# Chapter 40 - Expression Of Analytical Results

PARTS PER MILLION (PPM)

Water analysis involves the detection of minute amounts of a variety of substances. The expression of results in percentage would require the use of cumbersome figures. For this reason, the results of a water analysis are usually expressed in parts per million (ppm) instead of percentage. One part per million equals one ten-thousandth of one percent (0.0001%), or one part (by weight) in a million parts-for example, 1 oz in 1,000,000 oz of water, or 1 lb in 1,000,000 lb of water. It makes no difference what units are used as long as both weights are expressed in the same units.

When elements are present in minute or trace quantities, the use of parts per million results in small decimal values. Therefore, it is more convenient to use parts per billion (ppb) in these cases. One part per billion is equal to one-thousandth of one part per million (0.001 ppm). For example, in studies of steam purity using a specific ion electrode to measure sodium content, values as low as 0.001 ppm are not uncommon. This is more conveniently reported as 1.0 ppb.

In recent times, the convention for reporting analytical results has been shifting toward the use of milligrams per liter (mg/L) as a replacement for parts per million and micrograms per liter (µg/L) as a replacement for parts per billion.

Test procedures and calculations of results are based on the milliliter (mL) rather than the more common cubic centimeter (cc or cm3). The distinction between the two terms is very slight. By definition, a milliliter is the volume occupied by 1 g of water at 4°C, whereas a cubic centimeter is the volume enclosed within a cube 1 cm on each edge (1 mL = 1.000028 cm3).

MILLIGRAMS PER LITER (mg/L)

The milligrams per liter (mg/L) convention is closely related to parts per million (ppm). This relationship is given by:

ppm x solution density = mg/L

Thus, if the solution density is close or equal to 1, then ppm = mg/L. This is normally the case in dilute, aqueous solutions of the type typically found in industrial water systems. Control testing is usually conducted without measurement of a solution's density. For common water samples, this poses no great inaccuracy, because the density of the sample is approximately 1. Milligrams per liter (mg/L) and parts per million (ppm) begin to diverge as the solution density varies from 1. Examples of this are a dense sludge from a clarifier underflow (density greater than 1) or closed cooling system water with high concentrations of organic compounds (density less than 1). All of the analytical methods discussed in this text contain calculations required to obtain the results in milligrams or micrograms per liter.

EQUIVALENTS PER MILLION (EPM)

In reporting water analyses on an ion basis, results are also expressed in equivalents per million (epm). Closely allied to the use of parts per million, this approach reduces all constituents to a common denominator-the chemical equivalent weight.

The use of equivalents per million is not recommended for normal plant control. Parts per million is a simpler form of expressing results and is accepted as the common standard basis of reporting a water analysis. However, whenever extensive calculations must be performed, the use of equivalents per million greatly simplifies the mathematics, because all constituents are on a chemical equivalent weight basis. The remainder of this section provides a discussion of parts per million and equivalents per million for those who desire a working knowledge of these methods of expression for purposes of calculations.

The units of ppm and epm are commonly combined in normal reporting of water analyses, and many different constituents are frequently reported on a common unit weight basis. For example, calcium (equivalent weight 20.0) is reported in terms of "calcium as CaCO3" (equivalent weight 50.0). The test for calcium is calibrated in terms of CaCO3, so the conversion factor 2.5 (50/20) is not needed. Hardness, magnesium, alkalinity, and free mineral acid are often reported in terms of CaCO3; the value reported is the weight of CaCO3 that is chemically equivalent to the amount of material present. Among these substances, ionic balances may be calculated. When constituents are of the same unit weight basis, they can be added or subtracted directly. For example, ppm total hardness as CaCO3 minus ppm calcium as CaCO3 equals ppm magnesium as CaCO3. However, ppm magnesium as Mg2+ equals 12.2 (magnesium equivalent weight) divided by 50.0 (CaCO3 equivalent weight) times the ppm magnesium as CaCO3.

In every case, it is necessary to define the unit weight basis of the results-"ppm alkalinity as CaCO3" or "ppm sulfate as SO42- " or "ppm silica as SiO2". Where the unit weight basis is different, calculations must be based on the use of chemical equations.

The following rules outline where epm can be used and where ppm must be used. In general, either may be used where an exact chemical formula is known. When such knowledge is lacking, ppm must be used.

• The concentration of all dissolved salts of the individually determined ions must be in ppm.
• Two or more ions of similar properties whose joint effect is measured by a single determination (e.g., total hardness, acidity, or alkalinity) may be reported in either ppm or epm.
• The concentration of undissolved or suspended solids should be reported in ppm only.
• The concentration of organic matter should be reported in ppm only.
• The concentration of dissolved solids (by evaporation) should be expressed as ppm only.
• Total dissolved solids by calculation may be expressed in either ppm or epm.
• Concentration of individual gases dissolved in water should be reported in ppm. The total concentration of each gas when combined in water may be calculated to its respective ionic concentration in either ppm or epm.

CALCULATION OF TOTAL DISSOLVED SOLIDS BY EPM

Starting with a reasonably complete water analysis, total dissolved solids may be calculated as epm. In a complete water analysis, the negative ion epm should equal the positive ion epm. Where there is an excess of negative ion epm, the remaining positive ion epm is likely to be sodium or potassium (or both). For the sake of convenience, it is generally assumed to be sodium. Where there is an excess of positive epm, the remaining negative epm usually is assumed to be nitrate.

To calculate dissolved solids, convert the various constituents from ppm to epm and total the various cations (positively charged ions) and anions (negative ions). The cations should equal the anions. If not, add either sodium (plus) or nitrate (minus) ions to balance the columns. Convert each component ionic epm to ppm and total to obtain ppm dissolved solids. For example, to convert 150 ppm calcium as CaCO3 to epm (Table 40-1) divide by 50 (the equivalent weight of calcium carbonate) and obtain 3.0 epm. To convert 96 ppm sulfate as SO42- to epm, divide by 48 (the equivalent weight of sulfate) and obtain 2.0 epm. After balancing the cations and anions by adding sodium, convert to ionic ppm by multiplying the epm by the particular ionic equivalent of weight. For example, to convert 3.0 epm calcium to ppm calcium as Ca2+, multiply by 20 (the equivalent weight of calcium) and obtain 60 ppm calcium as Ca2+. To obtain the ppm dissolved solids, total the ppm of the individual ions.

Table 40-2. Conversion Table