CEE 680 |
Fall 2011 |
Homework Set #1
6 points total
1. Measures of Concentration & Charge Balance
|
Constituent |
Concentration |
Units |
|
Turbidity |
0.59 |
NTU |
|
TDS |
29 |
mg/L |
|
Color |
10 |
Color units |
|
Odor |
1 |
TON |
|
pH |
6.75 |
Log units |
|
Total Alkalinity |
13 |
mg-CaCO3/L |
|
Total Hardness |
20 |
mg-CaCO3/L |
|
Calcium |
6.7 |
mg/L |
|
Magnesium |
0.89 |
mg/L |
|
Aluminum |
<0.05 |
mg/L |
|
Potassium |
<1 |
mg/L |
|
Sodium |
5.0 |
mg/L |
|
Iron |
<0.05 |
mg/L |
|
Manganese |
0.016 |
mg/L |
|
Sulfate |
5.9 |
mg/L |
|
Chloride |
3.0 |
mg/L |
|
Silver |
<0.005 |
mg/L |
|
Copper |
<0.01 |
mg/L |
|
Zinc |
<0.05 |
mg/L |
|
TOC[1] |
3 |
mg/L |
a. Estimate the bicarbonate concentration assuming that all of the measured alkalinity is bicarbonate.
0.5 points
b. Calculate the ionic strength
1.0 points
Now its important to recognize that several of the constitutents in the table above are presented as being below a certain value (probably the lab’s method detection limit). It may be safest to assume a value of zero for all of these. This would give a lower bound to the estimates of ionic strength and ion charge. When calculating this, be careful to include the bicarbonate.
Therefore, in the traditional equivalent-based units:
I = 8.12 x 10-4 (molar units)
c. Determine the “analytical” concentration of [H+] using the Debye-Huckel equation.
0.5 points
d. Perform a charge balance on this water based on the measured concentrations. Is there apparent excess charge, and if so, why?
1.0 points
Total Cations = 0.626 meq/L
Total Anions = 0.467 meq/L
Note that the anions and cations are added together separately. This allows one to assess the relative degree of imbalance. In this case, there’s a substantial imbalance; about 25% of the total charge appears to be missing (negative charges). Why so large? Analytical error? A major constituent overlooked?
I would say that the natural organic matter (NOM), as represented by the TOC of 3 mg/L is a likely candidate. This material (NOM) is always negively charged, and a typical “charge density” is 20 meq/g-C. If we use this along with the TOC, we get an additional 0.06 meq/L negative charge from the NOM. This would bring the negative charges up to about 0.53 meq/L. Much better, but this still suggests we may be missing something. Some of this could come from nitrate which wasn’t measured. One can’t ignore the possibility of analytical error as well.
e. Calculate the “theoretical” TDS
based on the chemical analysis above and compare with the actual measured
TDS. Are they different, and if so why
do you think this is the case?
1.0 points
Calculation of TDS is normally a simple matter of adding the concentrations of known constituents (ignoring any water). Bicarbonate may be partly lost depending on the cations present and the temperature used in the TDS determination. The organic matter (NOM) may also be partly lost when using higher temperatures. The total mass of NOM can be estimated by assuming that it us usually 50% carbon by weight. This gives 4 possible answers ranging from 21.5 to 43.4 mg/L. If we assume that half of the bicarbonate and TOC are lost, this would give us a TDS of about 31 mg/L, a number that is not too far from the analytical determination (29 mg/L).
