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The Analytical ProcessThe Analytical Process

ExploringExploring ChemicalChemical AnalysisAnalysis

Fourth Edition

11

1-1 SI Units and Prefixes

Unit (symbol)

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Standards of length, mass, and time are the meter (m), kilogram (kg) (Figure 1-1), and second (s), respectively.

Temperature is measured in kelvins(K), amount of substance in moles (mol), and electric current in amperes (A).

Figure 1-1

Table 1-2 lists derived quantities that are defined in terms of the fundamental quantities.

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Table 1-3

It is convenient to use the prefixes in Table 1-3 to express large or small quantities.

1-2 Conversion Between Units

Although SI is the internationally accepted system of measurement in science, other units are encountered.

Conversion factors are found in Table 1-4.

0.1 nm10 Å= 1 nm

1-3 Chemical Concentrations

Molarity (M) is the number of moles of a substance per liter of solution.

Molarity (M) = moles of solute/liters of solution

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A mole is Avogadro’s number of atoms or molecules or ions (6.022×1023 mol-1).

Molality (m) is a designation of concentration expressing the number of moles of a solute per kilogram of solvent (not total solution).

MolaMolarrity and Molaity and Molallityity

MolaMolarrity and Molaity and Molallityity縮寫

The masses of solute and solvent do not change with temperature, as long as neither one is allowed to evaporate.

molality does not change with temperature.

The volume of solution always changes with temperature. (T , V↗

)↗

molarity changes with temperature.

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Figure 1-3 Concentration profiles of dissolved silicate and zinc in the northern Atlantic and northern Pacific oceans. of the atoms in the molecule.

Figure 1-3

Example: Example: Molarity of Salts in the SeaMolarity of Salts in the Sea

(a) Typical seawater contains 2.7g of salt (sodium chloride, NaCl) per deciliter (=dL=0.1L).

What is the molarity of NaCl in the ocean?

(b) MgCl2 has a typical concentration of 0.054 M in the ocean.

How many grams of MgCl2 are present in 25 mL of seawater?

SOLUTION:SOLUTION: (a) The molecular mass of NaCl is 22.99 (Na)+35.45

(Cl)=58.44 g/mol. The moles of salt in 2.7 g are

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Typical seawater contains 2.7g of salt (sodium chloride, NaCl) per deciliter (=dL=0.1L).

What is the molarity of NaCl in the ocean?

(b) The molecular mass of MgCl2 is 24.30 (Mg)+[2×35.45](Cl)=95.20 g/mol, so the number of grams in 25 mL is

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MgCl2 has a typical concentration of 0.054 M in the ocean.

How many grams of MgCl2 are present in 25 mL of seawater?

SOLUTION:SOLUTION:

Magnesium chloride MgCl2 is a strong electrolyte, which means that it is mostly dissociated into ions in most solutions.

Strong electrolyte: mostly dissociated into ions in solution

A weak electrolyte such as acetic acid, CH3CO2H, is partially split into ions in solution:

Weak electrolyte: partially dissociated into ions in solution

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In sea water, about 89% of Mg is as Mg2+ and 11% is found as complex ion, MgCl+. The concentration of molecular MgCl2 is almost 0.

Sometimes the molarity of a strong electrolyte is referred to as formal concentration (F) to indicate that the substance is really converted to other species in the solution.

formal concentration (F)

1.0 M MgCl2

89% Mg2+ , Cl-

11% MgCl+ , Cl-

1.0 F MgCl2

• A solution prepared by dissolving 0.01000 mol of acetic acid in 1.0 L is 0.01F.

• The actual molarity is 0.00959 M because 4.1% is dissociated.

Normally we say the solution is 0.01M although some is dissociated.

Percent CompositionPercent Composition The percentage of a component in mixture or

solution is usually expressed as a weight percent (wt%):

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Example: 95 wt% of ethanol

in 100 g of such a solution: 95 g ethanol + 5 g H2O

Another common expression of composition is volume percent (vol%):

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When you just see % it always means wt%

vol% must be vol%

Example:Example: Converting Weight Percent of MolarityConverting Weight Percent of Molarity

Find the molarity of HCl in a reagent labeled “37.0 wt% HCl, density =1.188 g/mL.”

The density of a substance is the mass per unit volume.

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SOLUTION:SOLUTION: The mass of 1 L of solution is

(1.188 g/mL)(1000 mL/L)=1188 g/L.

