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Monday, March 26, 2012

Conductivity of Water

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Abstract


This experiment was designed to explore nature of water as it pertains to conductivity. It can be shown that the conductivity of a substance is directly related to the amount of dissolved salts in the substance, as salts are ions. One contributor to water conductivity, therefore, is soil, as it contains many minerals and other substances which, when dissolved in water, form ions. The experiment focused on the effect of three variables on water conductivity the type of soil, the amount of time that the soil was saturated with water, and finally the amount of soil used in each solution. I therefore used two samples of soil, one normal sample from outside my apartment and another from a bag of potting soil. I also varied the amount of time that the soil was allowed to remain in the water for a sample of normal soil. Finally, for each type of soil, three different amounts were used in each trial. The results, as will be discussed more fully in the statistical analysis, indicate that in almost each case, changing the variable produces a significant difference in the result. The one exception involved time, which was found to be a factor, but with limits. That is to say, the conductivity leveled off after a few minutes.


Introduction


Electrical Conductivity estimates the amount of total dissolved salts, or ions, in water. It is a measure of how easily electricity can be conducted by water, and involves the concept of electrolytes. An electrolyte is a substance that conducts electricity, and is divided into strong and weak electrolytes. Depending on the type of salt dissolved in the water, the conductivity will vary accordingly. Stronger electrolytes correspond to higher conductivity. Electrical conductivity, or EC, is measured in Siemens, which is an equivalent unit to mhos. These mhos are simply the inverse of the ohm, the unit for resistance. Conductivity, therefore, is the inverse of a substances resistance. By dissolving ions in water, the overall resistance of the water is reduced, increasing the conductivity.


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Many factors contribute to the conductivity of water. Of course, the local geography of an area will determine the base level of conductivity. As a result, when speaking of the conductivity of a substance, one generally refers to the specific conductivity. Other sources of ions also exist. Pollution from urban areas, salts applied to roads, and agricultural runoff are a few examples of man’s contributions. Many natural factors besides the local geography are also involved, such as rainwater from ocean sources, evaporation as it leaves a higher concentration of ions behind, and bacterial metabolism. Because of the abundance of sources for ions, conductivity is not the most specific test of a water source’s quality. However, it serves as an indication that something has contributed to the ionic concentration of the body of water, so it can be useful as an easy test to determine changes in quality.


Experimental Design


The experiment was designed to study the effects of three different variables on the conductivity of distilled water. Distilled water, through purification processes, has a relatively low conductivity due to the removal of many ions. Therefore, changes in the conductivity should be easy to detect. The first variable examined was the effect of different types of soil samples on the conductivity. One sample was taken from a pile of dirt outside my apartment complex. The other sample it was compared with was taken from a typical bag of potting soil. A second variable was the amount of each soil type used in the experiment. I therefore used samples of five, ten, and fifteen grams for each type of soil. The final variable for this experiment was the amount of time that the soil was introduced to the water.


Exposing the soil to the water was the difficult part of the experiment. In order to determine the effects of the type and amount of soil used, the process was simple enough. I placed the particular soil sample in a coffee filter, then strained one hundred milliliters of water through the filter. In order to keep the exposure time as constant as possible, I would squeeze the water, in essence “ringing” the coffee filter to speed the process. To explore the variable of time, a new method was required, though. For this portion of the experiment, the soil was poured directly into the water, and the solution was stirred by means of a stir plate for the desired amount of time. The resulting solution was then strained through a coffee filter in order to remove any particles. To measure the conductivity of all the solutions, a beaker containing the water was placed on a stir plate, and the conductivity probe was suspended in the mixture using a clamp. Measurements were taken for ten seconds. After each measurement, the probe, beakers, and funnel were rinsed with distilled water to prevent contamination between trials.


Statistical Analysis


I performed three main types of statistical tests. A difference exists between my actual intuition and the hypothesis I employed when performing the tests. First I will state my hypothesis as I began the experiment. I believed that different types of soil should affect the conductivity of water differently, since different soil samples will inevitably contain different substances and hence could produce different ions upon dissolving in water. Since some of these different substances will result in weak electrolytes while others will be strong electrolytes, the conductivity will vary according to the concentration of each. Similar logic pertains to the different amounts of soil used. More soil corresponds to more substances within the sample, so more ions could possibly dissolve into the water. As far as time is concerned, the more time the soil is left in the water, the more opportunity for the substances to dissolve. This last proposition rests on my poor knowledge of the actual process of substances dissolving, and I assumed that some take longer than others. However, when testing my data, I chose to use the hypotheses that all of the samples would come from the same population. The reasoning for this was that otherwise, I would have to quantify the differences in means, a process which I was not able to do. I found no formulas governing the changes in conductivity other than that concerning resistance, and I knew of no way to calculate the resistance of a liquid after introducing an unknown quantity of unknown ions. Therefore, I used my initial hypotheses as my new alternative hypotheses, and chose to use the hypotheses of equality in all cases as the null hypotheses.


