## Hardness

Background

Originally, water hardness was a measure of the ability of water to precipitate soap. It was measured by the amount of soap needed for adequate lathering and served also as an indicator of the rate of scale formation in hot water heaters and boilers. Soap is precipitated as a gray "bathtub ring" deposit mainly by reacting with the calcium and magnesium cations (Ca2+ and Mg2+) present, although other polyvalent cations may play a minor role.

Hardness has some similarities to alkalinity. Like alkalinity, it is a water property that is not attributable to a single constituent and, therefore, some convention must be adopted to express hardness quantitatively as a concentration. As with alkalinity, hardness is usually expressed as an equivalent concentration of CaCO3. However, hardness is a property of cations (Ca2+ and Mg2+), while alkalinity is a property of anions (HCO3- and CO32-).

FIGURE 3.4 Total acidity-total carbonate diagram (Deffeyes diagram): In this figure, the relationships among total acidity, pH, and total carbonate are shown. If any two of these quantities are known, the third may be determined from the plot. The composition changes indicated in the figure refer to Example 3.5.

FIGURE 3.4 Total acidity-total carbonate diagram (Deffeyes diagram): In this figure, the relationships among total acidity, pH, and total carbonate are shown. If any two of these quantities are known, the third may be determined from the plot. The composition changes indicated in the figure refer to Example 3.5.

### Calculating Hardness

Current practice is to define total hardness as the sum of the calcium and magnesium ion concentrations in mg/L, both expressed as calcium carbonate. Hardness usually is calculated from separate measurements of calcium and magnesium, rather than measured directly by colorimetric titration.

Calcium and magnesium ion concentrations are converted to equivalent concentrations of CaCO3 as follows:

1. Find the equivalent weights of Ca2+, Mg2+, and CaCO3.

molecular or atomic weight magnitude of ionic charge or oxidation number eq. wt. of Ca2+ = ^^ = 20.04. 2

24 31

2. Determine the multiplying factors to obtain the equivalent concentration of CaCO3.

Multiplying factor of Ca2+ as CaCO3 = ——^—2+ 3 = ^^ = 2.497.

Multiplying factor of Mg2+ as CaCO3 = eq- wt: of CaCQ3 = 5004 = 4.118.

3. Calculate the total hardness.

Total hardness (as CaCO3) = 2.497 [Ca2+, mg/L] + 4.118 [Mg2+, mg/L]. (3.14) Equation 3.14 may be used to calculate hardness whenever Ca2+ and Mg2+ concentrations are known. Example 3.6

Calculate the total hardness as CaCO3 of a water sample in which:

Answer: From Equation 3.14,

Total hardness = 2.497 [98 mg/L] + 4.118 [22 mg/L] = 335 mg/L CaCO3.

Both alkalinity and hardness are expressed in terms of an equivalent concentration of calcium carbonate. As noted before, alkalinity results from reactions of the anions, CO32- and HCO3-, whereas hardness results from reactions of the cations, Ca2+ and Mg2+. It is possible for hardness as CaCO3 to exceed the total alkalinity as CaCO3. When this occurs, the portion of the hardness that is equal to the alkalinity is referred to as carbonate hardness or temporary hardness, and the amount in excess of alkalinity is referred to as noncarbonate hardness or permanent hardness.

### Importance of Hardness

Hardness is sometimes useful as an indicator proportionate to the total dissolved solids present, since Ca2+, Mg2+, and HCO3- often represent the largest part of the total dissolved solids. No human health effects due to hardness have been proven; however, an inverse relation with cardiovascular disease has been reported. Higher levels of drinking water hardness correlates with lower incidence of cardiovascular disease. High levels of water hardness may limit the growth of fish; on the other hand, low hardness (soft water) may increase fish sensitivity to toxic metals. In general, higher hardness is beneficial by reducing metal toxicity to fish. Aquatic life water quality standards for many metals are calculated by using an equation that includes water hardness as a variable.

The main advantages in limiting hardness levels (by softening water) are economical: less soap requirements in domestic and industrial cleaning, and less scale formation in pipes and boilers. Water treatment by reverse osmosis (RO) often requires a water softening pretreatment to prevent scale formation on RO membranes. Increased use of detergents, which do not form precipitates with Ca2+ and Mg2+, has lessened the importance of hardness for soap consumption. On the other hand, a drawback to soft water is that it is more "corrosive" or "aggressive" than hard water. In this context, "corrosive" means that soft water more readily dissolves metal ions from a plumbing system than does hard water. Thus, in plumbing systems where brass, copper, galvanized iron, or lead solders are present, a soft water system will carry higher levels of dissolved copper, zinc, lead, and iron, than will a hard water system.

Rules of Thumb

1. The higher the hardness, the more tolerant are many stream metal standards for aquatic life.

2. Hardness above 100 mg/L can cause significant scale deposits to form in boilers.

3. The softer the water, the greater the tendency to dissolve metals from the pipes of water distribution systems.

4. An ideal quality goal for total hardness is about 70-90 mg/L. Municipal treatment sometimes allows up to 150 mg/L of total hardness in order to reduce chemical costs and sludge production from precipitation of Ca2+ and Mg2+.

Water will be "hard" wherever groundwater passes through calcium and magnesium carbonate mineral deposits. Such deposits are very widespread and hard to moderately hard groundwater is more common than soft groundwater. Very hard groundwater occurs frequently. Calcium and magnesium carbonates are the most common carbonate minerals and are the main sources of hard water. A geologic map showing the distribution of carbonate minerals serves also as an approximate map of the distribution of hard groundwater. The most common sources of soft water are where rain water is used directly, or where surface waters are fed more by precipitation than by groundwater.

 Rules of Thumb Degree of Hardness mg CaCO3/L Effects Soft <75 May increase toxicity of dissolved metals. No scale deposits. Efficient use of soap. Moderately Hard 75 - 120 Not objectionable for most purposes Requires somewhat more soap for cleaning. Above 100 mg/L will deposit significant scale in boilers. Hard 120 - 200 Considerable scale buildup and staining. Generally softened if >200 mg/L. Very Hard >200 Requires softening for household or commercial use.

In industrial usage, hardness is sometimes expressed as grains/gallon or gpg. The conversion between gpg and mg/L is shown in Figure 3.5.

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### Responses

• Mustafa Negassi
What is multiplication factor in water treatment?
10 months ago