The purpose of this homework set is twofold: first to give you an introduction to the Santa Fe sink – rise system where we are planning to do some field work during the latter part of this class, and second to introduce you to the carbon system for water in a carbonate karst setting.  Much of the information needed for this homework can be found in Drever, The Geochemistry of Natural Waters or Stumm and Morgan, Aquatic Chemistry.  I hope to have covered most of this during the lecture.  All of the thermodynamic data you may need is listed below, but there may be some information that you don’t need.  The calculations you will need to do are repeated for each sample ( a total of 25 samples, and thus it will be easiest for you to do the calculations in a spreadsheet such as Excel.

(1) Read the following article:

Martin, J.B. and Dean, R.W., “Temperature as a natural tracer of short residence times for groundwater in karst aquifers”, in A.N. Palmer, M.V. Palmer, and I.D. Sasowsky, Karst Modeling, Karst Waters Institute Special Publications #5, 236-242.

There are two copies of it over in the Geology office.  Please have mercy on your fellow students and do not steal these copies.   This paper will give the background information on where samples came from that are included in the attached table.  You can compare the sample dates with the river stage by looking at Fig. 3 in the paper.

(2) Calculate a charge balance on the data in the attached table.  Be sure to convert from weight to molar units.  Do the charges balance?  Why or why not?

(3) Use the DIC and pH data in the attached table to calculate the bicarbonate and carbonate concentrations.  How do the alkalinity values compare with your calculated values for the bicarbonate and carbonate?  Why might they be different?

You will need some thermodynamic data which is tabulated below:
 

T(ºC)	pK1	pK2	pKcal
5	6.52	10.55	8.39
10	6.46	10.49	8.41
15	6.42	10.43	8.43
20	6.38	10.38	8.45
25	6.35	10.33	8.48

 

In order to account for the variations in temperatures for each samples, you may simply extrapolate between the temperatures.  They should be linear over the range from ~0 to 40 ºC.  Do you need to use different values for the K’s because of the temperature range of the samples?
 

(4) Create a plot of the Cl concentrations versus distance away from the sink well.  The distances are:
 

Location	Distance (km)
Sink	0.5
Sweetwater Lake	3
Rise	5
Rise well	7

Discuss the reasons for the variation in the Cl concentrations through time and “downstream”.  In particular, discuss why the Cl concentration decreases with time at the Rise well.  In order to answer this question look through the Martin and Dean paper again.

(5) Create a plot of the Ca concentrations versus distance from the sink well.  Why does this plot look different from the Cl plot?

(6) Calculate the saturation of calcite for each sample by comparing the ion activity product with the equilibrium constant for calcite, assuming the controlling reactions is:
 

CaCO₃ = Ca²⁺ + CO₃^2-

 You may calculate activities using the Debye-Huckel relationship.  You may assume that A = 0.5085 in this equation.  Why do you get the saturation that you do?
 

 (7) Assume that 1 cubic meter of water per second flows into matrix rocks (i.e. water that goes into the sink does not come back to the surface at the rise).  How much calcite will this water dissolved?