The following are three tables contain the chi-square probability of the trials arising from similar populations. In each is found the mean, standard deviation, and standard errors of each trial, as well as for different combinations of the populations. For the samples involving different soil and different amounts, sample A refers to the sample containing five grams, sample B to the ten gram trial, and sample C to the fifteen gram trial. In the case of the trial studying the effect of time variation, sample A is the result of one minute of exposure, sample B is the result of three minutes of exposure, and sample C is the result of five minutes of exposure.


Different Times


Mean Std Dev Std Error c^ for A c^ for B c^ for C


Sample A 55.85 0.6687 0.08514


Sample B 8.7768 0.604 0.0558


Sample C 8.65 0.6175 0.046





A,B,C 84.448 0.68455 0.018 0.7784 0.668 0.671


A & B 77.17 0.6806 0.006 0.4581 0.4581


A & C 77.758 0.6808 0.0005 0.4765 0.4765


B & C 8.747 0.647 0.057 0.7 0.7


Different Amounts of Regular Soil


Mean Std Dev Std Error c^ for A c^ for B c^ for C


Sample A 55.4561 0.5556 0.01876


Sample B 0.7877 0.67817 0.01404


Sample C 117.60 0.60617 0.0115





A,B,C 87.5674 5.47467 0.464174 1.0577E-08 4.485E-06 .8708E-08


A & B 7.11 0.6687 0.001 0.1181506 0.1181506


A & C 86.5414 0.600 0.01865 0.007567 0.007567


B & C 104.088 0.6457 0.006 0.4010001 0.4010001


Different Amounts of Potting Soil


Mean Std Dev Std Error c^ for A c^ for B c^ for C


Sample A 0.65 8.006 0.117


Sample B 444.04 5.5015 0.08765


Sample C 56.47 0.778 0.01064





A,B,C 6.608 5.00865 0.07 .104E-0 0.05181487 .0418E-1


A & B 6.66 7.140 0.10454 6.448E-10 6.448E-10


A & C 7.861 4.515481 0.0660 5.5E-17 5.5E-17


B & C 40.08 .61457 0.04147 0.0807 0.0807


The results of these calculations are fairly easy to interpret. However, I did encounter some quirks with regards to other calculations I performed. I also did a two sample t-test assuming unequal variances between all of the data, as well as z-tests for the data, and these tables are attached at the end of the paper. All of the results of these two particular tests, unless I have somehow interpreted the data incorrectly, indicated that the data for each trial most likely came from different sources. Actually, the probability in each case otherwise was zero, so the likelihood that the results could be drawn from the same population is very low. Since most of the c^ results indicated that the samples most likely came from different populations, the results agree between all of the tests. One set of results does not agree, however. According to the table above, the chance that the data collected after exposing the water to the soil for three minutes and that collected after five minutes could be produced by the same population with a probability of over %. After calculating this result, as well as the t-test and z-test (Unfortunately, technology strikes again and this file was unable to open from my disk. However, my claim is accurate, despite my not having the numbers directly in front of me.), both of which indicated a low probability of this occurring, I decided to do a bit more research into the subject. I am led, based on my findings, to believe the c^ test over the other two, due to the following fact. Conductivity is directly related to density, with almost a linear relationship. It therefore has a saturation point when the density becomes very high, at which time the ions that are dissolved in the water began counteracting each other, actually increasing the resistance of the water.


Conclusion


The results of my experiment have led me to the following conclusions. Based on the low probabilities returned by the c^ test, the amount of dirt is a definite factor in increasing conductivity. This is in accordance with the size of a watershed being influencing the conductivity of a body of water. The higher the dirt to water ratio, the higher conductivity will be. Also, the source of the soil is a huge factor. This too makes sense. The potting soil I used has many extra minerals added, which when dissolved will increase the conductivity of water much more than some sample of regular dirt. Finally, and perhaps most controversially, the amount of time that the soil soaks in water also is a significant factor relating to conductivity, but only to a certain extent. After some time, the conductivity levels off due to an overabundance of ions in the water. Were I to do this experiment again, I believe I would focus more on this aspect and attempt to devise some method of modeling this behavior. Since I only have one trial at my disposal, I did not feel confident in finding a model.





