Objective

In this lesson we will learn the following:

• Types of water hardness.
• Calculating water hardness as CaCO₃.
• Alkalinity determination.
• Lime dosage calculation for hardness removal.
• Calculating feed rates.
• Ion exchange capacity for water treatment.

Lecture

Introduction

Whether a water supply is labelled soft or hard is dependent on the presence of two highly soluble minerals, calcium and magnesium. From a health standpoint, these minerals have no adverse effects and are essential daily nutrients. However, when calcium and magnesium permeate water, they buildup on contact surfaces, possibly plug pipes and damage water heaters, as well as decrease the effectiveness of soaps and detergents. At this point the water is said to be hard.

Let's watch a video that shows you the connection between pH, alkalinity and hardness. This will help you better understand alkalinity and hardness for your state exam.

Water hardness is expressed in one of two units of measurement: ppm of calcium carbonate and grains per gallon (gpg) of calcium carbonate. One ppm means that one unit of calcium carbonate is dissolved in on million units of water. Remember that parts per million (ppm) is equivalent to mg/L. A gpg is used exclusively as a hardness unit and equals approximately 17 mg/L or ppm. Below are the classifications of water hardness:

The two primary constituents that determine the hardness of water are calcium and magnesium. If the concentration of these elements in the water is known, the total hardness of the water can be calculated. To make this calculation, the equivalent weights of calcium, magnesium and calcium carbonate must be known. These equivalents weights are given below:

The Langelier Saturation Index (LSI)

This is a commonly used index in the water utility industry. It determines the CaCO₃ deposition property of the water by caculating saturation pH (pHS). The saturation pH is calculated from total dissolved solids, temperature, alkalinity, and calcium contents of the water. If the pH of the water is equal to the pHS, the water is stable; if it is higher, the water is depositing; and if it is less, the water is corrosive.

The LSI is a gauge of whether a water will precipitate or dissolve calcium carbonate. If the pHS is equal to the actual pH, the water is considered "balanced". This means that calcium carbonate will not be dissolved or precipitated. If the pHS is less than the actual pH (the LSI is a positive number), the water will tend to deposit calcium carbonate and is scale-forming (nonaggressive). If the pHs is greater than the actual pH (the LSI is a negative number), the water is not saturated and will dissolve calcium carbonate (aggressive). In summary;

pHS = pHactual: water is balanced pHS< pHactual: water is scale forming (nonaggressive) pHS> pHactual: water is not scale forming (aggressive)

 

 

It is important to remember that the LSI value is not a quantitative measure of calcium carbonate saturation or corrosion and can be found using the following formula:

LSI = pH - pHS

The Langelier Saturation Index is one of several tools used by water operators for stabilizing water to control both internal corrosion and the deposition of scale. Water supply operators can optimize their water supply systems and identify leakage potentials with the Langelier Index. Experience has shown that a Langelier Index in the range of -1 to +1 has a relatively low corrosion impact on metallic components of the distribution system. Langelier Index values outside this range may result in laundry stains or leaks.

A perfect score on the Langelier Saturation Index (LSI) is zero (0.00). Zero is perfectly balanced water; saturated with the perfect amount of calcium carbonate, and has a stable pH. Being the universal solvent, if water is out of balance, it will naturally try to find its own balance and equilibrium, because it wants to be at 0.00 LSI.  The LSI is basically a way to determine if water is corrosive (negative LSI) or scale-forming (positive LSI). LSI between -0.30 and +0.30 is the widely accepted range, while 0.00 is perfect equilibrium. Water will stop at nothing to find equilibrium...so when it's hungry for calcium, it will aggressively look for it. When the water does not have a readily available source of calcium, corrosion and degradation can occur anywhere in the equipment. Another important thing to remember: water cannot over-saturate itself. It will take only what it can hold, and nothing more.

Example:

Water has a pH of 6.8. The saturation pH (pHS) is found to be 7.3. Does this water have corrosive or scaling tendencies?

LSI = pH - pHS

LSI = 6.8 - 7.3

LSI = -0.5

Since the LSI is negative (-0.5), the water has corrosive tendencies.

If you are not given the saturation pH (pHS), but need to determine it from other variables, you will need to know the following: water's measured pH, temperature, calcium hardness, total alkalinity and total dissolved solids (TDS). All of these are used in determine the saturation pH of the water. We will not go into that much detail here, but if you are curious, this is how it is derived:

To recap, if the LSI is negative, no potential to scale, the water will dissolve CaCO₃. If the LSI is positive, scale can form and CaCO₃ precipitation may occur. If LSI is close to zero, it has borderline scale potential. Water quality or changes in temperature, or evaporation could change the index.