The mass of HCl in 1 L is

The molecular mass of HCl is 36.46 g/mol, so the molarity is

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Parts per Million and Parts per BillionParts per Million and Parts per Billion

Concentrations of trace components of a sample can be expressed as parts per million (ppm) or parts per billion (ppb), terms that mean grams of substance per million or billion grams of total solution or mixture.

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Example: Example:

Converting Parts per Billion to MolarityConverting Parts per Billion to Molarity

Figure 1-4 shows the concentrations of hydrocarbons washed from the air by rain in the winter and summer.

The concentration of C29H60 in summer rainwater is 34 ppb. Find the molarity of this compound in nanomoles per liter (nM).

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Figure 1-4 Concentrations of alkanes (hydrocarbons with the formula CnH2n2) found in rainwater in Hannover, Germany, in the winter and summer in 1989 are measured in parts per billion ( g hydrocarbon/L of rainwater). Summer concentrations are higher, and compounds with an odd number of carbon atoms (colored bars) predominate. Plants produce mainly hydrocarbons with an odd number of carbon atoms. [K. Levsen, S. Behnert,and H. D. Winkeler, Fresenius J. Anal. Chem. 1991, 340, 665.]

SOLUTION:SOLUTION: A concentration of 34 ppb means 34×10-9 g(=34 ng)

of C29H60 per gram of rainwater, which we equate to 34 ng/mL.

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Figure 1-5 shows gas concentration measured in parts per trillion by volume (picoliters per liter).

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Concentration of highly reactive radicals ROx (parts per trillion by volume=pL/L) measured outdoors at the University of Denver.

ROx refers to the combined concentrations of HO (hydroxyl radical) HO2 (hydroperoxide radical) RO (alkoxy radical) RO2 (alkyl peroxide radical).

1-4 Preparing Solutions

To prepare a solution with a desired molarity, weigh out the correct mass of pure reagent, dissolve it in solvent in a volumetric flask.

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Figure 1-6 A volumetric flask contains a specified volume when the liquid level is adjusted to the middle of the mark in the thin neck of the flask.

SOLUTION:SOLUTION: An 8.00 mM solution contains 8.00×10-3 mol/L. Beca

use 250 mL is 0.250 L, we need

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Example:Example: Preparing a Solution with DesiredPreparing a Solution with Desired Molarity

How many groups of CuSO4 5H‧ 2O should be dissolved in a 250-mL volumetric flask to make a solution containing 8.00 mM Cu2+?

ExampleExample: Preparing 0.1 M HClPreparing 0.1 M HCl

How many milliliters of this reagent should be diluted How many milliliters of this reagent should be diluted to 1.00 L to make 0.100 M HCl? to 1.00 L to make 0.100 M HCl?

SOLUTION:SOLUTION:

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ExampleExample:

A More Complicated Dilution Calculation A More Complicated Dilution Calculation

The density of concentrated ammonium hydroxide, which contains 28.0 wt% NH3, is 0.899 g/mL. What volume of this reagent should be diluted to 500 mL to make 0.250 M NH3?

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SOLUTION:SOLUTION:

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1-5 The Equilibrium Constant

If the reactants A and B are converted to products C and D with the stoichiometry

equilibrium constant, K, is

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ExampleExample: Writing an Equilibrium ConstantWriting an Equilibrium Constant Write the equilibrium constant for the reaction

SOLUTION:SOLUTION:

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Manipulating Equilibrium ConstantsManipulating Equilibrium Constants

If the reverse reaction is written, the new K’ is the reciprocal (倒數 ) of the original K:

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If reactions are added, the new K is product of the original K’s.

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ExampleExample: Combining Equilibrium ConstantsCombining Equilibrium Constants

find the equilibrium constant for the reaction

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SOLUTION:SOLUTION:

Le Châtelier’s Principle (Le Châtelier’s Principle ( 勒沙特列原理勒沙特列原理 )) If a system at equilibrium is disturbed, the direction

in which the system proceeds back to equilibrium is such that the disturbance is partly offset.

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Example:

According to the principle of Le Châtelier, the reaction should go in the reverse direction.

When the system reaches equilibrium, reaction quotient Q=K.

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Because Q > K, the reaction must go in reverse to decrease the numerator and increase the denominator until Q = K.