Lab Methods Midterm

M (molarity)

M (molarity)

amount solute/volume solution

mol solute/L solution

F (formality)

= Molarity, used for strong electrolytes

mol solute/L solution

N (normality)

# equivalents solute/volume solution

# eq. solute/L solution

m (molality)

amount solute/mass solvent

mol solute/kg solvent

Mole (X)

mole A/total # moles

wt./wt.

mass A/total mass

wt./vol.

mass A/total Volume

vol./vol.

vol. A/total Volume

pph (Parts per hundred)

10² x wt./wt. fraction

10² x wt./vol. fraction

10² x vol./vol. fraction

ppm (Parts per million)

10⁶ x wt./wt.

10⁶ x wt./vol.

10⁶ x vol./vol.

ppb (Parts per billion)

10⁹ x wt./wt.

10⁹ x wt./vol.

10⁹ x vol./vol.

Chemical grades

Crude Grade< Technical Grade< Laboratory Grade< ACS Reagent Grade< Primary Standard Grade

Significant figures

• Use scientific notation as necessary to avoid confusion

• Final zeros to the right of the decimal place are significant

• Spacer zero to the left of the decimal place are not significant unless there is a number before the decimal point

Significant figures for addition/subtraction

Number with fewest decimal places determines number of decimal places in answer (least number decimal places)

Significant figures for multiplication/division

Number with fewest significant figures determines number of significant figures in answer (least number significant figures)

Significant figures for multiple calculations

When multiple calculations must be carried out, carry all digits through the calculation and then determine the number of significant figures for the final answer (make decision at end)

Significant Figures for numbers with calculated uncertainty

The calculated uncertainty should determine the number of digits reported in the measured value (first significant digit in uncertainty)

Absolute Uncertainty

the margin of uncertainty associated with a given measurement (absolute does not equal absolute value)

=experimental value - accepted value (retain sign)

Relative Uncertainty

Compares size of absolute uncertainty to size of measurement itself

=absolute error/accepted value

Percent Relative Uncertainty

Relative uncertainty × 100

Determinate (systematic) error

Errors having a definite value and an assignable cause (ex. a flow or limitation of the equipment or experimental design). Results from replicate analyses are consistently high or consistently low.

Three main types of determinate error

1. Method error

2. Instrumental error

3. Personal error

Indeterminate (random) error

Uncontrolled variable(s) in the experiment. Equally likely to be positive (higher) as they are to be negative (lower)

Propagation of Error

When a measurement with an associated uncertainty is combined with another measurement with an associated uncertainty, we can calculate standard deviation, S_y for the result, y (standard deviation of a computed mathematical result)

Null hypothesis

difference between values is not statistically significant and can be explained by intermediate (random) error *ASSUMED TO BE TRUE UNLESS TEST INDICATES OTHERWISE*

Alternative hypothesis

difference is statistically significant and difference between values is too great to be explained by indeterminate error

Grubbs Test (calculation of G)

Can provide statistical support for rejection of a questionable measurement (detection of statistical outliers)

G _calculated = |x _questionable - mean|/s

G _calculated > G _{tabular value}

Questionable point may be discarded (alternative hypothesis supported)

F test (calculation of F)

Can indicate whether standard deviations (i.e./ precision) of two methods/sample populations are statistically different (comparison of precision of two sets of measurements)

F _calculated = (s₁)² / (s₂)²

^{*Larger standard deviation always in numerator so F_calculated > 1*}

F_calculated> F_table

Difference in precision is statistically significant (alternative hypothesis supported)

Confidence Interval

T test to compare mean with refence (true/known/accepted) value (comparison of measured value to reference value)

Confidence interval= mean±(ts/√n)

Does reference value fall within 95% confidence interval range?

Yes= Difference between mean and true value can be attributed to random error. Difference is not statistically significant.

No= Difference between mean and true value cannot be attributed to random error. Difference between mean and true value is statistically significant.

Comparison of Two Means

T test to compare two mean values with similar precision

• Use t_calc and s_spooled

Degrees of freedom for this= n₁+n₂ — 2

Comparing individual differences (paired data)

When you have obtained a measurement for several samples using two different methods (“paired data”) and you want to determine whether the difference between the individual measurements using the two methods is statistically significant.

d (has a line over top of it)= average of differences in methods for different samples

s_d= √(∑(d_i−d)²/n-1))

Comparison of two means (T-test to compare two mean values with similar precision)

Function in excel= t Test: Two-sample Assuming Equal Variances

Compare: t Critical two-tail (tabular value) to t stat (calculated value)

Comparison of two means (T-test to compare two mean values with different precision)

Function in Excel: = t Test: Two-Sample Assuming Unequal Variances

Compare: t Critical two-tail (tabular value) to t Stat (calculated value)

Comparing individual differences — Paired data (T test for paired data)

Function in Excel: = t-test Paired 2 sample for means

Compare: Absolute value of t critical two-tail (tabular value) to t stat (calculated value)

Main types of gravimetric analysis

Precipitation:

• Reaction to form solid

• Weigh the product and use the stoichiometric ratio to determine amount of analyte

Volatilization/Combustion:

