# Monthly Archives: February 2011

## Measuring the pH of a Solution

Another frequently used measure of water quality along with electrical conductivity and turbidity is the pH. pH is a measure of the hydrogen ion activity in a solution. Solutions with high hydrogen (H+) or hydronium ion (H3O+) activity are called acids and solutions with low hydrogen ion activity are called bases. Another way of looking at it is by looking at the reciprocal quantity of hydroxyl ions (OH-). The more hydroxyl ions, the more basic a solution is and so on. pH is a mathematical way of quantifying these concentrations and placing them on a relative scale. It is defined as:

In a parallel fashion the quantity pOH is defined as:

Conversely, to determine the activity or concentrations given the pH or pOH, we have:

The relationship between pH and pOH at standard temperature conditions (25 degrees Celsius) is:

pH + pOH = 14

From here, we can see that the relative scale used is from a pH of 0 to a pH of 14 with 0 being very acidic, 14 being very basic, and 7 being neutral.

There are 2 basic types of techniques for measuring pH. The first type is called colorimetric measurement. The use of litmus paper is a colorimetric technique. The second type is called electrometric and is done using an electrical instrument. The instrument is calibrated with 3 standard solutions at known pHs of 4, 7, and 10. Then the instrument can be used to measure unknown solutions. The typical range for drinking water is ideally around 6 – 8.5.

## The Principle of Voltage Division

The principle of voltage division is derived from Ohm’s Law and from Kirchoff’s Voltage Law (KVL). KVL says that the sum of the voltage drops around a closed loop is equal to zero. Consider the following circuit.

If we apply KVL we have:

From Ohm’s Law we can say:

The current is the same through each resistor since this is a series circuit. If we combine these expressions we get:

If we solve each expression of Ohm’s Law above for the current (i) and substitute that into the last equation, we can show how the total voltage from the voltage source divides across each resistor in proportion to the magnitude of the resistance.

Likewise for resistors 2 and 3 we have:

Finally, we can summarize this in a general expression where V_{Rn} is voltage across any general resistor in the series circuit, and V_{s} is the magnitude of the voltage source.

## Specific Gravity of Soil

The specific gravity of soil is an important weight-volume property that is helpful in classifying soils and in finding other weight-volume properties like void ratio, porosity, and unit weight. In this lab we first weighed an empty 1000 mL graduated cylinder. Then we filled it to 500 mL with distilled water and weighed it again. This allowed us to find the density or unit weight of the water. Secondly we filled another graduated cylinder with a mixture of soil and water. This mixture was heated on a stove to remove air from the mixture. Then it was filled to the 500 mL mark with additional distilled water and weighed. Finally an oven-safe container was weighed empty and then the soil/water mixture was poured into the container and dried in the oven for a 24-hour period. This enabled us to find the weight of the dry soil solids. Once this procedure was completed and the data collected, the specific gravity could be obtained via the following computations.

The specific gravity is defined as the ratio of the unit weight of the soil solids to the unit weight of water.

The unit weight of the soil solids is given by:

Where W_{s} is the weight of the soil solids and V_{s} is the volume of the soil solids. Likewise the unit weight of water is given by:

Consequently we can substitute these expressions into the first equation and obtain:

To obtain the weight of the soil we subtracted the weight of a dish container from the weight of the dish container with the oven-dried soil.

The volume of water we used was known at 500 mL.

The weight of the water corresponding to this volume was simply obtained by subtracting the weight of the flask or graduated cylinder from the weight of the flask with the volume of water.

Determining the volume of the soil was more difficult. We used the mixture that consists of the flask, soil, and water. Here the volume of the soil will be the total volume minus the volume of the water. (The volume of air is negligible)

In order to evaluate this we make the assumption that the unit weight of the water is constant.

We know all the values in this last expression except W_{w2}. This is the weight of the water in the water-soil-flask mixture. It can be found by:

This is all the information we needed. Simply substitute the solution from this last equation into the equation for the second volume of water, the solution from that into the equation for volume of soil, and all the known and determined values into the substituted equation for specific gravity to obtain the specific gravity. Here are the values and calculations we obtained in our experiment.

This was a reasonable finding since the specific gravity of soils typically falls in the range of 2.6 to 2.9.

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## Turbidity and Suspended Solids

Another method of analyzing water quality is through the measurement of turbidity and its correlation with total solids. Turbidity is a relative measure of the clarity of a water sample by measuring the scatter of light as it passes through a sample. A sample with high turbidity will appear unclear while a sample with low turbidity will appear more clear because light passes through it with less scatter and absorption. It is relative in that it is measured against a standardized sample of stabilized formazin or gelex. The preferred units used in turbidity measurements are nephelometric turbidity units or NTUs. It is usually measured with a nephelometric turbidimeter or spectrophotometer. A key point here is that the turbidity can be measured in just a few minutes including calibration.

Total solids can be categorized into 4 categories: suspended solids, dissolved solids, settable solids, and volatile solids. They include all the solid materials that are contained in the water matrix. They can be measured as a concentration of the sample volume using gravimetric measurement techniques. This requires that we use an Imhoff cone to measure settlable solids, a filter to measure suspended solids, and the filtrate to measure dissolved solids. Usually suspended solids is the primary concern. These constituents are what typically affect the clarity of the water. However since it is time consuming and not necessarily practical to collect a sample, put it in an evaporating dish, evaporate the water in an oven over the course of 24 hours or more, and weight the solids remaining, we attempt to find a correlation between suspended solids and turbidity. Turbidity cannot by itself be used to quantify the concentration of suspended solids in a body of water. However by analyzing a few samples we can find and plot the correlation between concentration of suspended solids and turbidity. This gives us a relationship (valid only for a particular location and time) so that we can determine the amount of suspended solids in a body of water by simply measuring the turbidity.

The primary reasons that suspended solids are a concern is first, simple aesthetics and second, the harboring of pathogens or pathogen supporting envirnoments. The EPA has set primary drinking water quality standards at less than 1 NTU. Prior to 2002, less than 5 NTU was acceptable.