Chem 2100 Section 1 Notes

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General Concepts

andExperimental Error

Harris (8thEdition)

Chapter 3 => p. 51 - 67

Section 1

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1.1 I ntroduction

Analytical Chemistry = separating, identifying, and determining the

relative amounts of components in sample of matter.

Two main areas of analytical chemistry:

QualitativeAnalysis: reveals chemical identity.

-Whatelements or compounds present?

Quantitative Analysis: establishes relative amountof species

(analytes) in numerical terms.

-How much of substance is present?

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3

From: Analytical Chemistry, Gary D. Christian, John Wiley & Sons, 2004


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Classification of Analytical Methods

Two classes:

(i) Classical or wet-chemical methods (ii) Instrumental methods

(i) Classical or wet-chemical methods

- Group of analytical methods that only requires the use of chemicals,

a balance, calibrated glassware, and other commonplace apparatus

such as funnels, burners or hot plates, flasks, and beakers.

Qualitativeidentification by colour, indicators, boiling points, odours.

Quantitativemass (e.g., gravimetric) or volume (e.g., volumetric analyses).

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(ii) Instrumental methods

- Analytical methods that requires the use of an analytical instrument

in addition to the apparatus used for classical analyses.

Qualitativeidentification by measuring physical propertyExamples:

Spectroscopy =>

Electrochemistry =>

Chromatography =>

Capillary electrophoresis =>

Quantitativemeasuring property and determining relationship to

concentration

Examples:

Spectrophotometry =>

Mass spectrometry =>

Chromatography =>

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Calibration of Analytical Instrument

1. Prepare a number of standard solutions of increasing concentrations

e.g., 0.1 M, 0.2 M, 0.3 M, 0.4 M, 0.5 M

2. Measure a quantitative property (e.g., absorbance) for all solutions using

the instrument.

Example:

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3. Plot a curve for the values (Absorbance versus Concentrations)

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Selecting an Analytical Method

What accuracy is required?

How much sample is available?

What is the concentration range of the analyte?

What components of the sample will cause interference?

What are the physical and chemical properties of the sample matrix?

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Flow Diagram of the Steps in Quantitative Analysis


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1.2 Basic Concepts

Significant Figures for Mixed Operations Mixed operations are mathematical computations that involve

subtraction/addition and multiplication/division. Convert all numbers into scientific notation and do the computation.

Express the answer to conform to the number with the least number

of significant figures.

Example:

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Logarithms and Antilogarithms

For an expression: n = 10 a, the base 10 logarithm of nis the number a.

i.e., n = 10 ameans log n = a

nis referred to as the antilogarithm of a

A logarithm is composed of two parts:

Characteristic: integer part Mantissa: decimal part

Number of digits in mantissa of logx= number of significant figures inx.

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Chemical Concentrations

Molarity and Molality

- Molarity (M): concentration expressed as number of moles of substanceper liter of solution.

It also expresses number of millimoles of a solute per milliliter of solution.

Molality (m): concentration expressed as moles of substance per

kilogram of solvent (not total solution).

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Molarity changes with temperature because the volume of a solution

changes with temperature since volume depends on density, a

temperature dependent property.

Molality is independent of temperature.


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Formal Concentration (F)

- Number of moles of solute, regardless of chemical form, per liter of solution.

- Used for solutions of ionic salts that do not exist as molecules in the solid or in

the solution i.e., strong electrolytes, that ionize.e.g.,

- It is numerically equal to molarity if the substance dissolve without dissociating

into ions.

e.g.,

- For substances that ionize in solution, molarity and formality are different.

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Percent Composition

- Three forms:

(i) Weight percent (wt %; % w/w)

(ii)Volume percent (vol %; % v/v)

(iii) Weight-to-volume percent (% w/v)

- All are expressed as units of solute per 100 units of sample.

(i) Weight percent (wt %; % w/w)- Grams of solute per 100 g of solution.

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(ii) Volume percent (vol %; % v/v)

- Milliliters of solute per 100 mL of solution.

(iii) Weight-to-volume percent (% w/v)

- Grams of solute per 100 mL of solution.

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Part Per Thousand, Part Per Million and Part Per Billion

(i) Part per thousand (ppt or %)grams of substance per thousand

of total solution or mixture.

(ii) Part per million (ppm)grams of substance per million of totalsolution or mixture.

(iii) Part per billion (ppb)grams of substance per billion of total

solution or mixture.

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1 g of water is considered approximately equal to 1 mL of water.

Thus, ppm and ppb can be expressed as:

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Summary

Units used

Name Abbreviation w/w w/v v/v

Part per thousand or ppt mg/g mg/mL mL/L

Part per million ppm mg/g mg/mL nL/mL

mg/kg mg/L mL/L

Part per billion ppb ng/g ng/mL nL/L

mg/kg mg/L

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Conversion of Concentrations

(1) Converting ppb into molari ty

A water sample contains 15.0 ppb MgCO3. Calculate the molarity of the

MgCO3 solution.