Water Hardness Calculations

Calculating Calcium Hardness as CaCO₃

The hardness, in mg/L as CaCO₃ for any given metallic ion is calculated with the following equation: (Remember to look up the equivalent weights given above to save yourself some time.)

Example:

A water sample has calcium content of 51 mg/L. What is the calcium hardness, expressed as CaCO₃?

Calculating Magnesium Hardness as CaCO₃

To calculate magnesium hardness, use the following equation:

Example:

A water sample has a magnesium content of 24 mg/L. What is the magnesium hardness, expressed as CaCO₃?

Calculating Total Hardness

Calcium and magnesium ions are the primary cause of hardness in water. To find total hardness, we simply add the concentrations of calcium and magnesium ions, expressed in terms of calcium carbonate (CaCO₃):

Total hardness, mg/L as CaCO₃ = calcium hardness, mg/L as CaCO₃ + magnesium hardness, mg/L as CaCO₃

Example:

Determine the total hardness as CaCO₃, of a sample of water that has calcium content of 28 mg/L and magnesium content of 9 mg/L.

The first step is to determine the calcium hardness as CaCO₃:

Now determine the magnesium hardness as CaCO₃:

Now you can determine the total hardness:

Total hardness, mg/L as CaCO₃ = calcium hardness, mg/L as CaCO₃ + magnesium hardness, mg/L as CaCO

Total hardness, mg/L as CaCO₃ = 69.9 mg/L as CaCO₃ + 37.1 mg/L as CaCO₃

Total hardness, mg/L as CaCO₃ = 107 mg/L as CaCO₃

 

 

Calculating Carbonate and Noncarbonate Hardness

As mentioned, total hardness is comprised of calcium and magnesium hardness. Once total hardness has been calculated, it is sometimes used to determine another expression of hardness - carbonate and noncarbonate. When hardness is numerically greater than the sum of bicarbonate and carbonate alkalinity, that amount of hardness equivalent to the total alkalinity (both in units of mg/L as CaCO₃) is referred to as the carbonate hardness; the amount of hardness in excess of this is the noncarbonate hardness. When the hardness is numerically equal to or less than the sum of carbonate and noncarbonate alkalinity, all hardness is carbonate hardness, and noncarbonate hardness is absent. Again, the total hardness is comprised of carbonate hardness and noncarbonate hardness:

Total hardness = carbonate hardness + noncarbonate hardness

When the alkalinity (as CaCO₃) is greater than the total hardness, all the hardness is carbonate hardness:

Total hardness, mg/L as CaCO₃ = carbonate hardness, mg/L as CaCO₃

When the alkalinity (as CaCO₃) is less than the total hardness, then the alkalinity represents carbonate hardness and the balance of the hardness is noncarbonate hardness:

Total hardness, mg/L as CaCO₃ = carbonate hardness, mg/L as CaCO₃ + noncarbonate hardness, mg/L as CaCO₃

When carbonate hardness is represented by the alkalinity:

Total hardness, mg/L as CaCO₃ = alkalinity, mg/L as CaCO₃ + noncarbonate hardness, mg/L as CaCO₃

 Example 1:

A water sample contains 110 mg/L alkalinity as CaCO₃ and 105 mg/L total hardness as CaCO₃. What is the carbonate and noncarbonate hardness of the sample?

Because the alkalinity is greater than the total hardness, all the hardness is carbonate hardness:

Total hardness, mg/L as CaCO₃ = carbonate hardness, mg/L as CaCO₃
105 mg/L as CaCO₃ = carbonate hardness, mg/L as CaCO₃

 

No noncarbonate hardness is present in this water.

Example 2:

The alkalinity of a water sample is 80 mg/L as CaCO₃. If the total hardness of the water sample is 112 mg/L as CaCO₃, what is the carbonate and noncarbonate hardness, in mg/L as CaCO₃?

Alkalinity is less than total hardness; therefore, both carbonate and noncarbonate hardness will be present in the hardness of the sample.

Total hardness, mg/L as CaCO₃ = carbonate hardness, mg/L as CaCO3 + noncarbonate hardness, mg/L as CaCO₃
112 mg/L as CaCO₃ = 80 mg/L as CaCO₃ + noncarbonate hardness, mg/L as CaCO₃
112 mg/L as CaCO₃ - 80 mg/L as CaCO₃= noncarbonate hardness, mg/L as CaCO₃

noncarbonate hardness, mg/L as CaCO₃ = 32 mg/L as CaCO₃

Calculating Hardness Through EDTA Titration

Hardness is most commonly measured by titration with an EDTA solution. A titration involves adding small amounts of a solution to a water sample until the sample changes color. You can titrate a sample for total hardness using a buret or test kit. You can also measure calcium hardness separately from magnesium hardness. Total hardness kits that work best for natural water samples uses ManVer indicators during titration. When performing the hardness test through titration, hardness as mg CaCO₃/L can be determined with the following formula (only when the titration factor is 1.00 of EDTA, otherwise add the titration factor to the numerator (top) portion of the fraction):

Let's watch a video showing how to perform the EDTA titration experiment for hardness determination.

