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Analytical Chemistry: Sample Preparation, Experimental Error, and Statistics, Study Guides, Projects, Research of Chemistry

University of Nebraska–Lincoln (UNL)Chemistry

A comprehensive overview of key concepts in analytical chemistry, including sample preparation techniques, understanding and managing experimental errors, and applying statistical methods for data analysis. It covers various aspects of sample preparation, such as weighing by difference, taring, and addressing buoyancy errors. The document also delves into the importance of error analysis, defining different types of errors, and using formulas for propagation of uncertainty. Additionally, it explores statistical concepts like gaussian curves, standard deviation, confidence intervals, and statistical tests like student's t-test and calibration curves. Valuable for students seeking a thorough understanding of these fundamental principles in analytical chemistry.

Typology: Study Guides, Projects, Research

2023/2024

Uploaded on 10/10/2024

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Chapters 0-1: The Analytical Process/Measurements

1) Be able to define or describe the following general terms, as related to chemical analysis:

Analytical chemistry: the science of chemical measurements

Qualitative analysis: what is in the sample

Quantitative analysis: how much of the substance is in the sample

Wet chemical methods: classical methods (ex: gravimetry, titrations)

Instrumental methods: spectroscopy, separation methods

2) Know the seven basic steps that are involved in a chemical analysis, the purpose of each

step, and common factors to consider when selecting or using each step.

1. Formulate the question to be answered

2. Select a procedure to answer the question

3. Sampling

4. Sample preparation

5. Analysis

6. Report/Interpret Results

7. Drawing Conclusions

5) Be familiar with the SI system of measurements, the base units used in this system, and

the prefixes that can be used with SI units.

6) Be able to define or describe each of the following units and ways of describing chemical

concentration, including the types of situations in which each of these measures of

concentration may be used:

Molarity (M): moles per liter

- 1 mol of a substance is 6.022 x 1023 units

Formality (F, Formal Conc.): molarity but initial concentration before dissociation

- If no dissociation, then Molarity = Formality

Molality (m): moles of substance/kg solvent

- Not dependent on temp

Percent composition: weight or volume

Mass of solute/Mass of total solution x 100

Volume of solute/Volume of total solution x 100

Composition in ppm or ppb: mass of substance/mass of sample x ____

- ppm is 106  1 ug/mL

- ppb is 109  1 ug/L

8) Know the dilution formula and be able to use it in calculations involving solution/sample

preparation.

M1V1 = M2V2

Chapter 2: Tools of the Trade

1) Know the general operating principle of a balance and the way in which modern

electronic balances work.

- Old balances compare the force on an object versus the force on a reference (two sides like a

teeter totter)

- Forces are gravity (pushing down) and buoyancy (pushing up)

- Can provide the mass of the object based on the mass of the reference

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Chapters 0-1: The Analytical Process/Measurements 1) Be able to define or describe the following general terms, as related to chemical analysis: Analytical chemistry: the science of chemical measurements Qualitative analysis: what is in the sample Quantitative analysis: how much of the substance is in the sample Wet chemical methods: classical methods (ex: gravimetry, titrations) Instrumental methods: spectroscopy, separation methods 2) Know the seven basic steps that are involved in a chemical analysis, the purpose of each step, and common factors to consider when selecting or using each step.

Formulate the question to be answered
Select a procedure to answer the question
Sampling
Sample preparation
Analysis
Report/Interpret Results
Drawing Conclusions **5) Be familiar with the SI system of measurements, the base units used in this system, and the prefixes that can be used with SI units.

Be able to define or describe each of the following units and ways of describing chemical concentration, including the types of situations in which each of these measures of concentration may be used: Molarity (M):** moles per liter
- 1 mol of a substance is 6.022 x 10^23 units Formality (F, Formal Conc.): molarity but initial concentration before dissociation
- If no dissociation, then Molarity = Formality Molality (m): moles of substance/kg solvent
- Not dependent on temp Percent composition: weight or volume Mass of solute/Mass of total solution x 100 Volume of solute/Volume of total solution x 100 Composition in ppm or ppb: mass of substance/mass of sample x ____
- ppm is 10^6  1 ug/mL
- ppb is 10^9  1 ug/L 8) Know the dilution formula and be able to use it in calculations involving solution/sample preparation. M 1 V 1 = M 2 V 2 Chapter 2: Tools of the Trade 1) Know the general operating principle of a balance and the way in which modern electronic balances work.

