Analytical Chemistry

Analytical Chemistry|| CHEM 3111 || Yong Liu || SI 4112 2-3:15

Exam 1

Chapter 1 - What is Analytical Chemistry?Reading Assignment: Read the entire chapter with the exception of Feature 1-1, pp. 12-17.

Problem Assignment: Chapter problems are assigned to emphasize points of the chapter and to provide examples of testable problems. Chapter problems are not graded.

No assigned problems

Learning Objectives: Testable material for in-class examinations.

a. Distinguish between, and be able to give chemical examples for, the following terms:quantitative - qualitative (analysis classification)gravimetric - volumetric - instrumental (analysis techniques)selectivity - sensitivity

b. Know a minimum of five general factors which go into the selection of an analytical technique.c. Identify the importance of sampling to analytical chemistry.d. Define ‘replicate’ samples and explain their use in analytical chemistry.e. Outline the purpose of a ‘blank’ sample used in quantitative analysis. Indicate why distilled water is often a poor choice for a ‘blank’

sample.f. Define an ‘interference’ in the analysis of an unknown sample.

Chapter 3 - Important Chemical Concepts: Expressing Quantities and Concentrations

Reading Assignment: Read the entire chapter. This chapter is mostly a review of significant figure, stoichiometry and solution concentration units from general chemistry. Parts-per-million may be a new concentration concept and will be discussed in lecture.

Chapter 3 Calculations Used in Analytical ChemistrySI Units International System of Units - 7 fundamental base units

o 1) Mass 2) Length 3) Time 4) Temperature 5) Amount of a substance 6) Electric current 7) Luminous intensity

Use prefixes to multiply by various powers of 10o The angstrom is a non-SI unit of length used to describe wavelength

We determine the amount of a chemical species from mass measurementso Kilograms, grams, milligrams, micrograms

Volumes of liquids – liters, milliliters, microliters, nanoliterso The SI unit of Volume is the Liter, which is defined exactly as 10-3 m3

1 cm3 = 1 mLThe Difference Between Mass and Weight Mass is an invariant measure of the quantity of matter in an object Weight is the force of attraction between an object and its surroundings (the earth)

o Gravitational attraction varies with geographic location w = mg weight = mass × acceleration due to gravity

Chemical analysis is always based on masso Results do not depend on location

The verb “to weight” means the act of determining the mass of an objectThe Mole The mole is the SI unit for the amount of a chemical substance

Particles, ions, electrons, atoms, moleculeso It is the amount of the specified substance that contains the [same number of particles as the number of carbon atoms in 12 grams

of 12C] Avogadro’s Number NA = 6.022 ×1023

We calculate molar mass by [summing all of the atomic masses of the atoms that appear in the chemical formula] Relationship between mass units, moles, and grams - Unified atomic mass units (u) = daltons (Da)The Millimole Some calculations are easier using the millimole (mmol) 1000 millimole = 1 mole

-------------------------------------------------------------------------------------------------------EXAMPLE PROBLEM---------------------------------------------------------------------------------------------------------Find the number of moles and millimoles of benzoic acid (M = 122.1 g/mol) that are contained in 2.00 g of the pure acid.

To find molesAmount HBz=nHBz=2.00 gHBz× 1mol HBz

122.1 gHBz=0.0164mol HBz

To find millimolesAmount HBz=nHBz=2.00 g HBz× 1mol HBz

122.1 gHBz× 1000mmol

1mol=16.4mmolHBz

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---------------------------------------------------------------EXAMPLE PROBLEM - Factor Label Approach (dimensional analysis)-----------------------------------------------------------------------------------What is the mass in grams of Na+ (M = 22.99 g/mol) in 25.0 g of Na2SO4 (142.0g/mol)?