• Reaction to form volatile product

• Weigh volatile product or weigh difference in sample to get weight of analyte

Precipitation Method

1. Preparation of the solution

2. Chemical conversion of analyte to a sparingly soluble OR insoluble precipitate

3. Digestion

4. Filtration

5. Washing

6. Drying

7. Weighing

Crystal Growth

Need supersaturated solution (more dissolved solute then present at equilibrium) for crystal growth

Crystallization:

1. Nucleation— solute forms cluster then reorganizes into ordered structures

2. Particle growth— other molecules etc. condense onto nucleation site to create larger crystals, this is called Ostwald ripening

Digestion— After precipitation, heat reaction and allow to sit, slow recrystallization and expulsion of impurities

Volatilization (direct method)

1. Ignite sample

2. Collect water or other analyte of interest on solid desiccant or absorbent

3. Measure mass gain of desiccant or absorbent

Volatilization (indirect method)

1. React to form volatile product

2. Find difference in weight after release of volatile product

*Used most commonly to determine amount of water, carbon dioxide, sulfides and sulfites, carbon and hydrogen*

Accuracy

how close a measurement is to the true or accepted value

Precision

how close measurements of the same item are close to each other

% relative standard deviation ( aka Coefficient of variation)

%RSD or CV= s/mean ×100%

Standard error

SE= s/√n

Variance

s²

95% confidence interval formula

95% CI= ts/√n

Relative Standard Deviation

RSD= s/mean

Spread (or range)

difference between maximum and minimum value in a data sheet

Random sampling

Collected at random from target population

Judgmental Sampling

Opposite of random sampling. Use info to ID specific sampling locations

Systematic Sampling

sampling at specific intervals in space (and/or time)

Systematic-Judgmental Sampling

sampling that combines systematic and judgmental sampling

Stratified Sampling (aka Random-Judgmental Sampling)

Sampling combining random and judgmental sampling

Convenience Sampling

selecting areas that are easy to sample

Grab/selective Sampling

removing a portion of the bulk at a given time

Composite Sampling

Combining samples to have enough material

In situ Sampling

sample collected in real time

1. 10¹

2. 10²

3. 10³

4. 10⁶

5. 10⁹

6. 10¹²

7. 10¹⁵

8. 10¹⁸

9. 10²¹

10. 10²⁴

1. deca (da-)

2. hecto (h-)

3. kilo (k-)

4. mega (M-)

5. giga (G-)

6. tera (T-)

7. peta (P-)

8. exa (E-)

9. zetta (Z-)

10. Yotta (Y-)

1. 10⁻¹

2. 10⁻²

3. 10⁻³

4. 10⁻⁶

5. 10⁻⁹

6. 10⁻¹²

7. 10⁻¹⁵

8. 10⁻¹⁸

9. 10⁻²¹

10. 10⁻²⁴

1. deci (d-)

2. centi (c-)

3. milli (m-)

4. micro (µ-)

5. nano (n-)

6. pico (p-)

7. femto (f-)

8. atto (a-)

9. zepto (z-)

10. yocto (y-)

Typical Steps in Analytical Chemistry

1. Formulation of Question

2. Selection of Analytical Tools and Procedures

3. Sample Collection

4. Sample Preparation

5. Measurement and Analysis

6. Interpretation and Reporting, Drawing Conclusions

Preparing solution from Solid

1. Based on desired concentration and volume, determine amount of reagent required.
2. Obtain high purity, reagent grade solid. [In an oven, dry solid in a weighing bottle to
remove adsorbed impurities. Cool in a desiccator.]
3. Accurately weigh by difference ~calculated mass on balance; record actual mass.
4. Quantitatively transfer solid to a clean (wet) volumetric flask of the desired volume.
5. Fill the flask ~halfway with solvent. Swirl and gently shake to dissolve the solid.
6. Fill the flask to the bottom of the neck. Use a wash bottle or dropper to slowly add
solvent until the bottom of the meniscus reaches the mark.
7. Invert carefully 10-20 times. (Vent if necessary to release pressure.)
8. Transfer to a storage bottle that has been rinsed with several aliquots of the solution.
9. Calculate actual concentration based on measured mass.
10. Label the bottle with important info: [Concentration With units], substance, solvent,
preparation, date prepared, your name or initials

Preparing a Solution by Dilution

1. Calculate the volume of concentrated solution that needs to be
   transferred based on desired molarity (mol/L) and volume.
   C1 V1 =C2 V2

2. Usually not necessary to prepare an exactly specified
   concentration—it is more important that the concentration be
   measured precisely. Use analytical pipet to quantitatively deliver
   stock solution into volumetric flask of desired volume.*

3. Fill volumetric flask and invert as previously described.

4. Transfer to a storage bottle.

5. Calculate the actual concentration.

6. Label the bottle as previously described.
   

Chemical Handling

• Do not contaminate samples by putting a spatula, pipet, or anything
  into the bottle. Do not return unused chemical to the bottle.

• Keep bottles and flasks capped and beakers covered, and pay
  attention to special instructions for storing (e.g., sensitive to light)

• Double check the label and MSDS before using chemical.

• Assume that all chemicals contain significant impurities absorbed from
  air. Drying (at ~110 °C) for several hours or overnight is often (but not
  always) appropriate before use. Learn how to properly use
  desiccators, desiccants, and weighing bottles when needed.

• Be neat—clean up spills immediately.

• Adhere to waste treatment/disposal regulations.