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Brief review of important concepts

for quantitative analysis

Some important units of quantification

Units for expressing concentrations in solids and liquids

Concentration-dilution formula

CHM 235Dr. Skrabal

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Fundamental SI units

Remember the correct abbreviations!

Mass kilogram (kg)

Volume liter (L)

Distance meter (m)

Temperature kelvin (K)

Time second (s)

Current ampere (A)

Amount of substance mole (mol)

Luminous intensity candela (cd)

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Some other SI and non-SI units

Length angstrom ()

Force newton (N)

Pressure pascal (Pa), atmosphere (atm)

Energy, work, heat joule (J)

Power watt (W)

Electric charge coulomb (C)

Electric potential volt (V)

Electric resistance ohm ()

Electric capacitance farad (F)

Temperature degree Celsius (C)

degree Fahrenheit (F)

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Some common prefixes forexponential notation

1012 tera (T)109 giga (G)

106 mega (M)

103 kilo (k)

10-1 deci (d)10-2 centi (c)

10-3 milli (m)

10-6 micro ()

10-9 nano (n)10-12 pico (p)

10-15 femto (f)

10-18 atto (a)

Remember the correct

abbreviations!

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Commonly used equalities

103 mg = 1 g milli = thousandth1 mg = 10-3 g

106g = 1 g micro = millionth1 g = 10-6 g

109 ng = 1 g nano = billionth1 ng = 10-9 g

1012 pg = 1 g pico = trillionth1 pg = 10-12 g

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Concentration scales

Molarity (M) =

Molality (m) =

solutionofLiter

soluteofMoles

solventkgsoluteofMoles

Molarity is a temperature-dependent scale because

volume (and density) change with temperature. Molality is a temperature-independent scale becausethe mass of a kilogram does not vary with temperature.

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Concentration scales (cont.)

Formality (F) =

solutionofLiter

formchemicalofregardlesssoluteofMoles )(

Formality is sometimes used to express theconcentration of substances, such as electrolytes, acids,

and bases, that turn into different species in solution.

For example:

0.1 M NaCl (= 0.1 F NaCl) gives 0.1 M Na+ and 0.1 MCl- in solution

0.5 M HCl (= 0.5 F HCl) gives 0.5 M H+ and 0.5 M Cl- in

solution

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Concentration scales (cont.)

Weight / weight (w/w) basis

% (w/w) =

ppt (w/w) =

ppm (w/w) =

ppb (w/w) =

ppt (w/w) =

210)(

)(

gsamplemass

gsolutemass

310

)(

)(

gsamplemass

gsolutemass

610)(

)(

gsamplemass

gsolutemass

9

10)(

)(

gsamplemass

gsolutemass

1210)(

)(

gsamplemass

gsolutemass

ppt = parts perthousand

ppt = parts pertrillion

ppt = parts per billion

ppt = parts per million

percent

This scale is useful for solids or solutions.

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Concentration scales (cont.)

Weight / volume (w/v) basis

% (w/v) =

ppt (w/v) =

ppm (w/v) =

ppb (w/v) =

ppt (w/v) =

210)(.

)(

mLsamplevol

gsolutemass

310

)(.

)(

mLsamplevol

gsolutemass

610)(.

)(

mLsamplevol

gsolutemass

9

10)(.

)(

mLsamplevol

gsolutemass

1210)(.

)(

mLsamplevol

gsolutemass

ppt = parts perthousand

ppt = parts pertrillion

ppt = parts per billion

ppt = parts per million

percent

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Concentration scales (cont.)

Volume / volume (v/v) basis

% (v/v) =

ppt (v/v) =

ppm (v/v) =

ppb (v/v) =

ppt (v/v) =

210)(.

)(.

mLsamplevol

mLsolutevol

310

)(.

)(.

mLsamplevol

mLsolutevol

610)(.

)(.

mLsamplevol

mLsolutevol

9

10)(.

)(.

mLsamplevol

mLsolutevol

1210)(.