Amount Na+¿=n

Na+¿=25.0 g Na2 SO4×1mol Na2SO4142.0 g Na2SO 4

×2mol Na+¿

1mol Na2 SO4×22.99 g Na+ ¿

1molNa+¿=8.10 g Na+¿¿¿¿¿ ¿

¿

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5, 7a, 9a, 11c, 13 (a, c), 15(a, e), 18(a, g), 21(all), 23(all), 29a, 33, 39 (all).


a. Distinguish between, and be able to give chemical examples for, the following terms:millimole - molesolute - solutionanalytical concentration - equilibrium concentration (including symbolism)parts-per-million (gases) - parts-per-million (aqueous solution)volume - weight - weight/volume (% concentration expressions)density - specific gravity

b. Know the SI nomenclature and symbolism for volume, length, time, mass, and temperature. Know the prefix multipliers for 10–15 to 10+6 in increments of 103. See Tables 3-1 and 3-2.

c. Define the p-function used in chemistry to express concentrations. Briefly explain the utility of the p-function solution concentrations.d. Know how to work numerical problems involving concentration units of molarity, M; parts-per-million, ppm; and pX (p-function).

e. Know how to apply the proper number of significant figures to calculations involving addition and subtraction, multiplication and division, and logarithms and anti-logarithms.

f. Know the rounding conventions involving chemical calculations.

Chapter 4 - The Basic Approach to Chemical Equilibrium

Reading Assignment: Read the entire chapter, including the Spreadsheet Exercise, ‘Using Excel to Iterate,’ p. 99-100.

This chapter is mostly a review of stoichiometry and chemical equilibrium from general chemistry. Problem solving techniques will be reviewed in lecture, including simplification of mathematics through chemical assumptions and use of the quadratic equation.

Chapter 4 Chemical Equilibrium Aqueous solution chemistry – chemical equilibrium Water is the most plentiful solvent on Earth – easy to purify, not toxic Classifying solutions of Electrolytes

o Electrolytes are substances which, when dissolved in water, break up into cations (plus-charged ions) and anions (minus-charged ions)

Solutions conduct electricityo Strong Electrolyte – ionize completely

There are three categories of strong electrolytes: strong acids, strong bases, and salts Inorganic acids

HNO3 HClO4 H2SO4 HCl HI HBr HClO3 HBrO3

Alkali and alkaline-earth hydroxides Alkali hydroxide – Group 1A

o LiOHo NaOHo KOHo RbOHo CsOH

Alkaline-earth hydroxide o Be(OH)2o Mg(OH)2o Ca(OH)2o Sr(OH)2o Ba(OH)2

Salts NaCl KBr MgCl2

o Weak Electrolyte – ionize partially Inorganic acids

H2CO3 H3BO3 H3PO4

H2S H2SO3

Organic acids Ammonia(NH3) Organic bases Halides - F− Cl− I− At−

Cyanides (CN−) Thiocyanates (SCN−)

Hg(SCN)2 Zn(SCN)2 Cd(SCN)2

There are two main categories of weak electrolytes – weak acids and weak bases Acids and bases

o Bronsted-Lowry acid/base behavior theory Acid – is a proton donor

A substance only acts as an acid in the presence of a base Base – is a proton acceptor

A substance only acts as a base in the presence of an acido Conjugate acid/bas pair (conjugate pair)o Neutralization reaction – reaction proceeds to an extent that depends on the relative tendencies of the [two bases to accept a

proton]/[the two acids to donate a proton) Acid1 + base2 ↔ base1 + acid2 Many solvents are proton donors OR proton acceptors – and thus can induce basic or acidic behavior in solutes dissolved in

them

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4c, 7ae. 10c, 13b, 15c, 20ace, 21ac at 20% and 200%


a. Distinguish between, and be able to give chemical examples for, the following terms:weak - strong - non (classification of electrolytes)amphiprotic - differentiating - leveling (classification of solvents)acid/base - conjugate acid/base - conjugate pair

b. Write an equilibrium constant expression for a given equilibrium expression. Explain and be able to apply LeChâtelier’s principle.

c. Define an acid and a base using the Brønsted-Lowry convention. Be able to identify acids and bases in aqueous equilibrium reactions.

d. Know the list of common strong acids and strong bases, as presented in lecture.

e. Use the autoprotolysis constant, Kw, to relate concentrations of hydronium, H3O+, and hydroxyl ions, OH−, in water. Use the Kw constant to relate Ka and Kb constants.

f. Predict the numerical answer for problems before carrying out the mathematical solution.

g. Work acid-base equilibria problems using Ka, Kb and Kw equilibrium constants.

h. Understand solution conditions under which it is acceptable to simplify the Ka equilibrium expression by assuming [H3O+] is << CHA. Be able to utilize the quadratic formula when the simplification is invalid.

i. Work aqueous solubility and common ion solubility problems using Ksp.

