Chapter 3: Problems

In the problems listed below for which calculations are required, neglect the occurrence of ion associations or complexes such as \ce{CaSO}^{\circ}_4, \ce{MgSO^{\circ}_4}, \ce{NaSO^-_4}, \ce{CaHCO^+_3}, and \ce{CaCO^{\circ}_3}. Information that can be obtained from some of the figures in this text should serve as a guide in many of the problems.

  1. A laboratory analysis indicates that the total dissolved inorganic carbon in a sample of aquifer water is 100 mg/ℓ (expressed as C). The temperature in the aquifer is 15°C, the pH is 7.5, and the ionic strength is 0.05. What are the concentrations of H2CO3, CO32–, and \ce{HCO^-_3} and the partial pressure of CO2? Is the PCO2, within the range that is common for groundwater?
  1. Saline water is injected into an aquifer that is confined below by impervious rock and above by a layer of dense unfractured clay that is 10 m thick. A freshwater aquifer occurs above this aquitard. The Cl– content of the injected water is 100,000 mg/ℓ. Estimate the length of time that would be required for Cl– to move by molecular diffusion through the clayey aquitard into the freshwater aquifer. Express your answer in terms of a range of time that would be reasonable in light of the available information. Assume that the velocity of hydraulic flow through the clay is insignificant relative to the diffusion rate.
  1. Two permeable horizontal sandstone strata in a deep sedimentary basin are separated by a 100-m-thick bed of unfractured montmorillontic shale. One of the sandstone strata has a total dissolved solids of 10,000 mg/ℓ; the other has 100,000 mg/ℓ. Estimate the largest potential difference that could develop, given favorable hydrodynamic conditions, across the shale as a result of the effect of osmosis (for water activity in salt solutions, see Robinson and Stokes, 1965). The system has a temperature of 25°C. What factors would govern the actual potential difference that would develop?
  1. Rainwater infiltrates into a deposit of sand composed of quartz and feldspar. In the soil zone, the water is in contact with soil air that has a partial pressure of 10–1.5. The system has a temperature of 10°C. Estimate the pH of the soil water. Assume that reactions between the water and the sand are so slow that they do not significantly influence the chemistry of the water.
  1. The results of a chemical analysis of groundwater are as follows (expressed in mg/ℓ): K+ = 5.0, Na+ = 19, Ca2+ = 94, Mg2+ = 23, \ce{HCO^-_3} = 334, Cl– = 9, and SO42– = 85; pH 7.21; temperature 25°C. Determine the saturation indices with respect to calcite, dolomite, and gypsum. The water sample is from an aquifer composed of calcite and dolomite. Is the water capable of dissolving the aquifer? Explain.
  1. Is there any evidence indicating that the chemical analysis listed in Problem 5 has errors that would render the analysis unacceptable with regard to the accuracy of the analysis?
  1. Groundwater at a temperature of 25°C and a PCO2 of 10–2 bar flows through strata rich in gypsum and becomes gypsum saturated. The water then moves into a limestone aquifer and dissolves calcite to saturation. Estimate the composition of the water in the limestone after calcite dissolves to equilibrium. Assume that gypsum does not precipitate as calcite dissolves.
  1. A sample of water from an aquifer at a temperature of 5°C has the following composition (expressed in mg/ℓ): K+ = 9, Na+ = 56, Ca2+ = 51, Mg2+ =104, \ce{HCO^-_3} = 700, Cl– = 26, and SO42– = 104; pH 7.54. The pH was obtained from a measurement made in the field immediately after sampling. If the sample is allowed to equilibrate with the atmosphere, estimate what the pH will be. (Hint: The PCO2 of the earth’s atmosphere is 10–3.5 bar; assume that calcite and other minerals do not precipitate at a significant rate as equilibration occurs with respect to the earth’s atmosphere.)
  1. Field measurements indicate that water in an unconfined aquifer has a pH of 7.0 and a dissolved oxygen concentration of 4 mg/ℓ. Estimate the pE and Eh of the water. Assume that the redox system is at equilibrium and that the water is at 25°C and 1 bar.
  1. The water described in Problem 9 has a \ce{HCO^-_3} content of 150 mg/ℓ. If the total concentration of iron is governed by equilibria involving FeCO3(s) and Fe(OH)3(s), estimate the concentrations of Fe3+ and Fe2+ in the water. What are the potential sources of error in your estimates?
  1. A water sample has a specific conductance of 2000 \mu S at a temperature of 25°C. Estimate the total dissolved solids and ionic strength of the water. Present your answer as a range in which you would expect the TDS and I values to occur.
  1. Groundwater has the following composition (expressed in mg/ℓ): K+ = 4, Na+ = 460, Ca2+ = 40, Mg2+ = 23, \ce{HCO^-_3} = 1200, Cl– = 8, and SO42– = 20; pH 6.7. How much water would have to be collected to obtain sufficient carbon for a 14C determination by normal methods?
  1. Compute the PCO2 for the water described in Problem 12. The PCO2 is far above the PCO2 for the earth’s atmosphere and is above the normal range for most groundwaters. Suggest a reason for the elevated PCO2.
  1. In the normal pH range of groundwater (6–9), what are the dominant dissolved species of phosphorus? Explain why.
  1. Prepare a percent occurrence versus pH graph similar in general form to Figure 3.5 for dissolved sulfide species (HS–, S2–, H2S) in water at 25°C.
  1. Radiometric measurements on a sample of inorganic carbon from well water indicate a 14C activity of 12 disintegrations per minute (dpm). The background activity is 10 dpm. What is the apparent age of the sample?
  1. Groundwater at 5°C has a pH of 7.1. Is the water acidic or alkaline?
  1. Does precipitation of calcite in zones below the water table (i.e., closed-system conditions) cause the pH of the water to rise or fall? Explain.