lecture 3 - activity water chemistry

8/11/2019 Lecture 3 - Activity Water Chemistry

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EES 3204C Fall 2014

Jong-Yeop Kim, Ph.D., P.E.Associate Professor

Department of Environmental and Civil Engineering

Florida Gulf Coast University



Announcements

No class on 9/1 (Labor day observed)

Office hours

M &W: 10:30–11:30 am, T & R 9:00–10:30 am or by

appointment

Contact: email – [email protected], phone – 239.590.1363

Office location: Holmes Hall, Room 311 (inside 317)

Reading assignment

Chapter 1.5 (p.g 19-35)

Assignments

HW 1 due Aug 25, at the beginning of class

Prep quiz#2 due Aug 25 by 7:30 am. Read pg 12-34 before



Today’s Learning Objectives Recall equivalent concepts for expressing concentrations

of various chemical compounds.

Identify important types of chemical reactions in the

natural environment.

Define chemical reactivity (activity) and the standard

state. Explain the physical/chemical significance of activity

coefficient.

Compute the ionic strength (I) of a solution containingvarious dissolved ions.

Predict the activity coefficient of each dissolved ion by

using various equations and the calculated I for the

solution.



Important types of chemical rxns in natural waters

4. Redox (Oxidation and reduction)

e.g. Reduction of O2(g) with e-

O2 + 4e- + 4H+ H2O

5. Sorption (Adsorption/Desorption):

e.g. adsorption Pb2+ onto a sediment surface

S + Pb2+ S - Pb

6. Combination of two or more types of reactions

In the natural environment, a number of difference types of

chemical reactions are often taken place either in series(one after the other) or simultaneously…



Chemical Activity

Standard state (Section 1.5.2)

Reference state: standard temperature and pressure

(STP)T = 25°C = 298.15 K

P = 1 bar = 0.987 atm

Infinite dilution (solutes), Ideal gas behavior (gas)

Standard concentration

dissolved solutes: [i] = 1.0 mole per liter = 1.0 M;

bulk liquids, solids: xi = 1.0 (mole fraction);

pure substance

gases: Pi = 1 bar (~ 1 atm); pure substance;



Chemical Activity Activity is a measure of relative reactivity (dimensionless)

activity of compound i is ai or {i}

defined for a standard state (“STP”)

at standard state, the activity is always {i} = 1

in system different from standard state

{i} > 1 means more reactive than standard state

{i} < 1 means less reactive than standard state

activity related to concentration (Eqn. 1.8b)

statestandardini""of reactivity

systemrealini""of reactivity}{ i

][}{thus,1/][

}{[i]/[i]

{i}std.

iiii

ii I : the activity coefficient[i]: the concentration



Activity Ionic strength (p. 19)

composite effect of all ionic charge in solution

expressed as I (or ) in mole/L (or M)

where ci is the molar concentration of i and zi is the charge

on i (individual species) (Eqn. 1.6)

Example problem 1 (also see Example 1.5)

What is the ionic strength (I) of a 10-3 M NaCl and

0.2 x 10-3 N K 2SO4 solution?

21

2 i i

i

I c z

I = 1.3x10-3 M



Example 1: Ionic strength

Calculate the ionic strength (I) for a 1 L solution in

which 0.01 mole of FeCl3 and 0.02 mole of H2SO4 are

dissolved and completely dissociated into ions:



Worksheet 1: Ionic strength

The following quantities of salts were added to a

volume of water to make 1 liter of solution:

1170 mg/L NaCl

0.03 N CaCl2

1042 mg/L BaCl2

What is the ionic strength of the solution?



Solution chemistry and activity coefficient

from infinite dilution to ~1 M ionic strength

ions are electrostatically attracted to each other associated ions decrease ability of ion to react ({i})

increasing ionic strength ( I ) more associated ions = less reactive ions

increase ionic charge ( z)

more electrostatic attraction = less reactive ions

effect accounted for by i

Na+

Cl-

Cl-

Ca2+

Cl-

Cl- Cl-

Chemical Activity



Activity Activity coefficient ( i) characterizes the difference between

chemical environment in real system and that in the reference state

Estimating the activity coefficient i Three methods (See Table 1.4a)

Debye-Hückel limiting law: applicable at I < 0.005 M

Ions can be treated as point charges

Extended Debye-Hückel: applicable at I < 0.1 M

Ionic size are taken into account. But only same ionic size

Davies: applicable at I < 0.5 M Davies usually best for fresh water

1/ 22

1/ 2log 0.21i

I Az I I

D e b y e

H ü c k e l

ii i



Activity Typo (for old version textbook)

Table 1.4a (pg 30)

Extended Debye-Hückel, parameter B

B ≈ 0.33 in water at 25oC

1/ 2

1/ 2

50.3

50.3

B T

should be

B T



1/ 2

21/ 2

6 3/ 2

6 3/ 2

log 0.21

1.82 10 ( )

1.82 10 [(78.4)(298.2 )]

0.51

i I Az I I

A T

A K

A

Activity Estimating the activity coefficient i

parameter A in Debye-Hückel and Davies

= 78.4 T = 298 K (25oC)

a number t o remember

ii i



Worksheet 1 (cont.) - (activity coeff.)

With the ionic strength (I) that you calculated in the

worksheet 1, please predict by using the following

equations:

b) Debye-Huckel limiting law (1, 2)

c) Davis (1, 2)

d) Compare the results from b) and c) and discuss any

difference or similarity between them.

i i



Activity Difference between calculations: Na+

spreadsheet

ionic strength (M)10

-6

10-5

10-4

10-3

10-2

10-1

100

a c

t i v i t y

c o e f f i c i e n t

0.0

0.2

0.4

0.6

0.8

1.0

Debye-Hückel

ExtendedDebye-Hückel

Davies

ii i

i i



Activity (by Davies equation)

Effect of z : Na+, Ca2+, and Al3+

ionic strength (M)

10-6 10-5 10-4 10-3 10-2 10-1 100

a c t i v i t y

c o e f

f i c i e n t

0.0

0.2

0.4

0.6

0.8

1.0

Al3+

Ca2+

Na+

ii i

Why increases?

i i



Activity

Solution chemistry and activity coefficient

above ~1 M ionic strength

water molecules attracted to ions

activity of water decreases

“less water” increases abilityof ion to react ({i})

ii i



Example problem -2: Application of

What is the concentration of Pb2+ in water in equilibriumwith Pb(OH)2(s) in 0.1 M NaCl at pH 11 and 25C?

Pb(OH)2(s) = Pb2+ + 2 OH- K sp = 10-10.9

Pb2+

2 2

2

2 2

{ }{ }

{ }{ }

sp

sp

Pb OH K

Pb OH s

K Pb OH

i i

i i



Activity What is the concentration of Pb2+ in water in equilibrium

with Pb(OH)2(s) in 0.1 M NaCl at pH 11 and 25C?

Pb(OH)2(s) = Pb2+

+ 2 OH-

K sp = 10-10.9

activity coefficients by Davies equation

I = 0.1 M

2

2

2 2 2 2 2

22 2

{ }{ } [ ] [ ]

[ ][ ]

sp Pb OH

sp

Pb OH

K Pb OH Pb OH

K Pb

OH

[Pb2+

] = 3.54 x10-5

M

ii i

lecture 3 - activity water chemistry

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