Learnt Chapters Chemical Measurements Experimental Errors Statistics Quality Assurance Chemical Equilibrium Titration Fundamentals of Electrochemistry Redox Titration SI Units Chemical Concentrations.
Trang 1Learnt Chapters
Chemical Measurements
Experimental Errors
Statistics
Quality Assurance
Chemical Equilibrium
Titration
Fundamentals of Electrochemistry
Redox Titration
SI Units
Chemical Concentrations
Preparing Solutions
Stoichiometry Calculations for Gravimetric Analysis
Significant Figures
Significant Figures in Arithmetic
Types of Error
Propagation of Uncertainty from Random Error
Propagation of Uncertainty from Systematic Error
Gaussian Distribution
Comparison of Standard Deviations with the F Test
Confidence Intervals
Comparison of Means with Student's t
t Tests with a Spreadsheet
Grubbs Test for an Outlier
The Method of Least Squares
Calibration Curves
A Spreadsheet for Least Squares
Basics of Quality Assurance
Method Validation
Standard Addition
Internal Standards
The Equilibrium Constant
Equilibrium and Thermodynamics
Solubility Product
Complex Formation
Protic Acids and Bases
pH
Strengths of Acids and Bases
Titrations
Titration Calculations
Precipitation Titration Curves
Titration of a Mixture Calculating Titration Curves with a Spreadsheet
End-Point Detection
Basic Concepts
Galvanic Cells
Standard Potentials
Nernst Equation
E° and the Equilibrium Constant
Biochemists Use E° ′
The Shape of a Redox Titration Curve
Finding the End Point
Adjustment of the Analyte Oxidation State
Solution Solute Solvent Mole Atomic mass Formula mass Molecular mass Molarity(mol/V) Molality(mol/m solvent)
Formal concentration Electrolyte
Strong electrolyte Weak electrolyte
Percent concentration
Weight percent Volume percent Distillation
Deionization Preparing solution by dillution Mconc.Vconc = Mdil.Vdil
Gravimetric Analysis Volumetric Analysis
9.25 x 10^4 - 3 significant figures 9.250 x 10^4 - 4 significant figures 9.250 0 x10^4 - 5 significant figures 0.000 925 - 3 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
Addition and Subtraction
exceed or be less than the number of significant figures in the original data
Multiplication and Division the fewest significant figures
Logarithms and Antilogarithms
Number of digits in mantissa of log x = number of significant figures in x Number of digits in antilog x (=10x) = number of significant figures in mantissa of x
Systematic
Random
Gross (blunders)
arises from a flaw in equipment or experiment design
arises from uncontrolled variables in measurement
due to accidental but significant departures from procedure
Precision and Accuracy Absolute and Relative Uncertainty
Addition and subtraction:
Multiplication and division Mixed operations
Mean Value and Standard Deviation
Mean(average)
Standard deviation
measures how closely data are clustered about the mean
Other Statistical Parameters
Degrees of freedom Variance
Relative standard deviation (coefficient of variation):
Null hypothesis: states that two sets of data are drawn from populations with the same properties
Ftest > Fcalculated > Reject the null hypothesis Fcalculated = s1^2 / s2^2 ( s1 >= s2)
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
Three cases
Comparing Measured Result with “K nown” Value Comparing Replicate Measurements When Standard Deviations Are Not Significantl
y Different (2a) Comparing Replicate Measurements When Standard Deviations Are Significantly Different(2b) Paired t Test for Comparing Individual Differences One-Tailed and Two-Tailed
Significance Tests
a statistical test to decide whether to discard a datum that appears discrepant (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) 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
is what we do to get the right answer
Use objectives
Raw data Treated data Results
Type of Blanks
Method blank Reagent blank Field blank
Spike recovery Matrix
Spike(or fortification) the process of proving that an analytical method is acceptable for intended purpose
Selectivity
extent to which an analytical method can distinguish analyte from everything else in the sample
Linearity measures how well a calibration curve follows straight line
Residual Plots
emphasize the difference between calibration data and the least-squares line
Type of precision
Instrument precision Intra-assay precision Intermediate precision Interlaboratory precision
Range and Robustness
Linear range Dynamic range 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
Mattrix effect
change in analytical sensitivity caused by something in the sample other than analyte
Graphical Procedure for Standard Addition to Single Solution
Graphical Procedure for Multiple Solutions with Constant Volume
Standard addition
Internal standards
External standards
known amount of a compound—different from analyte—added to the unknown
Multipoint Calibration Curve for Internal Standard
known amount of a compound—same substance as analyte—added to the unknown
solutions with known concentrations of analyte used
to prepare a calibration curve
Equilibrium constant, K Reaction is favored if K > 1 Equilibrium constants are dimensionless Each quantity in the ratio is given as concentration at standard state
Manipulating Equilibrium Constants
•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
Enthalpy
Entropy
The heat absorbed or released
the dispersal of energy into molecular motions
•ΔH positive, heat is absorbed and the reaction is endothermic
•ΔH negative, heat is released and the reaction is exothermic
ΔS = qrev/T
• If ΔS is positive, the products have greater entropy than the reactants
• If ΔS is negative, the products have lower entropy than the reactants
Free energy
Gibbs free energy (Δ G) is the arbiter between opposing tendencies of ΔH and ΔS At constant temperature (T):
A reaction is favored if ΔG is negative
