Analytical chemistry mindmap

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 - 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

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 do 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 > 1
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 < 7 --> Acidic solution
pH > 7 --> Basic solution
pH = 7 --> Neutral

pH Scale

• However, these are
not the limits of pH
• Very high
concentrations of
acid can reach pH =

1

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 0 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 = 0 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 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