EXAM 2

Quiz Questions

Homework Problems

Chapter 5 - Errors in Chemical Analyses: Assessing the Quality of ResultsReading Assignment: Read the entire chapter. Include in the reading the Spreadsheet Exercise, ‘A Mean Calculation,’ pp. 112-115.This chapter is an introduction to error analysis and statistical treatment of data. The chapter also introduces the use of Excel’s built in functions and formula generation.Class Notes: Chapter 5 – Errors in Chemical Analysis: Assessing the quality of Results where errors come from and how they arise Errors are unavoidable

o The best we can do is try to minimize errors to acceptable levels Mean (average) is [the sum of the measured values] divided by [the number of measured values]

o Each individual data point is represented by [xi]

o The mean is a measure of “central tendency” – the central/typical value for a probability distribution The mean can be used to represent a group of data with a single number

o The mean gives each data point equal weight Median is the middle number in a set of measurements

o Arrange the data lowest to highest If there is an odd number of data points, the middle data point is the median If there is an even number of data points, the median is the average of the two central values

Mode is the most common result in a set of replicateso Is not used very often in analytical chemistry

-------------------------------------------------------------------------------------------------------EXAMPLE PROBLEM---------------------------------------------------------------------------------------------------------The data set contains 5 replicates of the same measurement:

5.23 g, 5.15 g, 5.62 g, 5.26 g, 5.10 g

What is the average?x=5.23g+5.15g+5.62 g+5.26 g+5.10 g

5=5.272=5.27

What is the median?In increasing order, the points are

5.10 g, 5.15 g, 5.23 g, 5.26 g, 5.62 gAnd the middle point is 5.23 g

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- The true value µ = accepted/expected value = the ideal value we are trying to reach

o We can never know the true value

Always the possibility of erroro In lab, the true value usually isn’t known

However, if we take many replicates (measurements) and eliminate everything but random errors, we can assume that the average is close to the true value

Precision is a measure of the variability in a data set shows how close the data points are relative to each other “relationship of data to itself”

o when a sample is analyzed multiple times, the individual results are rarely the same the data is randomly scattered around some value

o The absolute mathematical expression of precision is “the deviation from the mean” = the absolute value of [the difference of the individual measurement from the mean]

Range is the difference between the highest and lowest data points

Standard deviationo σ is used for a population (large data set)o s is used for a sample (small data set)

Variance is the square of the standard deviationo σ2 is used for a population (large data set)o s2 is used for a sample (small data set)

The relative mathematical expression of precision accounts for the size and spread with respect to the size of the measured values

o Relative deviation from the mean

o The Coefficient of Variance (CV) Tight precision is a good indicator of good accuracy but not always When precision is poor (wide spread of data points) accuracy is very low

o Poor precision means that your bad at taking data Accuracy is a measure of how close a data point is to the true value (expected, accepted)

o The difference between the true value and the actual value is called erroro The absolute mathematical expression of accuracy is Absolute error =

o The relative mathematical expression of accuracy is Relative error =

o The goal of analytical chemistry is accuracy A large number of replicates is required to reliably determine the true value µ

Classification of errorso Random (indeterminate error)

Are unavoidable Are scattered on both sides of the true value symmetric

Therefore the mean of data tends to be close to the true value The amount of random error is reflected by [the degree of the scattering pattern] precision

o Systematic (determinate error) are avoidable if discovered tend to be skewed in one direction relative to the true value because of an error made in making the measurement

o all measurements are too higho all measurements are too low

the average of this data set does not approximate the true value How systematic error s occur

Instrument errors: problems with a measure device/instrument Calibration removes this type of error

o Examples A pipet calibrated for 25°C used on a solution that isn’t 25°C Pipet mark is in the incorrect location The calibration of a balance wasn’t performed The circuit in an instrument is dusty and is slow to respond

