CHAPTER 4

Calculations Used in Analytical Chemistry

In this chapter, we describe several methods used

to compute the results of a quantitative analysis

▶ Anal. Chem. 많이 쓰이는 단위:

• Mass: g = 103 mg = 106 μg

• Volume: L = 103 mL = 106 μL

• Temperature: K = 273.15 + ℃

Example

590 nm = 59010–9 m = 5900 Å

20 L = 20 10–6 L

6 pmol = 610–12 mol

20 Gbite = 20109 bite

1 mL = 10–6 m3 = 1 cm3

The angstrom unit A is a non-SI unit of length that is widely used to express the wavelength of very short radiation such as X-rays (1 A 5 0.1 nm 5 10210 m). Thus, typical X-radiation lies in the range of 0.1 to 10 A.

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4A-2 The Distinction between Mass and Weight

Mass : An invariant measure of the quantity of matter in an object.

Mass is constant.

Weight : The force of attraction exerted between an object and the

earth.

Weight(w) equals mass(m) times the gravitational attraction

(g=980.665 cm/s2).

w = g m

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nx:number of mole of X (mol), Mx: mole mass of X (g/mol)

massx: mass of X (g)

▶ moles of X ▶ mmoles of X

4A-3 The Mole

The mole (abbreviated mol) is the SI unit for the amount of a

chemical substance.

It is the amount of the specified substance that contains the same

number of particles as the number of carbon atoms in exactly 12

grams of 12C. This important number is Avogadro’s number

NA = 6.022 x 1023.

Ex) Formaldehyde(CH2O) 및 glucose(C6H12O6)의 몰질량?

Los Alamos National Lab http://pearl1.lanl.gov/periodic/

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4A-5 Calculating the amount of a substance in moles or millimoles

4B Solutions and their Concentration

1) Molarity : molar concentration : M

M = (no. moles of solute) / [volumes (liter) of solution]

= (mmoles) / (mL)

A mole is defined as the number of atoms of 12C in exactly 12

g of 12C (12 amu or daltons).

Avogadro’s number = 6.02214381023.

A mole of a chemical species is 6.02214381023 atoms,

molecules, ions, electrons, ion pairs, or subatomic particles.

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2) Formality ; formal or analytical concentration

F = M

Strong electrolyte : completely dissociated

Ex. NaCl mol wt 58.44 g/L = 1 M

2.7g/100 mL sea water = x M

x = 0.46 M = 0.46F

Weak electrolyte : partially dissociated

Ex. HAC 0.1 F (1.3% dissociated)

3) Molality m = (mol solute) / (kg solvent)

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Analytical molarity is the total number of moles of a solute, regardless of its

chemical state, in 1 L of solution. The analytical molarity describes how a

solution of a given molarity can be prepared.

Equilibrium molarity is the molar concentration of a particular species in a

solution.

Ex. 1.0 M H2SO4

[H2SO4] = 0.00 M [H+] = 1.01 M

[HSO4–] = 0.99 M [SO4

–2 ] = 0.01 M

Analytical molarity of H2SO4 is given by c H2SO4 = [HSO4–] + [SO4

–2 ]

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Ex. Calculate the analytical and equilbrium molar concentrations of the solute

species in an aqueous solution that contains 285 mg of trichloroacetic acid,

Cl3CCOOH (163.4 g/mol), in 10.0 mL (the trichloroacetic acid is 73% ionized

in water).

Cl3CCOOH = HA 163.4 g = 1 mol

285 mg = x mol x = 1.744 10-3 mol

Analytical concentration :

163.4 g / 1000 mL = 1 M

285 mg / 10.0 mL = y M y = 0.174 M

Equilibrium concentration:

HA H+ + A–

initial 1 0 0

Final 1–0.73 0.73 0.73

[HA] = y M (1 – 0.73) = 0.174 0.27 = 0.047 M

[H+] = [A–] = y M 0.73 = 0.127 M 13

Percent concentration (%) Solution

= solute + solvent

Parts per million (ppm) and parts per billion (ppb)

Solution-diluent volume ratios

진한용액의 부피 : 묽히는 용액의 부피 = A : B

⇒ 1 : 4 HCl 용액 = 진한 HCl 부피 1 + 4 부피의 물

p-function

The density of a substance is its mass per unit volume, and its specific

gravity is the ratio of its mass to the mass of an equal volume of water at 4°C.

Density has units of kilograms per liter or grams per milliliter in the metric

system. Specific gravity is dimensionless and so is not tied to any particular

system of units.

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4C. Chemical Stoichiometry

4C-1 Empirical formulas and molecular formulas

▶ Empirical formula: 가장 간단한 원소비로 나타낸 화학식

▶ Molecular formula : 실제 원소의 수로 나타낸 화학식

▶ Structural formula : 원자의 결합형태를 나타낸 화학식

⇒ CH2O: formaldehyde 의 실험식 및 분자식, C2H4O2(acetic acid) 및

C3H6O3(glyceraldehyde) 등의 실험식

⇒C2H6O 실험식 : 구조식 C2H5OH(ethanol), CH3OCH3(dimethyl ether)

4C-2 Stoichiometric calculations

⇒ 양론계수가 맞추어진 화학방정식은 반응물과 생성물의

몰비에 대한 정보를 제공

2 mol 1 mol 2 mol 1 mol

Summary

SI unit

Prefix of unit

mole

Concentration

Molarity, Normality

%,

density

ppm,

Dilution NV = N’V’ nMV = n’M’V’

p-function

Stoichiometric calculation

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