Results of t-test and z-test


Regular Soil


z-Test Two Sample for Means


Sample A Sample B


Mean 55.4561 0.7877


Known Variance 0.546 0.4551


Observations 1004 1004


Hypothesized Mean Difference 0


z -140.47


P(Z=z) one-tail 0


z Critical one-tail 1.64485


P(Z=z) two-tail 0


z Critical two-tail 1.56


z-Test Two Sample for Means


Sample B Sample C


Mean 0.7877 117.60


Known Variance 0.4551 0.676


Observations 1004 1004


Hypothesized Mean Difference 0


z -4.61


P(Z=z) one-tail 0


z Critical one-tail 1.64485


P(Z=z) two-tail 0


z Critical two-tail 1.56


z-Test Two Sample for Means


Sample A Sample C


Mean 55.4561 117.60


Known Variance 0.546 0.676


Observations 1004 1004


Hypothesized Mean Difference 0


z -18.1


P(Z=z) one-tail 0


z Critical one-tail 1.64485


P(Z=z) two-tail 0


z Critical two-tail 1.56


t-Test Two-Sample Assuming Unequal Variances


Sample A Sample B


Mean 55.4561 0.78761


Variance 0.546 0.4551


Observations 1004 1004


Hypothesized Mean Difference 0


df 17


t Stat -140.47


P(T=t) one-tail 0


t Critical one-tail 1.64566


P(T=t) two-tail 0


t Critical two-tail 1.61166


t-Test Two-Sample Assuming Unequal Variances





Sample B Sample C


Mean 0.7877 117.60


Variance 0.4551 0.676


Observations 1004 1004


Hypothesized Mean Difference 0


df 181


t Stat -4.61


P(T=t) one-tail 0


t Critical one-tail 1.64564


P(T=t) two-tail 0


t Critical two-tail 1.6116


t-Test Two-Sample Assuming Unequal Variances





Sample A Sample C


Mean 55.4561 117.60


Variance 0.546 0.676


Observations 1004 1004


Hypothesized Mean Difference 0


df 005


t Stat -18.1


P(T=t) one-tail 0


t Critical one-tail 1.645615


P(T=t) two-tail 0


t Critical two-tail 1.61148


Potting Soil


z-Test Two Sample for Means


Sample A Sample B


Mean 0.487 44.844


Known Variance 107.7885 56.11058


Observations


Hypothesized Mean Difference 0


z -578.77


P(Z=z) one-tail 0


z Critical one-tail 1.64485


P(Z=z) two-tail 0


z Critical two-tail 1.56


z-Test Two Sample for Means


Sample B Sample C


Mean 44.844 56.0


Known Variance 56.11058 0.547


Observations


Hypothesized Mean Difference 0


z -88.476


P(Z=z) one-tail 0


z Critical one-tail 1.64485


P(Z=z) two-tail 0


z Critical two-tail 1.56


z-Test Two Sample for Means


Sample A Sample C


Mean 0.487 56.0


Known Variance 107.7885 0.547


Observations


Hypothesized Mean Difference 0


z -.815


P(Z=z) one-tail 0


z Critical one-tail 1.64485


P(Z=z) two-tail 0


z Critical two-tail 1.56


t-Test Two-Sample Assuming Unequal Variances


Sample A Sample B


Mean 0.487 44.844


Variance 107.7885 56.11058


Observations


Hypothesized Mean Difference 0


df 1816


t Stat -578.77


P(T=t) one-tail 0


t Critical one-tail 1.64564


P(T=t) two-tail 0


t Critical two-tail 1.6171


t-Test Two-Sample Assuming Unequal Variances


Sample B Sample C


Mean 44.844 56.0


Variance 56.11058 0.547


Observations


Hypothesized Mean Difference 0


df 1017


t Stat -88.476


P(T=t) one-tail 0


t Critical one-tail 1.64654


P(T=t) two-tail 0


t Critical two-tail 1.68


t-Test Two-Sample Assuming Unequal Variances


Sample A Sample C


Mean 0.487 56.0


Variance 107.7885 0.547


Observations


Hypothesized Mean Difference 0


df 1008


t Stat -.815


P(T=t) one-tail 0


t Critical one-tail 1.64667


P(T=t) two-tail 0


t Critical two-tail 1.61





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