Water Hardness Calculations

As mentioned earlier, the hardness of a water sample is often reported as parts per million of calcium carbonate. Using our definition of parts per million for liquid solutions (Table 5.4), we have 

At the end point of the titration, the moles of CaC03 reacted are the same as the moles of EDTA added (it is a one-to-one reaction see Equation (5.43))  

The moles of EDTA, and therefore the moles of CaC03, are computed from the titration data  

The grams of CaC03 can be computed by multiplying by the formula weight of CaC03 (100.03 g/mol) and converted to milligrams by multiplying by 1000 mg/g  

The dimensional analysis of this equation is as follows, using 100.09 g/mol as the formula weight of CaC03  

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Matrix extrapolation undertaken by this model means that the model calculates the free metal ion concentration as the toxic species, given a total metal concentration and site-specific conditions in terms of water hardness, DOC, salinity, and so on. As an example, according to the MINTEQ model, a type of water with a hardness of 10 mg/L CaC03, a DOC content of 10 mg/L, a total Zn concentration of 10 mg/L, and a variable pH gives a distribution of Zn species as given in Table 2.5. 

These are useful insights, but they should be kept in perspective. This particular study did not take into account other important variables such as temperature and water hardness. The effects produced by these other independent variables can be handled separately in other studies, and their respective contour maps generated. These could also be used as factors in calculating the "Performance" variable. 

Replicate water samples are analyzed for water hardness with the following results 102.2, 102.8,103.1, and 102.3 ppm CaC03. Calculate (a) the standard deviation, (b) the relative standard deviation, (c) the standard deviation of the mean, and (d) the relative standard deviation of the mean. 

Calculate the following descriptive statistics for the data on water hardness (mmoll ) given as follows arithmetic mean, median, standard deviation, variance, standard error, confidence interval at a significance level of 0.01, range, and the interquartile distance - 8.02 7.84 7.98 7.95 8.01 8.07 7.89. 

Standard solutions of calcium ion used to test for water hardness are prepared by dissolving pure calcium carbonate, CaC03, in dilute hydrochloric acid. A 1.745-g sample of CaCO is placed in a 250.0-mb volumetric flask and dissolved in HCb Then the solution is diluted to the calibration mark of the volumetric flask. Calculate the resulting molarity of calcium ion. 

Both values calculated using a water hardness of 50 mg/L... 

Once median survival times have been determined at a series of stress levels, the median survival times are plotted against the stress level and the results extrapolated to an infinite survival time, assuming of course that the data permit such an extrapolation. The hypothetical concentration of the toxicant corresponding to an infinite median survival time is called the incipient lethal level. Figure 6 illustrates how incipient lethal levels are calculated. The data are taken from a study of the toxicity of zinc to rainbow trout. Median survival times were calculated as a function of zinc concentration at three levels of water hardness. Note that both axes are plotted on a logarithmic scale. At water hardness levels of 50 and 320 mg/L, the data show distinct curvature, and a function of the form (C — (1 — T[) = K... 

An analogous equation for the final chronic value may be calculated by simply dividing the equation for the final acute value by the final acute/chronic ratio. However, if there is evidence that there is a difference in the functional dependence of chronic toxicity and acute toxicity on water quality characteristics such as temperature and hardness, then the final chronic equation may be determined independently of the final acute equation. In the case of cadmium, for example, chronic toxicity appears to be less sensitive to water hardness than acute toxicity appears to be, thus a final fi eshwater chronic equation was developed solely from chronic toxicity studies performed with 16 fi eshwater species. The final chronic equation for dissolved cadmium in fi eshwater is... 

Hardness was originally designed to measure the capacity of the water to react with and precipitate a standard soap. Although other cations, including H+ and Fe +, can react with soaps, hardness is currently defined as the sum of the Ca + and Mg + concentrations because these cations are usually the most abundant ones in natural waters. Water hardness is reported as mg CaC03/L equivalent and this quantity is calculated as... 

Methods and previous articles 16, 25, 27). A Perkin Elmer AAnalyst 400 FAAS with auto-sampler was used. The auto-sampler expedited the measurement of the standard solutions and samples that were used by about 30 students in each of the three class periods. Each pair of students calculated their own average water hardness from both the titration and FAAS data and then compared the two methods to each other and then to the accepted value for water hardness. Statistical comparison using student s t-tests could have been done, but was not in this case. Table 4 shows proposed student outcomes from the research project and two experiments. 

A colorless, colloidal precipitate was formed and stirred thoroughly for about 15 minutes, whereupon it was filtered by suction. The raw product thus obtained was washed with water until It contained only about Va% water-soluble salts. After drying for 12 hours In a vacuum apparatus at 60°C and under a pressure of 12 mm Hg, the product had the form of hard pieces. The pieces were comminuted to powder in a ball mill and the powder was passed through a sieve (3,600 meshes per cm ). The small residue on the sieve was again pulverized and passed through the same sieve. The yield was 870 g, or 99% of theoretical, calculated on the assumed formula... 

The surface water runoff from paved/hard standing areas also depends on rainfall intensity calculated from the geographical locations of the site and storm-return period. However, the return period for a site will be far higher than for a building in order to ensure prevention of persistent flooding of the site. In many instances the local authority may specify the storm-return period as the design criterion. 

In treated water for high-pressure boilers or where radiation effects are important, as in some nuclear projects, impurities are measured in very small units (e.g. g/litre or p.p. 10 ), but for most purposes it is convenient to express results in mg/litre. In water analysis, determinations (except occasionally for dissolved gases) are made on a weight/volume basis but some analysts still express results in terms of parts per million (p.p.m.). The difference between mg/litre and p.p.m. is small and for practical purposes the two units are interchtmgeable. For some calculations, the use of milli-equivalents per litre or equivalents per million (e.p.m.) has advantages but has not found much application. Hardness, whatever the constituent salts, is usually expressed as p.p.m. CaCOs (see Table 2.10). 

Calculate the temporary hardness of the water by subtracting the permanent hardness from the total hardness. 

The extent of the agreement of the theoretical calculations with the experiments is somewhat unexpected since MSA is an approximate theory and the underlying model is rough. In particular, water is not a system of dipolar hard spheres.281 However, the good agreement is an indication of the utility of recent advances in the application of statistical mechanics to the study of the electric dipole layer at metal electrodes. 

The last state in Fig. 11.1 that has not yet been discussed is the state of the neat liquid compound X. For liquid compounds this is the relevant initial state for solubility, but almost aU drug-Uke compounds are solid at room temperature. In this case the neat liquid is a virtual state of a supercooled liquid which can hardly be accessed experimentally. However, it is an interesting intermediate state because it allows us to split the calculation of solubility into two separate steps, which are conceptually and for some methods computationally easier to handle than the complete step from the crystaUine state of the drug to the liquid state of the drug dissolved in water. In the first step we only have to transfer the compound from its neat crystalline state to its neat liquid state. The free energy of this fusion transfer is usually called AG s (or if considered in the opposite direction). 

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