ways of expressing concentration

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Ways of Expressing Concentration

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Page 1: Ways of Expressing Concentration

Ways of Expressing Concentration

Page 2: Ways of Expressing Concentration

Outline

Molarity

Analytical molarity (formality)

Equilibrium molarity

Molality

Percent concentration

% (w/w)

% (v/v)

% (w/v)

Parts per thousand (ppt), parts per million (ppm), and parts per billion (ppb)

Solution-diluent volume ratio

p-function

Normality

Titer

Density and specific gravity

Page 3: Ways of Expressing Concentration

Molarity, M

nsol' mL

solute mmol

nsol' L

solute molM

Page 4: Ways of Expressing Concentration

Analytical molarity (formality), Cx

nsol' L

solute mol totalCx

Page 5: Ways of Expressing Concentration

Analytical molarity, Cx

= Formality, F

When solute dissociates or ionizes completely in H2O formality is preferred to molarity in expressing concentration.

Cx describes the preparation of a solution of particular molarity.

Page 6: Ways of Expressing Concentration

Examples

1. Describe the preparation of NaOH sol’n with analytical concentration equal to1.00 M.

Page 7: Ways of Expressing Concentration

Examples

Answer:

Dissolve 1.00 mol NaOH (98.00 g NaOH) in H2O.

Dilute to 1.00 L.

Page 8: Ways of Expressing Concentration

Examples

2. Calculate the molar concentration of ethanol in an aqueous solution that contains 2.30 g of C2H5OH (46.07 g/mol) in 3.50 L.

Page 9: Ways of Expressing Concentration

Examples

Answer:

0.0143 M

Page 10: Ways of Expressing Concentration

Examples

3. Calculate the analytical concentration of the solute species in aqueous solutions that contains 285 mg trichloroacetic acid, Cl3CCOOH (163.4 g/mol), in 10.0 mL.

Page 11: Ways of Expressing Concentration

Examples

Answer:

0.174 M

Page 12: Ways of Expressing Concentration

Equilibrium molarity, [X]

- molarity of a given species in a solution at equilibrium

Page 13: Ways of Expressing Concentration

Example

Calculate the equilibrium molar concentration of the solute species in aqueous solutions that contains 285 mg trichloroacetic acid, Cl3CCOOH (163.4 g/mol), in 10.0 mL (the acid is 73% ionized).

Page 14: Ways of Expressing Concentration

Example

Answer:

[Cl3CCOOH] = 0.047 M

[Cl3CCOO-] = 0.127 M

Page 15: Ways of Expressing Concentration

Molality, m

solvent kg

solute molm

Page 16: Ways of Expressing Concentration

Percent concentration

100%solution of weight

solute of weight%(w/w)

Page 17: Ways of Expressing Concentration

Percent concentration

100%solution of volume

solute of volume%(v/v)

Page 18: Ways of Expressing Concentration

Percent concentration

100%mL solution, of volume

g solute, of weight%(w/v)

Page 19: Ways of Expressing Concentration

Examples

1. What is the molality of 87.0% (w/w) H3PO4 (98.00 g/mol) solution?

Page 20: Ways of Expressing Concentration

Examples

Answer:

68.3 m

Page 21: Ways of Expressing Concentration

Examples

2. What is the molarity of 37.7% (w/w) HCl (36.46 g/mol) solution? The density of the solution is 1.19 g/mL.

Page 22: Ways of Expressing Concentration

Examples

Answer:

12.3 M

Page 23: Ways of Expressing Concentration

Parts per thousand (ppt)

1000solution mass

solute masscppt

Page 24: Ways of Expressing Concentration

Parts per million (ppm)

6ppm 10

solution mass

solute massc

1 ppm = 1 mg/L

Page 25: Ways of Expressing Concentration

Parts per billion (ppb)

9ppb 10

solution mass

solute massc

1 ppb = 1 μg/L

Page 26: Ways of Expressing Concentration

Examples

1. There is 0.050 mg of PCB in 2 700 kg of soil. What is the concentration in ppb of PCB in the sample?

Page 27: Ways of Expressing Concentration

Examples

Answer:

0.019 ppb

Page 28: Ways of Expressing Concentration

Examples

2. What is the molarity of K+ in aqueous solution that contains 63.3 ppm K3Fe(CN)6 (329.3 g/mol)?

Page 29: Ways of Expressing Concentration

Examples

Answer:

5.77 X 10-4 M

Page 30: Ways of Expressing Concentration

Solute-diluent volume ratios

solute: solvent

Example:

1:4 HCl solution = 1 volume of conc. HCl +

4 volumes of H2O

Page 31: Ways of Expressing Concentration

p-function

[X] -logpX

Page 32: Ways of Expressing Concentration

Example

The pAg of a solution is 9.00. Calculate the molar concentration of Ag+ in the solution.

