9.7. Given the following ground-water analysis at 25°C: Ca-134mgl; Mg 44 mg/l; N
ID: 703474 • Letter: 9
Question
9.7. Given the following ground-water analysis at 25°C: Ca-134mgl; Mg 44 mg/l; Na-145 mg/l; S04 429 mg/l; HCO3-412 mgl: Cl-34 mg/: pH-8.0: TDS-1205 mg/l (A) Convert all analyses into molal concentrations (B) Compute ionic strength. (C) Compute activity coefficient for each ion using Debye-Huckel. (D) Find activity of each ion. (E) Convert analyses to meq (F) Calculate the cation-anion balance. (G) Find the Kiap of anhydrite (CaS04). (H) Compare the Kiap of anhydrite with the Ksp of anhydrite (10-4.5). (I) Find the Kiap of calcite (CaCO3). J) Compare the Kiap of calcite with the Ksp of calcite (10-8.35).Explanation / Answer
SOLUTION:
Density of water, ? = 1 kg/L
Molal concentration = (X mg / L) / (1000 * MW of ion g /mol) / (?)
a)
Table of molal concentrations is shown below:
Ions
mg/L
MW of ion
Molal concentraion (mol/kg)
Charge of ion, z
Ca2+
134
40.078
0.00334
2
HCO3-
412
61.0168
0.00675
1
Mg2+
44
24.305
0.00181
2
Cl-
34
35.453
0.000959
1
Na+
145
22.9898
0.006307
1
SO42-
429
96.06
0.004466
2
b)
Molar concentration ~ Molal concentration
Ionic strength, I = ½ * sum(Ci zi2)
I = ½ * (0.00334 * 22 + 0.00675 * 12 + 0.00181 * 22 + 0.000959 * 12 + 0.006307 * 12 + 0.004466 * 22)
= 0.026249 M
c)
Activity coefficient, f
Log (f) = -0.51 z2 I0.5 / (1 + I0.5)
For z = 1
Log(f1) = -0.071
f1 = 0.85
For z = 2
Log(f2) = -0.284
f2 = 0.52
Ions
Charge of ion, z
z2
log(f)
f
Ca2+
2
4
-0.284
0.52
HCO3-
1
1
-0.071
0.85
Mg2+
2
4
-0.284
0.52
Cl-
1
1
-0.071
0.85
Na+
1
1
-0.071
0.85
SO42-
2
4
-0.284
0.52
d)
Activity = activity coefficient (fi) * molar concentration (M)
Ions
Molal concentraion (mol/kg), M
f
Activity, M * f
Ca2+
0.00334
0.52
0.001737
HCO3-
0.00675
0.85
0.005732
Mg2+
0.00181
0.52
0.00094
Cl-
0.00096
0.85
0.000814
Na+
0.00631
0.85
0.005355
SO42-
0.00447
0.52
0.00232
Ions
mg/L
MW of ion
Molal concentraion (mol/kg)
Charge of ion, z
Ca2+
134
40.078
0.00334
2
HCO3-
412
61.0168
0.00675
1
Mg2+
44
24.305
0.00181
2
Cl-
34
35.453
0.000959
1
Na+
145
22.9898
0.006307
1
SO42-
429
96.06
0.004466
2
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