: a column packed with zinc coated with a zinc amalgam • Zinc is a powerful reducing agent • Not very selective • Mercury is a toxic waste hazard, so its use should be minimized Walden reductor: a column filled with solid silver and M HCl • It is more selective than the Jones reductor Finding Environmentally Friendly Replacements for Toxic Reductants Classical Nitrate Assay Environmentally Friendly Nitrate Assay