Method errors: caused by non-ideal chemical physical behavior of the set up usedo Slow reaction timeo Incomplete reactiono Unstable specieso Side reactionso Incomplete solubility

Personal errors: carelessness, personal limitations, or inattentiono Measurements require judgment

Estimating the last digit of a reading Deciding when a reaction is complete linin

o Gross error Tends to deviate in a large way from the rest of the data “outliers” Statistics can be used to determine whether a measurement is an outlier that can be left out of future data calculations

o

Problem Assignment: Chapter problems are assigned to emphasize points of the chapter and to provide examples of testable problems. Chapter problems are not graded. 2, 5, 7a, 9a, 10a (calculator or spreadsheet)

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a. Distinguish between, and be able to give chemical examples for, the following terms:precision - accuracymean - median random - systematic - gross (types of errors)constant - proportional (types of errors)absolute - relative (calculation of errors)

b. Explain why analytical measurements are never free of error.

c. Be able to calculate the arithmetic mean and median for a set of analytical results. Know various terms that are interchangeable for ‘arithmetic mean.’

d. Explain, and be able to give examples for, systematic errors of an instrumental, method, or personal nature.

e. Describe the importance of analyzing standard samples and using an independent analytical method for maintenance of quality control in the analytical laboratory.

f. Explain the use of an analytical ‘blank’ determination. Explain what types of errors are corrected by using an analytical blank.

Chapter 6 - Random Error: How Certain Can We Be?Reading Assignment:

Read the entire chapter with the exception of Feature 6-2, ‘How Do You Calculate Those Areas Under a Curve,’ pp. 124-125. Include in the reading the Spreadsheet Exercise, ‘Computing the Standard Deviation,’ pp. 128-133.

This chapter concentrates on how statistics are used to treat random, or indeterminate, errors. The chapter emphasizes the spreadsheet calculation of standard deviation, variance, and coefficient of variation. Students will be expected to perform the same calculations in class using a scientific calculator with a statistical package.

Chapter 6 Random Error: Sources and Effects Random (indeterminate) errors are present in every measurement

o Sources of random errors Determine their magnitude Their effect on computed results of chemical analyses

o Significant figure conventionThe Nature of Random Errors Random errors cannot be positively identified

o Even if we identify the source of the error, it is impossible to detect/measure the error because they are so smallGaussian curve (normal error curve) – bell shaped curve that shows the symmetrical distribution of data around the mean of an infinite set of data A spread of data results from an accumulation of random uncertainties in an experiment

o A spread in a set of replicated measurements is the difference between the highest and lowest result A histogram is a bar graph Small errors tend to cancel each out and have a minimal effect on the mean value

o When errors occur in the same direction, they produce a large positive/negative net errorSources of random uncertainties

o Visual judgments The level of the water

o Variations in the drainage time o Temperature fluctuations

Affects the volume and viscosity of the liquido The performance of the balance

The cumulative influence of these variables is the observed scatter of results around the meanStatistical treatment of random errors We base statistical analyses on the assumption that random errors in analytical results follow a Gaussian distribution

o Rule of thumb: if we have more than 30 results and the data is not heavily skewed, we can use the Gaussian distributionSamples and Populations

o A population (universe) is a collection of all measurements of interest to the experimenter can be [finite and real] OR [ hypothetical and conceptual in nature]

o A sample is a subset of measurements selected from the population In a study, we infer information about a population from observations made on a sample

o EXAMPLE: The production of multivitamin tablets produces hundreds of thousands of tablets The population is fininte, but we don’t have the time or resources to test every single tablet for quality control

Instead, we select a sample of tablets (according to statiscial sampling principles) We can infer the characteristics of the population from those of the sample

Statistical sample vs analytical sampleo Analytical sample - ______ number of samples taken from a populationo Statistical sample – the [group of analytical samples] make up a single statistical sample

Properties of Gaussian Curves Gaussian curves can be described by an equation with two parameters

o (1) the population mean μo (2) the population standard deviation σ

A parameter is a quantity used to define a population or distribution Data values are variable The term statistic refers to an estimate of a parameter that is made from a sample of dataPopulation Mean vs. Sample mean