|
# |
TDS (mg/L) |
Calculation |
Explanation |
|
1 |
21.5 |
Sum of all ions above except bicarbonate |
Low bound; ignoring all Carbon compounds; assuming they volaltilize t |
|
2 |
27.5 |
Same as #1, but with 2*TOC |
Assumes that bicarbonate volatilizes but NOM remains |
|
3 |
37.4 |
Same as #1, but with bicarbonate |
Assuming bicarbonate remains, but NOM is volatilized |
|
4 |
43.4 |
Same as #3, but with 2*TOC |
Assumes all C-compounds remain |
2. Activity
A series of 10-3 F HCl solutions are prepared[2], each solution containing a different concentration of KCl in the range of 0.01 F to 0.50 F. Plot pH (i.e., -log{H }) vs log I using:
|
|
a. Davies Equation; |
|
|
b. Extended Debye-Huckel Equation. |
2.0 points
Solution to 2
Ionic Strength equation
Extended Debye-Hückel equation:
Davies Equation
|
|
|
Davies |
|
|
Extended D-H |
|
|
|
[KCl] |
I |
log f |
f |
{H} |
log f |
f |
{H} |
|
0.01 |
0.011 |
-0.04636 |
0.898747 |
3.046363 |
-0.03989 |
0.912243 |
3.03989 |
|
0.02 |
0.021 |
-0.06119 |
0.868589 |
3.061186 |
-0.0505 |
0.890222 |
3.050502 |
|
0.03 |
0.031 |
-0.07175 |
0.847706 |
3.071755 |
-0.05761 |
0.875777 |
3.057606 |
|
0.04 |
0.041 |
-0.08009 |
0.831583 |
3.080094 |
-0.06298 |
0.865002 |
3.062983 |
|
0.05 |
0.051 |
-0.08701 |
0.818439 |
3.087014 |
-0.06731 |
0.856422 |
3.067312 |
|
0.06 |
0.061 |
-0.09293 |
0.807362 |
3.092932 |
-0.07093 |
0.849311 |
3.070933 |
|
0.07 |
0.071 |
-0.0981 |
0.797814 |
3.098098 |
-0.07404 |
0.843253 |
3.074042 |
|
0.08 |
0.081 |
-0.10268 |
0.78945 |
3.102675 |
-0.07676 |
0.837988 |
3.076762 |
|
0.09 |
0.091 |
-0.10678 |
0.782032 |
3.106776 |
-0.07918 |
0.833342 |
3.079177 |
|
0.1 |
0.101 |
-0.11048 |
0.775388 |
3.110481 |
-0.08135 |
0.82919 |
3.081346 |
|
0.11 |
0.111 |
-0.11385 |
0.769391 |
3.113853 |
-0.08331 |
0.825444 |
3.083312 |
|
0.12 |
0.121 |
-0.11694 |
0.763943 |
3.116939 |
-0.08511 |
0.822036 |
3.085109 |
|
0.13 |
0.131 |
-0.11978 |
0.758968 |
3.119776 |
-0.08676 |
0.818914 |
3.086762 |
|
0.14 |
0.141 |
-0.1224 |
0.754404 |
3.122396 |
-0.08829 |
0.816036 |
3.088291 |
|
0.15 |
0.151 |
-0.12482 |
0.750202 |
3.124822 |
-0.08971 |
0.813371 |
3.089711 |
|
0.16 |
0.161 |
-0.12708 |
0.746319 |
3.127075 |
-0.09104 |
0.81089 |
3.091038 |
|
0.17 |
0.171 |
-0.12917 |
0.742722 |
3.129173 |
-0.09228 |
0.808573 |
3.092281 |
|
0.18 |
0.181 |
-0.13113 |
0.739382 |
3.131131 |
-0.09345 |
0.806401 |
3.093449 |
|
0.19 |
0.191 |
-0.13296 |
0.736272 |
3.132961 |
-0.09455 |
0.804357 |
3.094551 |
|
0.2 |
0.201 |
-0.13467 |
0.733373 |
3.134675 |