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(2) Conversion into ppm

A 50.0-mL serum sample contains 5.34 x 105g glucose. Calculate the

concentration of glucose in ppm.

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(3) Conversion of ppm to molari ty of ion

What is the molarity of K+in a solution that contains 32.5 ppm K3Fe(CN)6?

[K3Fe(CN)6 = 329.3 g/mol].

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(4) Preparation of solution containing ppm of an ion

(a) Calculate the molar concentration of 2.00 ppm solutions each of Li+ and Pb2+.

(b) What weight of Pb(NO3)2will have to be dissolved in 1 liter of water to

prepare 200 ppm Pb2+solution?

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(5) Conversion of wt % into molari ty and molali ty

Concentrated HCl (MW 36.46) has a density of 1.19 g/mL andis 37.0 wt% HCl.

Calculate the molarity and molality for this acid.

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P i i d A


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Precision and Accuracy

Precision

- A measure of the reproducibility of the method.

How close the results, obtained in the same way, are.

- Usually expressed as a percent relative standard deviation, % RSD.

Accuracy

- Indicates how close a measured value is to the truevalue.

- Normally expressed as the relative percent error.

A 1% error indicates that a measured concentration is within 1% of

the true analyte concentration. 25


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Example:


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Absolute Uncertainty and Relative Uncertainty

Absolute Uncertainty

- indicates the margin of uncertainty associated with a measurement.

Example:

Relative Uncertainty

- compares the magnitude of the absolute uncertainty with the magnitude

of its associated measurement.

Example:

- When expressed as a percentage, it is referred to as percent

relative uncertainty.

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1.3 Types of Error in Exper imental Data

Two main types:

(i) Systematic error

(ii) Random error

(i) Systematic error

- Also called Determinate error.

- Error is either high every time or low every time.- Causes mean of a set of data to differ from accepted value.

affects accuracyof result.

- Originates from a flaw in equipment or the design of an experiment.

- Key feature of this error is that it is reproducible.

- Definite causes (sources) can be identified and eliminated.

Statistics not used here.

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Examples:

Incorrect standardization of a pH meter.

Uncalibrated buret

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(ii) Random error

- Also called Indeterminate error.

- Produces a value that sometimes is high and sometimes is low.

- Originates from effects of uncontrolled variables in a measurement,

and thus, it is always present.

- Random errors follow a normal distribution, or a Gaussian curve.

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- Causes data to be scattered more or less symmetrically around

mean value of the normal distribution.

affects precisionof measurement.

- Not readily discovered and not eliminatedStatistics used.

Hence it is taken into account when reporting analytical results.

Repeated measurement of same quantity can reduce it.

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Note:

Example:

Flipping coins

- appearance of heads or tails is a random event.

- distribution follows a Gaussian or Normal curve

- a coin was flipped ten times by 395 students over a 13-year period


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1.4 Propagation of Uncertainty

- It could occur from two sources:

From random error From systematic error

From Random Error

- In an analysis, the greater the number of measurement steps we take,

the less certain we become of the true measurement.

- Each of the uncertainties contributes its part to the final, larger

possible uncertainty.

- Since each of the uncertainties is carried along to the final measurement,

the process is called propagation of uncertainty.

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E t d L ith


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Exponents and Logarithms

(i) Uncertainty for powers and roots

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(ii) Uncertainty for logarithm

- Relative uncertainty, not percent relative uncertainty, is used in calculations.

=> Because one side of equation has relative uncertainty and the other has

absolute uncertainty.

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(iii) U t i t f t l l ith


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(iii) Uncertainty for natural logarithm

- Relative uncertainty, not percent relative uncertainty, is used in calculations.

(iv) Uncertainty for 10x

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(v) Uncertainty for ex

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(vi) Uncertainty in H+ concentration


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(vi) Uncertainty in H concentration

Example: For pH = 5.21 0.03, find [H+] and its uncertainty.

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From Systematic Error

- Two common examples are encountered in Chemistry.

(i) Uncertainty in Molecular Mass

- The uncertainty is hardly from random error in measuring the

atomic mass.

- It is mainly from isotopic variation in samples of oxygen from

different sources.

Example 1: Identical atoms

- Uncertainty in mass of nidentical atoms = nx (uncertainty in atomic mass).

Consider the atomic mass of oxygen = 15.9994 0.0003 g/mol.

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Example 2: Non-identical atoms

- For C2H4

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(ii) Multiple Deliveries from One Pipet

- Consider a 25-mL volumetric pipet which is certified by manufacturer to

deliver 25.00 0.03 mL.

- The volume delivered by such a pipet is reproducible but it can lie within the

range 24.97 to 25.03 mL.

- Difference between 25.00 mL and the actual volume delivered by the pipet is

a systematic error.

Chem 2100 Section 1 Notes

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