Old balances compare the force on an object versus the force on a reference (two sides like a teeter totter)
Forces are gravity (pushing down) and buoyancy (pushing up)
Can provide the mass of the object based on the mass of the reference

Modern balances use electromagnetic force (electric current is needed to generate the force) to return the pan to original position, and the current required to return the pan is proportional to the mass of the object 2) Know basic operational rules and approaches for weight/mass measurements, including possible sources of errors in weighing.
Chemicals should never be place directly on weighing pan because it could damage the pan
Errors
- Dirty/wet sample container
- Sample not at room temp
- Absorption of water by sample
- Vibrations or wind currents
- Unlevel balance
- Buoyancy errors (upward force exerted on an object in a liquid or gaseous fluid) 3) Be able to define or describe the following general terms: Weighing by difference: good for samples that change weight upon exposure to the atmosphere. Weigh empty container, transfer sample, weigh container again and then subtract to find mass of sample Taring : container is set on balance before sample is added, and containers weight is set to 0 Hygroscopic : samples that readily absorb water from the air Buoyancy error: failure to correct for weight difference due to displacement of air by the sample, results in the object seeming lighter 4) Know the buoyancy equation, when it is important to use this equation, and how to use this equation in calculations to find the true mass of a sample.
Buoyancy errors get larger as the measured mass gets larger
Errors are larger for liquid samples than for solid samples m = true mass (will be greater) m’ = mass read from balance (will be lighter) d = density of sample da = density of air (always 0.0012 g/mL at 1 bar and 25°C) dw = density of calibration weights (always 8.0 g/mL) 5) Be able to define or describe each of these items or terms as related to volume measurements: Buret: delivers multiple aliquots of a liquid in known volumes, estimate to +/- 0.01. Used a lot for titration Micropipette: delivers volumes of 1-1000 microliters (small amounts) Oven drying: used for reagent or sample prep by removing water at a higher temp than a desiccator

A number that is found by multiplying or dividing other numbers: use the number of sig figs of each given number in the final answer, and choose the least number of sig figs A number that is found by taking a logarithm or antilogarithm: For a log, the whole number in the parenthesis determines the sig figs in the mantissa (the number after the decimal) in the final answer. For an antilog, the mantissa (the numbers after the decimal) of the number that is taken the antilog of, determines the sig figs in the final answer. Its backwards 5) Be able to define each of the following terms, as related to types of errors and describing experimental results: Systematic error: error that is in all results, comes from inappropriate methods or experimental techniques, can be eliminated Random error: error from random variations in the measurement of a physical quantity, results in a bell curve around the mean, this is always present and can’t be eliminated Precision: how the results of a single measurement compare from one trial to the next (related to random error), results in relation to each other Propagation of uncertainty (“propagation of error”) Accuracy: how close an answer is to the true value (related to systematic error), results in relation to the true number Absolute uncertainty: uncertainty associated with a measurement Relative uncertainty: uncertainty in relation to the measured value, a percent Round-off error: error that can come from rounding the answer too early, don’t round until the end 7) Know how to use formulas for the propagation of uncertainty/error to determine the absolute or relative uncertainty for the final values in each of the following situations: A number that is found by adding or subtracting other numbers

Absolute uncertainty can be calculated, then relative uncertainty calculated using absolute A number that is found by multiplying or dividing other numbers
Relative Uncertainty must be found first, and then absolute uncertainty found from the relative uncertainty A number that is found by using a combination of addition/subtraction with multiplication/division
Do the addition or subtraction first and find absolute uncertainty
Convert absolute uncertainties to relative uncertainties to be able to carry out the multiplication or division
Can convert back to absolute or keep as relative depending on what is needed

Chapter 4: Statistics 1) Be able to describe the general properties of a Gaussian curve, the general factors used to describe such a distribution, and methods for determining the probability that a given result will occur in a particular range of such a distribution.

Same as the “Normal Curve”
+/- 1 standard deviation contains 68.2% of data, +/- 2 standard deviations contains 95.4% of the data, +/- 3 standard deviations contains 99.8% of the data
mean value is the middle of the curve
“z” can tell us how many standard deviations a value is above or below the mean 2) Know the definitions and equations to calculate or find the following values for a set of data: Mean (average): central overall value Standard deviation: width/variation of values within the data set Variance: used to describe how precise a distribution of results is, Variance = s^2 Range: difference in the highest and lowest values in a data set Median: value which has an equal number of data values above it and below it when ranked from lowest to highest Confidence interval: tells us the probability that the range of numbers contains the “true” mean. As n increases, the confidence interval decreases (aka become more confident)
50% CI means that range of numbers only contains true mean 50% of the time, also 50/ trials will include the true mean (lots of ways of looking at the meaning of a CI) 3) Be able to define each of the following terms: Student’s t-value: table of critical t-values used to compare to a calculated t-value Standard deviation of the mean: standard deviation that is already divided by the square root of n. Used for calibration curve confidence interval. For degrees of freedom for standard deviation of the mean, its n-2 instead of n- Outlier: a data point that is very different from others obtained under supposedly identical conditions, can use the Grubbs test to determine if it is an outlier