Le Châtelier’s Principle
Equilibrium Problems
make thermodynamic predictions, not kinetic predictions
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
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 Châtelier’s principle
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
Brønsted-Lowry Acids and Bases
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
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 Scale
pH < 7 > Acidic solution
pH > 7 > Basic solution
pH = 7 > Neutral
• However, these are not the limits of pH
• Very high concentrations of acid can reach pH = 1
• Strong acids/bases react nearly “completely” to produce H+
/OH
• Weak acids/bases react only “partially” to produce H+
/OH
Weak Acids and Bases
The acid dissociation constant (Ka) is the equilibrium constant for a weak acid reacti
ng with water Ka is “small” for weak acids
The base hydrolysis constant (Kb) is the equilibrium constant for a weak base reacting with water Kb is “small” for weak acids
Common Classes of Weak Acids and Bases
• Most carboxylic acids are weak acids
• Most carboxylate anions are weak 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
Equivalence point
quantity of added titrant is exact amount necessary for stoichiometric reaction with the analyte
End point
actual measurement, marked by a sudden change in physical property
of the solution
the ideal (theoretical) result based on stoichiometry
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
Types of Titrations
Direct titration Back titration Gravimetric titration The key step in any titration calculation is to relate moles of titrant to moles of analyte
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]
Equivalence Point of Precipitation Titration Before the Equivalence Point
At the Equivalence Point After the Equivalence Point Shape of the Titration Curve Ksp Affects Titration Equivalence Point Calculating Concentrations During a Precipitation Titration
If a mixture of two ions is titrated, the less soluble precipitate forms first
Volhard Titration
commonly used to measure [Cl ] (can be adapted for other anions)
Fajans Titration can be applied to many systems Adsorption Indicators
Electrochemistry
Redox Reactions
involves transfer of electrons from one reagent to another reagent
Redox reactions involve electron transfer
• 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
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
Electric Charge
is a measurable property of the electrons that are transferred in a redox reaction
Calculating the total charge of an ion
Electric Current
is the quantity of charge flowing each second through a circuit
The unit of current is the ampere, abbreviated A
Voltage, Work, and Free Energy
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
• 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 ΔG: Gibbs Free Energy of Reaction
Ohm’s Law
A battery gives off its energy as either heat or work 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
Power
is the work done per unit time
The SI unit of power is the watt (W) uses a spontaneous redox
reaction to generate electricity
A Cell in Action
Half-Reactions and Net Reactions
The net reaction is composed of a reduction and an oxidation, each of which is called a half-reaction
The two half-reactions are written with equal numbers of electrons before adding to obtain the net reaction
The potentiometer in the circuit measures the difference in electric potential (voltage) between the two metal electrodes
Emeasured = E+ -
E-A single-vessel Galvanic cell does not always work
Divided cell with a salt bridge
is a U-shaped tube filled with a gel containing KNO3 or other electrolyte not involved in the reaction
Line Notation for Galvanic cells
The design of a galvanic cell can be summarized using line notation
Potentiometer
The instrument that is used to measure the voltage of a galvanic cell
Practical application of galvanic cells: pH meters Measured cell potential
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
Standard conditions for galvanic cells
Standard cell potential
When all components of both half-cells are present
at standard concentrations, pressures, and temperatures, then the measured 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
How are standard half-reaction potentials measured?
The standard hydrogen electrode (S.H.E.) is a half-reaction whose standard reductio
n potential is defined to be 0 at 25°C The S.H.E is used as a reference half-reaction
to measure other standard half-reaction potentials
How is a nonstandard potential calculated?
• The cell voltage for standard cells can be readily predicted using the tabulated half-reaction standard reduction potentials
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
• 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 = 0 V)
Finding K for Net Reactions That Are not Redox Reactions
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
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
Redox Indicators
is a compound that changes colors when going from its oxidized
to reduced state
Gran Plot
uses data from well before Ve
to locate Ve Starch-Iodine Complex
Preadjustment of Analyte Oxidation State
Oxidation state adjustment is especially useful for analytes that contain an element i
n multiple oxidation states
must be quantitative
Excess preadjustment reagent must be eliminated so that it does not interfere in the subsequent titration
Preoxidation Prereduction
Prereduction Columns
An important prereduction technique uses a packed column with a solid reducing agent
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 1 M HCl
• It is more selective than the Jones reductor
Finding Environmentally Friendly Replacements for Toxic Reductants Classical Nitrate Assay
Environmentally Friendly Nitrate Assay