AUCHE 220 Midterm #1

Analytical Chemistry

The branch of chemistry that deals with isolating, identifying, and quantifying material of interest (the analyte).

Qualitative vs Quantitative analysis

Qualitative: determination of non-numerical properties

Quantitative: Determination of the numerical amount

Steps in chemical analysis

formulating the question, selecting analytical procedures, sampling, sample preparation, analysis, reporting and interpretation, drawing conclusions

Formulating a Question

Asking a meaningful question

Selecting an analytical procedure

availability, cost, speed. Composition and amount of sample available

Sampling

Lot: Total material from which a sample is taken

Sample: A dmaller, representative collection of units from the lot used to determine something about the lot

Sampling: process of selecting a representative material to analyze from the lot.(largest source of uncertainty)

Stratified sampling

Compositive sample

involves diving the lot into specific zones based on homogeneous characteristics

a sample formed by combining subsets of samples

Sample preparation

converts a representative bulk sample into a form suitable for analysis

Masking

To transform an interfering species into an undetectable form

Sample Prep diagram

Aliquot is portions taken for individual analysis

Solution

a homogenous mixture of two or more substances

Solute vs solvent

-substance that is being dissolved

-substance that is used to dissolve the solute

Concentration

amount of solute in a given volume or mass of solution or solvent

Mole(mol)

amount of substance that contains the same number of elementary entities as there are atoms in exactly 12g of carbon-12 isotope

Avogrado's number (Na)

6.02214199 times 10^23 mol^-1. Number of elementary entities in 1 mole of a substance

Molarity (molar conc.(M))

number of moles of solute per liter of solution. Changes with temperature

Molality(m)

number of moles of solute per kg of solvent. Independent of temperature

Avogrado's Law

Part of ideal gas law; the volume of an ideal gas is proportional to the number of moles when pressure and temperature is constant.

Percent composition

The percent of each element present in a compound

Dilution of Solutions

When preparing a solution of a certain molarity, a reagent is weighted out and dissolved in a volumetric flask.

Diluted for time efficiency and consistency

Moles taken from conc. solution = moles placed in dilute solution

Stoichiometry

used to determine the quantitative relationship between reactants and products in a chemical reaction.

Mole ratio is used to relate the number of moles of any two substances in a reaction

How is a balance chosen?

based on the performance range required.

Top loading vs. analytical balance

for large quantities and approximate weights.

for small quantities and precise weighings.

Weighing errors

- balance not level - check the liquid bubble on the floor of the weighing chamber

-balance pan is dirty

-air current/draft = close ALL windows on the balance

-fingerprints (can transfer 0.3-0.5 mg) - use finger clots or folded paper

-static charge - use an anti-static brush prior to weighing

-Beaker + sample must be at ambient temperature

-beaker + sample must be dry

Weighing by addition

the standard procedure

- weigh container = W1

add sample to container

weigh container and sample = W2

Wsample= W2-W1

Weighing by difference

For hydroscopic compounds and multiple weighings.

-tare

weigh sealed bottle of hydro agent = W1

Quantitatively transfer reagent from bottle to beaker

reweigh sealed bottle = W2

W sample = W1-W2

What are the differences between weighing by addition vs. difference?

Addition:

2n weighings for n samples

Difference:

req n+1 weighings for n samples

Buoyancy effect

Buoyancy: upward force on an object in a liquid or gaseous fluid

Archimedes principle: an object in fluid will experience a loss in weight = weight of fluid it displaces

balances are calibrated with dense, steel weights

Buoyancy error

errors develop when weighing objects of a significantly different density. Density of liquids is much lower than the density of steel weights

m=true mass

m1=observed mass

da=density of air = 0.0012g/ml @ 1 bar, 25C

dw = density of sstandard steel weight = 8.0g.mL

ds = density of sample

Volumetric Flask

type of flask that has been calibrated to contain a precise volume at a certain temperature

How to use a volumetric flask

- add components of solution, fill 1/3, and swirl

- fill close to final volume and mix again

= carefully adjust to final volume use a medicine dropper so meniscus is even with calibration line

-cap firmly, invert, and swirl flask several times

Pipet

delivers fixed volumes of liquid

- labeled TD (to deliver)

- more accurate and precise than a buret

What are the three types of pipets?

