Analytica Chem

ppm

(grams analyte/grams sample)x10^6

Molarity

moles analyte/liter of solution

Volume Percent

(volume solute/volume soution)x100

Volume ppm

(volume solute/volume solution)x10^6

kilo-

10^3

deci-

10^-1

centi-

10^-2

milli-

10^-3

micro-

10^-6

nano-

10^-9

pico-

10^-12

femto-

10^-15

weight percent

(grams analyte/grams sample)x100

ppt

(grams analyte/grams sample)x10^3

ppt simplified

gram analyte/liter solution

ppm simplified

mg analyte/liter solution

ppb simplified

micrograms analyte/liter solution

pptr simplified

nanograms analyte/liter solution

buoyancy correction

m\=(m'(1-(air density/weight density)))/(1-(air density/object density))

accuracy

closeness of the mean to the "true value"

precision

reproducibility of individual measurements

Uncertainty in Addition/Subraction

e\=sqrt(ex1^2+ex2^2+ex3^2+...)

Uncertainty in Multiplication/Division

e\=y*sqrt((ex1/x1)^2+(ex2/x2)^2+(ex3/x3)^2+...)

Significant Figures in Logarithms and antilogarithms

the number of significant figures in the log should equal the number of digits in the mantissa

How many significant figures in log(205.5)

four significant figures, so you will need four decimal places in your answer

pH

-log[H3O+]

\[H3O+]

10^-pH

Absorbance

-log(transmittance)

Random Error

-repeated measurements are sometimes high and sometimes low

-cannot be corrected for

Systematic Error

-repeated measurements are usually always high or always low

-can and should be corrected for

Relative uncertainty\=

absolute uncertainty/magnitude of measurement

68% of measurements in a Gaussian Curve will lie

between the mean-1 and the mean+1

Variance in standard deviation

standard deviation squared

mean\=

true value +-time*standard deviation

T-test Case 1

measure sample of known composition

T-test case 2

compare replicate measurement of an unknown sample

T-test case 3

compare individual difference of an unknown sample

- two sets of data analyzed by both methods being used

T-test case 1 equation

true value\= mean (+-) (time*standard deviation)/sqrt(number of measurements))

T-test case 1 Tcalc\=

(sqrt(n)Iknown value-calculated meanI)/standard deviation

For Case 1:

If Tcalc\>Ttable

the actual value isn't in the range and it is bad

For Case 1:

If Tcalc

the actual value is close to our calculated value

For Case 2:

you need to first solve for Fcalc\=

(larger standard deviation)^2/(smaller standard deviation)^2

If Fcalc

Case 2A

If Fcalc\>Ftable, you should use

Case 2B

T-Test Case 2A: Tcalc\=

(Icalculated mean 1-calculated mean 2I/spooled)*sqrt((n1*n2)/(n1+n2))

For Case 2A:

if Tcalc < Ttable, then

the two sets of data are statistically indistinguishable

For Case 2A:

spooled(standard deviation pooled)\=

sqrt((s1^2(n1-1)+s2^2(n2-1))/(n1+n2-2))

where s\=standard deviation and n\=number of measurements

For Case 2B:

Tcalc\=

(Icalculated mean 1-calculated mean 2I)/sqrt((s1^2/n1)+(s2^2/n2))

For case 2B:

if Tcalc

the two sets of data are indistinguishable

For Case 3:

Sd\=

sqrt((sum of (difference-average difference)^2)/n-1)

For Case 3:

Tcalc\=

(Iaverage differenceI/Sd)*sqrt(n)

Q-test

Q\=gap/range

For the Q-test, if Qcalculated\>Qtable,

the value in question can be rejected with 90% confidence

Grubbs test

Gcalculated\= Iquestionable value-calculated meanI/standard deviation

-calculated mean and standard deviation need to include the questionable point

For the Grubbs test, if Gcalculated

you need to keep the questionable point in the set of data

Absorbance corrected for dilution\=

Absorbance measured*(total volume/initial volume)

Energy\=

Plancks constant*frequency

Planck's constant\=

6.626x10^-34 Js

c\=(in terms of energy and absorption)

wavelenght*frequency

E\=

(planck's constant*c)/wavelength

Beer's Law Equation

Absorbance\= constant*distance*concentration

Transmittance Equation\=

P/Po

Po\= particular intensity at a specific wavelength

Percent Transmittance\=

Transmittance x100

Acid

has a conjugate base and could potentially donate a proton

Base

has a conjugate acid and could potentially gain another proton

what k do you have when you have a base + water on the reactants side?

Kb

what k do you have when you have an acid + water on the reactants side?

Ka

what k do you have when you have a base + water on the products side?

1/Kb

what k do you have when you have an acid + water on the products side?

1/Ka

what is the k equation?

k\=products/reactants

- this does not include any solids or liquids, only aqueous solutions

what is the k-value associated with the dissociation of water molecules or 2H20⇌H3O+ + OH-

Kw\=1.0x10^-14

Kw\=

\[H30+][OH-]

Kw\= (in terms of other k values)

Ka*Kb

pKw\=

pH+pOH

A weak acid consists of a Ka value of

10^-3 or less

Direct Titration

standardized titrant is added to the analyte until the end point is observed

Indirect Titration

includes a back titration, and occurs whenever a direct titration is not feasible

Dilution Factors

M1V1\=M2V2

Push the reaction to the products side if you have a

very large K value

Push the reaction to the reactants side if you have a

very small K value

You need to consider the autoprotolysis of water when

the concentration is

How to write a charge balance equation

You put all of the positive charges on the left hand side and all of the negative charges on the right hand side. You need to take the number of charges and use it as a coefficient out front.

In Example: NO3^4- : 4[NO3^4-]

How to write a mass balance equation

Concentration of Solution\= concentration of both products. If one of the products can add or lose a proton that needs to be included in the equation. *metals and chloride ions do not gain or lose any protons.