-0.09559 |
0.802429 |
3.095593 |
|
0.21 |
0.211 |
-0.13628 |
0.730666 |
3.136281 |
-0.09658 |
0.800606 |
3.096581 |
|
0.22 |
0.221 |
-0.13779 |
0.728134 |
3.137789 |
-0.09752 |
0.798878 |
3.09752 |
|
0.23 |
0.231 |
-0.1392 |
0.725764 |
3.139205 |
-0.09841 |
0.797236 |
3.098413 |
|
0.24 |
0.241 |
-0.14054 |
0.723542 |
3.140536 |
-0.09927 |
0.795673 |
3.099265 |
|
0.25 |
0.251 |
-0.14179 |
0.721459 |
3.141789 |
-0.10008 |
0.794182 |
3.10008 |
|
0.26 |
0.261 |
-0.14297 |
0.719503 |
3.142967 |
-0.10086 |
0.792758 |
3.100859 |
|
0.27 |
0.271 |
-0.14408 |
0.717666 |
3.144077 |
-0.10161 |
0.791395 |
3.101606 |
|
0.28 |
0.281 |
-0.14512 |
0.715941 |
3.145123 |
-0.10232 |
0.79009 |
3.102324 |
|
0.29 |
0.291 |
-0.14611 |
0.71432 |
3.146107 |
-0.10301 |
0.788837 |
3.103013 |
|
0.3 |
0.301 |
-0.14703 |
0.712796 |
3.147035 |
-0.10368 |
0.787633 |
3.103676 |
|
0.31 |
0.311 |
-0.14791 |
0.711363 |
3.147909 |
-0.10432 |
0.786475 |
3.104315 |
|
0.32 |
0.321 |
-0.14873 |
0.710017 |
3.148731 |
-0.10493 |
0.785359 |
3.104932 |
|
0.33 |
0.331 |
-0.14951 |
0.708753 |
3.149505 |
-0.10553 |
0.784284 |
3.105527 |
|
0.34 |
0.341 |
-0.15023 |
0.707565 |
3.150234 |
-0.1061 |
0.783247 |
3.106101 |
|
0.35 |
0.351 |
-0.15092 |
0.706449 |
3.150919 |
-0.10666 |
0.782244 |
3.106658 |
|
0.36 |
0.361 |
-0.15156 |
0.705403 |
3.151563 |
-0.1072 |
0.781275 |
3.107196 |
|
0.37 |
0.371 |
-0.15217 |
0.704422 |
3.152167 |
-0.10772 |
0.780338 |
3.107717 |
|
0.38 |
0.381 |
-0.15273 |
0.703504 |
3.152734 |
-0.10822 |
0.77943 |
3.108223 |
|
0.39 |
0.391 |
-0.15326 |
0.702644 |
3.153264 |
-0.10871 |
0.778549 |
3.108714 |
|
0.4 |
0.401 |
-0.15376 |
0.701841 |
3.153761 |
-0.10919 |
0.777696 |
3.10919 |
|
0.41 |
0.411 |
-0.15422 |
0.701092 |
3.154225 |
-0.10965 |
0.776867 |
3.109653 |
|
0.42 |
0.421 |
-0.15466 |
0.700394 |
3.154657 |
-0.1101 |
0.776063 |
3.110103 |
|
0.43 |
0.431 |
-0.15506 |
0.699746 |
3.15506 |
-0.11054 |
0.775281 |
3.110541 |
|
0.44 |
0.441 |
-0.15543 |
0.699144 |
3.155433 |
-0.11097 |
0.774521 |
3.110967 |
|
0.45 |
0.451 |
-0.15578 |
0.698588 |
3.155779 |
-0.11138 |
0.773781 |
3.111382 |
|
0.46 |
0.461 |
-0.1561 |
0.698074 |
3.156098 |
-0.11179 |
0.773061 |
3.111786 |
|
0.47 |
0.471 |
-0.15639 |
0.697603 |
3.156392 |
-0.11218 |
0.772359 |
3.112181 |
|
0.48 |
0.481 |
-0.15666 |
0.697171 |
3.156661 |
-0.11257 |
0.771676 |
3.112565 |
|
0.49 |
0.491 |
-0.15691 |
0.696778 |
3.156906 |
-0.11294 |
0.771009 |
3.11294 |
|
0.5 |
0.501 |
-0.15713 |
0.696421 |
3.157128 |
-0.11331 |
0.770359 |
3.113307 |