1. volumetric

2. Mohr pipet

3. Micropipet

Buret

delivers variable volumes

less accurate than pipet

What is parallax error?

reading the meniscus right

Sig figs

minimum number of digits in a value/measurement necessary to reflect its precision. higher sig figs = higher precision and less uncertainty

Experimental error

every measurement we make has some level of uncertainty to it

Systematic error

determinate, reproducible. due to poor technique, faulty calibration, poor experimental design. Controls accuracy of measurement

Random error

indeterminate, non-reproducible

errors are distributed about a mean value

easily treated with statistical methods

Controls the precision of a measurement

Certified reference materials (CRMs)

used to assess the accuracy of analyticaal procedure, calibrate instruments, and check product quality

Uncertainty vs. error

error is the difference between a measurement and the true value

uncertainty is the range where the true value could be within

What are the 3 types of uncertainty?

1. Absolute uncertainty (delta y): the margin of uncertainty associated with a measurement

2. Relative uncertainty (delta y/y): compares the absolute uncertainty with the measurement itself

3. % relative uncertainty : delta y/y expressed as a percentage

Mean

average value

reporting the mean is most useful when the variation between replicate measurements are small and randomly distributed

Standard deviation

used to describe the scatter in data set.

Useful when scatter is random

estimates absolute error

smaller SD --> higher precision

Degrees of freedom (DF)

indicates the number of measurement values that went into calculating the estimated error

DF= n-1

Relative standard deviation

used to show whether the SD is small or large compared to the mean

often expressed as %, ppm, etc

x +/- RSD

RSD= SD/mean

Median

middle value in a data set that has been arranged in order of size. Most useful when there is an outlier.

Median is less affected by outliers than mean.

also useful for small data sets with large scatter

Range

difference between the highest and lowest values in a dataset

Mean vs median

Mean-

statistically the most valid measure

data uniformly distributed around the mean

Median-

useful for small data sets with considerable scatter

less affected by outliers

Q Test

Qobs is compared to Qtab

Qobs>Qtab can reject the data point

Qobs

Grubbs Test

similar to Q test but uses the mean and standard deviation in its calculation

Gobs>Gtab can reject data point

- must report the mean +/- SD

Gobs

Gaussian Curve

represents the normal distribution of independent, random variables around a mean

random errors behave under Gaussian/normal statistics

Hypothesis tests

Null hypothesis: there is no effect in the population

Alternative hypothesis: an effect in the population; what we are testing.

A test is calculated from the sample mean or proportion

two-tailed test

non-directional

tests for effects on the sample mean in either direction. Does not tell you which direction, only that the sample mean does not equal target value

one-tailed test

directional

tests effects on the sample mean in one direction from the target value

used when you have a preconceived reason to believe that a method gives systematically low values or high values

Confidence intervals

the range around the observed mean in which you expect the true mean to be within, at a certain probability

t-Tests and different types

used to compare to sets of measurements by their mean

1. comparison of measured mean to a known standard value - one-sample

2. camparing two measured means - two sample

3. comparing the means of two methods - paired t-test

One sample t-test

used to check if chosen method is acceptable for intended analysis

tcalc < ttab = values are not significantly different

tcalc>ttab = values are different within the confidence limit selected

tcalc = |mean-known value|/s times square root of n

Two sample t-test

determines whether two sets of replicate measures give the same or different results within a certain confidence level.

DF= (n1+n2-2)

tcalcttab results are different within the confidence limit selected

F-test

used to compare two or more sets of measurements by their variance = SD

larger SD is always the numerator so F greater than or equal to 1

Calibration curve

shows relationship between the instrument and the analyte

- constructed by measuring the resonse of standards(has a known analyte)

-used to interpolate unknown (analyte) in a sample

In linear range, reponse is proportional to analyte

dynamic range

concentration range over which there is measurable response, even if response is not linear

Constructing a calibration curve

1. Prep blank (without analyte)

2. Prep standards

3. measure the blank and standards

4. Plot calibration curve

What are the best practices when making a calibration curve?

- use at least 6 concentrations and 2 replicates

- visually inspect for outliers before drawing a best fit line

Advantages and disadvantages of using graphical method to find a best fit line

advantage: by visually inspecting data, it becomes obvious if the data falls on a straight line

disadvantage: line is drawn by "eye", a subjective process leading to imprecision in interpretation of data

Advantages and disadvantages of using method of least squares to find best fit line

Advantage: the method is objective and without systematic bias hence more used than graphical method

Disadvantage: the method is accurate only if the data truly fall on a straight line.

-best to cross-check the least squares method results with the graphical approach.

What are some assumptions on the Method of Least Squares?

a. linear relationship

b. Error in y is substantially greater than in x

c. uncertainties in y value are similar

d. any error in y is due to measurement (random error)

Method of Least Squares

goal is to minimize the vertical deviation between the data points and the best fit line