Problem Assignment: Chapter problems are assigned to emphasize points of the chapter and to provide examples of testable problems. Chapter problems are not graded. 5e, 7ace, and 9a(1st sample set)

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-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Learning Objectives: Testable material for in-class examinations.

a. Distinguish between, and be able to give chemical examples for, the following terms:sample (analysis) - sample (statistics)sample - population (statistics)degrees of freedom - number of replicate samplessample standard deviation (s) - population standard deviation (σ)standard deviation - variance - coefficient of variation (measures of precision)

b. Explain the conditions under which the mean can be considered the true value, μ.

c. Know how to calculate mean, standard deviation (sample and population), and variance for a set of replicate results using the statistical package in your scientific calculator.

Chapter 7 - Statistical Analysis: Evaluating the Data

Reading Assignment: Read the entire chapter. Students will not be expected to perform least-squares calculation or to graph x-y data in lecture as part of an in-class examinations.

Problem Assignment: Chapter problems are assigned to emphasize points of the chapter and to provide examples of testable problems. Chapter problems are not graded. 1e, 2a, 3a, 4c, 10a, 16ab, 19abcd

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a. Distinguish between, and be able to give chemical examples for, the following terms:population - infinite number of replicate measurementsconfidence interval - confidence limit - confidence level t - z (statistical values measured in units of standard deviation)σ - s (types of standard deviation)

b. Explain the meaning of a confidence interval for statistical treatment of data.

c. Use Table of Student t values to calculate confidence intervals for a given confidence level.

d. Briefly explain (qualitatively and quantitatively) how the use of replicate samples increases confidence in the data results.

e. Apply t-Test to determine whether two experimental means are significantly different.

f. Define ‘outlier’ data. Apply Q-Test to reject outlier data.

Chapter 8 - Gravimetric Methods of AnalysisReading Assignment: Skim (not read) the entire chapter with the exception of Section 8D, ‘Applications of Gravimetric Methods,’ pp. 194-198. All testable material will be covered in lecture.

Problem Assignment: Chapter problems are assigned to emphasize points of the chapter and to provide examples of testable problems. Chapter problems are not graded. 5, 9aeg, 12, 18, 22

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a. Distinguish between, and be able to give chemical examples for, the following terms:precipitation - volatilization (types of gravimetric analysis)colloidal - cyrstalline (types of precipitates)coagulation - peptization

b. Define colloidal precipitates in terms of physical properties. Briefly explain why colloidal precipitates hinder gravimetric analysis techniques.

c. Identify the three major types of coprecipitation: surface adsorption, mixed-crystal, and occlusion. Briefly explain how each type of coprecipitation can be avoided or minimized.

d. Briefly explain how digestion of precipitate and precipitation from homogeneous solution can be used to increase purity and growth of precipitate crystals.

e. Use mass measurement and stoichiometry to calculate gravimetric analysis problems.

Chapter 9 - Electrolyte Effects: Activity or Concentration

Reading Assignment:Skim (not read) the entire chapter. This is a short but important chapter. Chemistry majors will expand the discussion of activity in physical chemistry. All testable material will be covered in lecture.

The Spreadsheet Exercise, ‘Using Circular References for Iteratively Solving Equations,’ is a powerful tool for solving equilibrium equations.

Problem Assignment: Chapter problems are assigned to emphasize points of the chapter and to provide examples of testable problems. Chapter problems are not graded. 5, 7a, 8a, 11a

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a. Distinguish between, and be able to give chemical examples for, the following terms:activity - activity coefficientthermodynamic-based - concentration-based (equilibrium constants)

b. Know what is meant by the term ‘limiting law.’

c. Be able to qualitatively describe the term ‘ionic strength’ and be able to quantitatively calculate the ionic strength, μ, for a solution of inert electrolyte(s).

d. Use the Debye-Hückel equation to solve for activity coefficients. Describe the simplified Debye-Hückel Limiting Law.

e. Apply activity coefficients to equilibrium calculations.

f. Define the conditions under which effects of electrolytes can be neglected and the use of concentration results in minimal error when using mass-action law equilibrium calculations.

Analytical Chemistry

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