Determine the Gtable value and if Gcalculated > Gtable, the questionable value can be rejected
If you do need to discard as an outlier, recalculate the average and standard deviation without the number
With the same sample *Whenever the calculated value is > the table value, you reject the null hypothesis (they are different, or it is an outlier) 6) Be able to describe the process of linear regression and the types of calculations that are used when determining the fit of data to a line by this approach. Slope: describes the direction of the data on the graph y-Intercept: where x = 0 7) Know how to evaluate the goodness of fit for a line by using a correlation coefficient or a residual plot. Correlation coefficient: a value between -1 and +1 that indicates how well a best-fit line describes the data
- r = 0 means that there is a totally random relationships between the data points and the best-fit line
- The R^2 value indicates that ____% of the y-axis variation is explained by the variation in the x-axis
- Not always great at determining the fit of the line, so use residual plot too Coefficient of determination: r^2 , gives a value between 0 and 1 Residual plot: a plot of the difference between each y value and the value predicted by the best- fit line (yi – ycalc)
line at yi – ycalc = 0 should be included because that is where it should perfectly agree (basically just a horizontal line at 0, kind of like what we did for the buret)
there should be no trend, but if there is a trend in the residual plots then an alternative fit is needed Chapter 5: Calibration Methods 1) Be able to define what is meant by a “calibration curve” in chemical analysis and to describe how such a curve can be constructed and used to determine the amount of an analyte in an unknown sample.
graph that shows analytical response as a function of the known quantity of analyte, which helps determine unknown quantities by looking at their responses in relation to the known ones
want to prepare known samples of analyte, measure the response of the analyte using whatever procedure you are using, and then subtract average response of the blank with no analyte
graph analyte concentration on x-axis, and corrected response on y-axis
prefer to use the area that is linear
Linear Range: analyte concentration range over which the response is directly proportional to the concentration
Dynamic Range: concentration range over which there is any measurable response to analyte (not always linear)
- Includes the linear range though, but doesn’t include where the line goes horizontal 2) Be able to define each of the following terms: Detection limit (lower limit of detection): smallest quantity of an analyte that is significantly different from the blank Signal

Signal detection limit (minimum detectable signal) Noise Minimum detectable concentration (Detection limit): removes the uncertainty of what is a real signal Signal-to-noise ratio (S/N): when equal to 3, the signal is readily detectable

Still too small for accurate measurement, so have to use LOQ instead Lower limit of quantitation (LOQ): when the signal is 10 times as great as the noise
Adds more certainty that we really have a peak there **Response factor:

Be able to calculate the signal detection limit and minimum detectable concentration at a signal-to-noise ratio of 3, and at a signal-to-noise ratio of 10 to get the limit of quantitation for an analytical method.** Detection Limit:

Where yblank is the average of the signals of the blanks
Where s is the standard deviation of the samples Corrected Signal (proportional to sample concentration): Minimum Detectable Concentration: LOQ = Limit of Quantitation
Where s is the standard deviation of the samples
Where m is the slope 4) Be familiar with the technique of standard addition, including the purpose of this method and the way it is carried out as part of a chemical analysis. - Protocol to determine the quantity of an unknown
Known quantities of an analyte are added to the unknown
Useful for complex mixtures 5) Be able to calculate the concentration of an unknown sample using data from the method of standard addition. [X]i = concen. of analyte in initial solution [S]f = concentration of standard in final solution [X]f = concentration of analyte in final solution *X is the unknown 6) Be familiar with the use of internal standards, including the purpose of using internal standards and the way they are used as part of a chemical analysis.
Known amount of a compound, different from analyte but similar in its properties, added to the unknown

Solubility changes depending on polar/nonpolar (like dissolves like) 6) Be able to identify and describe ways of promoting crystal growth and minimizing the relative supersaturation in a gravimetric analysis.
To decrease R
Increase temp which increases S
Add precipitating reagent slowly while vigorously mixing
Keep volume of solution large
Control S through chemical means (pH, etc.) 7) Be familiar with the types of impurities that may occur during precipitation, including those involving adsorbed impurities or absorbed impurities (e.g., the latter due to occlusion or inclusion). Adsorbed Impurities: external impurities, adsorbed to the surface Absorbed Impurities: internal impurities, absorbed or trapped in pockets in the crystal
Occlusion: impurities trapped inside that possibly contain solvent
Inclusion: impure ions randomly are in the crystal that shouldn’t be 8) Be able to describe general techniques that can be used to minimize the effects of impurities.
Small R
Use digestion: converts the solid to a liquid to analyze for impurities
Wash the precipitate and redissolve it in fresh solvent and reprecipitate
Add a masking agent: keeps impurities from precipitating, but not analyte 9) Know the reasons for washing and drying or igniting some precipitates.
Drying/igniting can get rid of H 2 O
To dry, weigh and get stable mass measurements
Ignite (heat up) can convert a certain thing to a given chemical form to get rid of it (burn off water for example)

Analytical Chemistry: Sample Preparation, Experimental Error, and Statistics, Study Guides, Projects, Research of Chemistry

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