Example:

A 50 mL sample of water requires 23.25 mL of the standardized EDTA solution for complete reaction to occur. Determine the hardness of the water as mg CaCO₃/L.

Alkalinity Determination

Alkalinity is a measure of the capacity of water to neutralize acids. Alkaline compounds in the water, such as bicarbonates, carbonates, and hydroxides, remove hydrogen ion and lower the acidity of the water (which means increased pH). The higher the alkalinity, the greater the capacity of the water to neutralize acids; conversely, the lower the alkalinity, the less the neutralizing capacity. Total alkalinity is determined by measuring the amount of acid needed to bring the sample to a pH of 4.5. At this pH all the alkaline compounds in the sample are "used up.

Let's watch a video showing how to perform the alkalinity test in a water treatment lab.

The alkalinity can be determined with the following formula and recorded as mg/L of CaCO₃.

Example:

A 100 mL sample of water is tested for alkalinity. The normality of the sulfuric acid used for titrating is 0.02N. If 8.2 mL of titrant is used to reach a pH of 4.5, what is the alkalinity of the water, in mg/L as CaCO₃?

At this point you have determined if you have hard or soft water. If you have hard water, let's look at the alternatives available for treatment.

Lime Softening

Chemical precipitation is one of the more common methods used to soften water. The chemicals normally used are lime (calcium hydroxide) and soda ash (sodium bicarbonate). Lime is used to remove chemicals that cause carbonate hardness. Soda ash is used to remove chemicals that cause non-carbonate hardness. The appropriate chemical dosage for various unit processes is typically determined by lab testing, monitoring and historical experience of the plant. Once the chemical dosage is determined, the feed rate can be calculated using the typical feed rate calculation already covered:

Feed rate, lb/day = Chemical dose, mg/L x Flow, MGD x 8.34 lb/gal

Example:

Lab tests indicate that the optimum lime dosage is 180 mg/L. If the flow to be treated is 2.8 MGD, what should the chemical feeder setting be in lb/day and lb/min?

Calculate the feed rate in lb/day:

Feed rate, lb/day = Chemical dose, mg/L x Flow, MGD x 8.34 lb/gal

Feed rate, lb/day = 180 mg/L x 2.8 MGD x 8.34 lb/gal

Feed rate, lb/day = 4203.36 lb/day

Now determine the lb/min setting:

Summary

Whether a water supply is labelled soft or hard is dependent on the presence of two highly soluble minerals, calcium and magnesium. From a health standpoint, these minerals have no adverse effects and are essential daily nutrients. However, when calcium and magnesium permeate water, they buildup on contact surfaces, possibly plug pipes and damage water heaters, as well as decrease the effectiveness of soaps and detergents. At this point the water is said to be hard. Water hardness is expressed in one of two units of measurement: ppm of calcium carbonate and grains per gallon (gpg) of calcium carbonate. One ppm means that one unit of calcium carbonate is dissolved in on million units of water. Remember that parts per million (ppm) is equivalent to mg/L. A gpg is used exclusively as a hardness unit and equals approximately 17 mg/L or ppm. The Langelier Saturation Index is one of several tools used by water operators for stabilizing water to control both internal corrosion and the deposition of scale. The LSI is basically a way to determine if water is corrosive (negative LSI) or scale-forming (positive LSI). LSI between -0.30 and +0.30 is the widely accepted range, while 0.00 is perfect equilibrium. Alkalinity is a measure of the capacity of water to neutralize acids. Alkaline compounds in the water, such as bicarbonates, carbonates, and hydroxides, remove hydrogen ion and lower the acidity of the water (which means increased pH). The higher the alkalinity, the greater the capacity of the water to neutralize acids; conversely, the lower the alkalinity, the less the neutralizing capacity. Total alkalinity is determined by measuring the amount of acid needed to bring the sample to a pH of 4.5. At this pH all the alkaline compounds in the sample are "used up.

Assignment

Complete the math worksheet for this lesson. You must be logged into Canvas to submit this assignment. Make sure you choose the appropriate semester.