ENVE 501 Problem Set 1 Fall 2011

1. Mallard Lake Forest Preserve in Hanover Park is part of the DuPage County Forest Preserve District. That forest preserve includes a solid waste landfill; operations at the landfill ended in 1999. Data summarized in the table below (from samples collected in 1990) describe the major ion composition of leachate from the landfill (leachate is the water that forms in the landfill). According to the analytical results, the pH of the sample was about 7.2.

Constituent mg/L Constituent mg/L

Ca2+ 220 HCO3- 2733

Mg2+ 256 Cl- 1460

K+ 246 Total PO43- (as PO4

3-) 41

Na+ 838

Fe2+ 70

NH4+ (as N) 203

Use this information to address the following questions:

a. In a few weeks we will see that the total alkalinity of a solution is the sum of its parts. How much alkalinity (expressed in mg as CaCO3/L) does bicarbonate (HCO3

-) contribute to the total alkalinity of the leachate?

b. Estimate the total hardness expressed in mg as CaCO3/L. c. Phosphoric acid (H3PO4) is a triprotic acid. When it dissociates to give up one proton, the

product is H2PO4-, when it gives up the second proton the product is HPO4

2-, and when it gives up the third proton the product is PO4

3-. All four of these species are present in solution at the same time, concentrations of the individual species depend on the solution pH, and the sum of their concentrations is what is reported as the total PO4

3- concentration. At pH = 7.2 the dominant species are H2PO4

- and HPO42- so that each one

makes up about half the total PO43-. What are the concentrations of HPO4

2- and H2PO4-

expressed as HPO42- and H2PO4

-, respectively? d. One way to assess the accuracy of a water quality measurement is to check the charge

balance against the following equation: ∑𝑐𝑎𝑡𝑖𝑜𝑛𝑠 − ∑𝑎𝑛𝑖𝑜𝑛𝑠∑ 𝑐𝑎𝑡𝑖𝑜𝑛𝑠 + ∑𝑎𝑛𝑖𝑜𝑛𝑠

× 100 = % 𝑒𝑟𝑟𝑜𝑟

In the above expression the summation terms are the cation and anion concentrations expressed as meq/L. How well do these results satisfy the electroneutrality condition?

e. Determine the ionic strength of the leachate. f. Examine Table 1.4 in our text, pick an appropriate method, and calculate activity

coefficients for monovalent, divalent, and trivalent ions in the leachate.

Solutions – The amount of alkalinity contributed by HCO3

- is:

2.733 �𝑔 𝐻𝐶𝑂3−

𝐿� ×

161�

𝑚𝑜𝑙 𝐻𝐶𝑂3−

𝑔 𝐻𝐶𝑂3−�× 1�

𝑒𝑞𝑚𝑜𝑙 𝐻𝐶𝑂3−

� × 50 �𝑔 𝑎𝑠 𝐶𝑎𝐶𝑂3

𝑒𝑞� = 2.24 �

𝑔 𝑎𝑠 𝐶𝑎𝐶𝑂3𝐿

�

The total hardness expressed as CaCO3 is:

0.22 �𝑔 𝐶𝑎2+

𝐿 �×1

40.08�𝑚𝑜𝑙𝑔� × 2 �

𝑒𝑞𝑚𝑜𝑙

� = 1.10 × 10−2 �𝑒𝑞𝐿�

0.256 �𝑔 𝑀𝑔2+

𝐿 �×1

24.305�𝑚𝑜𝑙𝑔� × 2 �

𝑒𝑞𝑚𝑜𝑙

� = 2.11 × 10−2 �𝑒𝑞𝐿�

0.07 �𝑔 𝐹𝑒2+

𝐿 �×1

55.847�𝑚𝑜𝑙𝑔� × 2 �

𝑒𝑞𝑚𝑜𝑙

� = 2.51 × 10−3 �𝑒𝑞𝐿�

Total hardness = 3.46×10-2 (eq/L) × 50 (g CaCO3/eq) = 1.73 g as CaCO3/L

The concentrations of the phosphate species are:

0.041�𝑔 𝑃𝑂43−

𝐿 �×1

94.974�𝑚𝑜𝑙

𝑔 𝑃𝑂43−� = 4.32 × 10−4 �

𝑚𝑜𝑙 𝑃𝐿

�

Each of the phosphate species is about one-half of this total.

(𝐻2𝑃𝑂4−) = 2.16 × 10−4 �𝑚𝑜𝑙𝐿� × 96.974 �

𝑔𝑚𝑜𝑙

� = 2.09 × 10−2 �𝑔𝐿�

(𝐻𝑃𝑂42−) = 2.16 × 10−4 �𝑚𝑜𝑙𝐿� × 95.974 �

𝑔𝑚𝑜𝑙

� = 2.07 × 10−2 �𝑔𝐿�

Calculations to check the charge balance and to determine the ionic strength are summarized in the following table. The charge balance error is less than 3% and the ionic strength is 0.11.

Constituent mg/L g/mol mol/L eq/L z^2*c Ca2+ 220.00 40.08 5.49E-03 1.10E-02 2.20E-02 Mg2+ 256.00 24.305 1.05E-02 2.11E-02 4.21E-02 Na+ 838.00 22.99 3.65E-02 3.65E-02 3.65E-02 K+ 246.00 39.098 6.29E-03 6.29E-03 6.29E-03 Fe2+ 70.00 55.847 1.25E-03 2.51E-03 5.01E-03 NH4+ 261.00 18 1.45E-02 1.45E-02 1.45E-02 Total = 9.18E-02 1.26E-01 HCO3- 2733.00 61 4.48E-02 4.48E-02 4.48E-02 Cl- 1460.00 35.453 4.12E-02 4.12E-02 4.12E-02 H2PO4 20.90 96.974 2.16E-04 2.16E-04 2.16E-04 HPO42- 20.70 95.974 2.16E-04 4.31E-04 1.73E-03

Total = 8.66E-02 8.79E-02 TDS = 6125.60

I = 1.07E-01

CB error = 2.89

For ionic strength I = 0.11, the Davies equation is the only method we can use. The specific interaction model would also work, but we don’t have values for the specific interaction terms. Assuming water at T = 25°C, A = 0.51; the calculations are summarized in the table below.

z log γ γ

1 -1.15E-01 0.77

2 -4.59E-01 0.35

3 -1.03E+00 0.09