Page 33: Ways of Expressing Concentration

Example

Answer:

1.000 X 10-9 M

Page 34: Ways of Expressing Concentration

Normality, N

nsol' L

solute equivalentN

solute EW

solute gsolute equivalent

n

MWEW

Page 35: Ways of Expressing Concentration

Determining n

n depends on the type of reaction:

1. Acid-base reaction

2. Oxidation-reduction reaction

3. Precipitate formation and complex formation

Page 36: Ways of Expressing Concentration

Acid-base reaction

Acid:

n = number of H+ a mole of the acid supplies

Base:

n = number of H+ a mole of the base reacts with

Page 37: Ways of Expressing Concentration

Examples

1. H3PO4 + NaOH → NaH2PO4 + H2O

H3PO4: n = 1

NaOH: n = 1

Page 38: Ways of Expressing Concentration

Examples

2. H3PO4 + 2NaOH → Na2HPO4 + 2H2O

H3PO4: n = 2

NaOH: n = 1

Page 39: Ways of Expressing Concentration

Oxidation-reduction reaction

Species:

n = number of moles of electrons a mole of the species gains or loses

Half-reaction or net reaction can be used in determining n.

Page 40: Ways of Expressing Concentration

Examples

1. MnO4- + C2O4

2- → Mn2+ + CO2

KMnO4: n = 5

Na2C2O4: n = 2

Page 41: Ways of Expressing Concentration

Examples

2. I2 + S2O32- → I- + S4O6

2-

I2: n = 1

S2O32-: n = 1

Page 42: Ways of Expressing Concentration

Precipitate and complex formation

cation:

n = charge of cation

anion:

n = charge of cation x coefficient of cation

coefficient of anion

Page 43: Ways of Expressing Concentration

Examples

1. Ag+ + Cl- AgCl(s)

AgNO3: n = 1

KCl: n = 1

Page 44: Ways of Expressing Concentration

Examples

2. Ba2+ + SO42- BaSO4(s)

Ba(NO3)2: n = 2

Na2SO4: n = 2

Page 45: Ways of Expressing Concentration

Examples

3. Ag+ + 2CN- Ag(CN)2-

AgNO3: n = 1

KCN: n = 1/2

Page 46: Ways of Expressing Concentration

Examples

4. 3Cu(NO3)2 + 2Na3PO4 Cu3(PO4)2(s) + 6NaNO3

Cu(NO3)2: n = 2

Na3PO4: n = 3

Page 47: Ways of Expressing Concentration

Relation between N and M

N = nM

Page 48: Ways of Expressing Concentration

Significance of normality

Consider titration of analyte A with titrant B

aA + bB → cC + dD.

At the endpoint,

eq A = eq B.

Hence,

NAVA=NBVB.

Page 49: Ways of Expressing Concentration

Examples

1. Calculate g of Na2CO3 needed to prepare 5.000 L of 0.100 N Na2CO3 (105.99 g/mol) from the primary standard solid, assuming the reaction is to be used for titrations in which the reaction is

CO32- + 2H+ → H2O + CO2

Page 50: Ways of Expressing Concentration

Examples

Answer:

26.50 Na2CO3

Page 51: Ways of Expressing Concentration

Examples

2. A 0.2121-g sample of pure Na2C2O4 (134.00 g/mol) was titrated with 43.31 mL KMnO4. What is the normality of KMnO4 solution. The reaction is

2MnO4- + 5C2O4

2- + 16H+ → 2Mn2+ + 10CO2 8H2O

Page 52: Ways of Expressing Concentration

Examples

Answer:

0.07309 N

Page 53: Ways of Expressing Concentration

Titer

- weight of pure substance (other than the solute) corresponding to 1 mL of solution

Corresponding means:will react exactly withis chemically equivalent tois contained inmay be obtained frommay be substituted for

Page 54: Ways of Expressing Concentration

Titer

unit: mg/mL

Page 55: Ways of Expressing Concentration

Relation between titer and N

Titer = Nsoln x EWpure substance

Page 56: Ways of Expressing Concentration

Examples

1. 1.00 mL HCl neutralizes 4.00 mg NaOH.

HCl + NaOH → NaCl + H2O

What is the NaOH titer of the HCl solution?

Page 57: Ways of Expressing Concentration

Examples

Answer:

Titer = 4.00 mg/mL

Page 58: Ways of Expressing Concentration

Examples

2. What is the NH3(17.00 g/mol) titer of a 0.120 N solution of HCl?

Page 59: Ways of Expressing Concentration

Examples

Answer:

Titer = 2.04 mg/mL

Page 60: Ways of Expressing Concentration

Examples

3. Calculate the normality of an HCl solution having a Na2CO3(105.99 g/mol) titer of 5.00 mg/mL.

Page 61: Ways of Expressing Concentration

Examples

Answer:

Titer = 0.0943 N

Page 62: Ways of Expressing Concentration

Density

volume

massdensity

Page 63: Ways of Expressing Concentration

Specific gravity

- ratio of the mass of a substance to the mass of an equal volume of H2O at 4°C