)(.

mLsamplevol

mLsolutevol

ppt = parts perthousand

ppt = parts pertrillion

ppt = parts per billion

ppt = parts per million

percent

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Concentration examples

Concentrated HCl

Alcoholic beverage

Color indicator for

titrations

)/(%0.37100.100

0.37 2 wwsolutiong

HClg

)/(%4.10105.38

00.4 223

vvbeveragemL

OHCHCHmL

)/(%10.010

0.50

050.0 2 vw

solutionmL

aleinphenolphthg

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Concentration example: %(w:v)

What is the concentration, on a %(w:v) basis, of vanadium

in a solution that contains 281.5 mg/L of vanadium?

):(%10815.2):(%02815.0

10

1000

1

1000

15.281):(%

2

2

vwxorvw

mL

L

Vmg

Vg

L

Vmgvw

2

10)(.

)(

):(%

mLsamplevol

gsolutemass

vw

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Concentration scales (cont.)

Parts per million, billion, trillion are very often used todenote concentrations of aqueous solutions:

L

g

solutionL

solutionmL

solutionmL

solutiong

g

g

solutiong

solutegppb

1

1

1000

1

1

1

10

10

11

6

9

Lng

solutionLsolutionmL

solutionmLsolutiong

gng

solutiongsolutegppt 1

11000

11

110

1011

9

9

L

mg

solutionL

solutionmL

solutionmL

solutiong

g

mg

solutiong

solutegppm 1

1

1000

1

1

1

10

10

11

3

6

Note: ppt = parts per trillion

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Concentration scales (cont.)

It is important to memorize:

1 part per million (ppm) = 1 mg / L

1 part per billion (ppb) = 1 g / L

1 part per trillion (ppt) = 1 ng / L

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Concentration examples

Conversion of molarity to ppm

Solution of 0.02500 M K2SO4

ppm

L

SOKmg

g

mg

SOKmol

SOKg

L

SOKmol

4356

4356100026.17402500.0 42

42

4242

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Concentration examples

What is concentration (in ppm) of K+ in this solution?

Solution of 0.02500 M K2SO4

ppm

L

Kmg

g

mg

Kmol

g

SOKmol

Kmol

L

SOKmol

1955

1955100010.39

1

202500.0

42

42

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Concentration-dilution formula

A very versatile formula that you

absolutely must know how to use

C1 V1 = C2 V2where C = conc.; V = volume

M1 V1 = M2 V2where M = molarity

Cconc Vconc = Cdil Vdil

where conc refers to the more concentrated solutionand dil refers to the more dilute solution. Note thatyou can use any units you want for conc. and vol. aslong as they are the same on both sides of theequation.

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Concentration-dilution formula example

Problem: You have available 12.0 M HCl (conc. HCl) and

wish to prepare 0.500 L of 0.750 M HCl for use in an

experiment. How do you prepare such a solution?

Cconc Vconc = Cdil Vdil

Write down what you know and what you dont know:

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Concentration-dilution formula example

Problem: You have available 12.0 M HCl (conc. HCl) and

wish to prepare 0.500 L of 0.750 M HCl for use in an

experiment. How do you prepare such a solution?

Cconc Vconc = Cdil Vdil

Cconc = 12.0 mol L-1 Cdil = 0.750 mol L

-1

Vconc = ? Vdil = 0.500 L

Vconc = (Cdil)(Vdil) / Cconc

Vconc = (0.750 mol L-1) (0.500 L) / 12.0 mol L-1

Vconc = 3.12 x 10-2 L = 31.2 mL

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Concentration-dilution formula example

Great! So how do you prepare this solution of0.750 M HCl?

1. Use a pipet or graduated cylinder to measure exactly31.2 mL of12.0 M

2. Transfer the 31.2 mL of12.0 M HCl to a 500.0 mLvolumetric flask3. Gradually add deionized water to the volumetric flask

and swirl to mix the solution

4. As the solution gets close to the 500.0 mL graduation onthe flask, use a dropper or squeeze bottle to add waterto the mark

5. Put the stopper on the flask and invert ~20 times to mix