Understanding Water Hardness, Softening, and Coal Analysis
Understanding Water Hardness and Treatment
Temporary hardness is caused by dissolved bicarbonates of calcium and magnesium (e.g., Ca(HCO₃)₂ and Mg(HCO₃)₂). It can be removed by boiling the water, which precipitates the bicarbonates as insoluble carbonates. Permanent hardness is caused by dissolved chlorides, sulfates, or nitrates of calcium and magnesium (e.g., CaCl₂, MgSO₄). It cannot be removed by boiling and requires chemical treatment for removal. Hardness is measured in various units:
Milligrams per liter (mg/L) as CaCO₃. Parts per million (ppm), which is equivalent to mg/L.
Grains per gallon (gpg); 1 gpg = 17.1 mg/L as CaCO₃.
Degrees of hardness:
- Clark degree: 1° Clark = 14.3 mg/L as CaCO₃.
- German degree (°dH): 1° dH = 17.8 mg/L as CaCO₃.
- French degree (°fH): 1° fH = 10 mg/L as CaCO₃.
- These units are related as follows:
- 1 mg/L = 1 ppm.
- 1 gpg = 17.1 mg/L.
- 1 Clark degree = 14.3 mg/L.
- 1 German degree (°dH) = 17.8 mg/L.
- 1 French degree (°fH) = 10 mg/L.
- The hardness of water is primarily caused by the presence of divalent metal ions, mainly calcium (Ca²⁺) and magnesium (Mg²⁺). These ions come from the dissolution of minerals such as limestone (CaCO₃), dolomite (CaMg(CO₃)₂), and gypsum (CaSO₄·2H₂O). Other metal ions, like iron (Fe³⁺) and manganese (Mn²⁺), can also contribute to water hardness, though typically to a lesser extent.
Analysis of Water Sample for Hardness
Given:
Mg(HCO₃)₂ = 73 mg/L
Ca(HCO₃)₂ = 84 mg/L
MgCl₂ = 94 mg/L
CaSO₄ = 74 mg/L
CaCl₂ = 85 mg/L
To determine the total, permanent, and temporary hardness, we first convert each concentration to its equivalent CaCO₃ hardness
Temporary Hardness (from bicarbonates): Hardness (mg/L as CaCO₃) = Concentration (mg/L) × 50 / Equivalent weight of the compound
For Mg(HCO₃)₂ and Ca(HCO₃)₂: Mg(HCO₃)₂ = 73 mg/L × 50 / 73 = 50 mg/L as CaCO₃ Ca(HCO₃)₂ = 84 mg/L × 50 / 81 = 51.85 mg/L as CaCO₃
Total temporary hardness: 50 + 51.85 = 101.85 mg/L as CaCO₃
Permanent Hardness (from chlorides and sulfates): MgCl₂ = 94 mg/L × 50 / 47.6 = 98.74 mg/L as CaCO₃ CaSO₄ = 74 mg/L × 50 / 68.05 = 54.35 mg/L as CaCO₃ CaCl₂ = 85 mg/L × 50 / 55.5 = 76.58 mg/L as CaCO₃
Total permanent hardness: 98.74 + 54.35 + 76.58 = 229.67 mg/L as CaCO₃
Total Hardness: Total Hardness = Temporary Hardness + Permanent Hardness = 101.85 + 229.67 = 331.52 mg/L as CaCO₃
Techniques for Water Ion-Exchange Process
Q3: Calculate the hardness of water softened by the zeolite process:
Given:
30,000 liters of hard water were softened.
200 liters of NaCl solution containing 250 g/L for regeneration.
Total amount of NaCl used: 200 L × 250 g/L = 50,000 g
Converting to equivalents: 50,000 g ÷ 58.5 g/mol = 854.7 equivalents
To calculate the reduction in hardness, we need the ion exchange capacity of the zeolite. Typically, zeolite can exchange calcium and magnesium ions for sodium ions on a 1:1 molar basis. For precise calculation, specific details of the ion exchange capacity are required, which are not provided here.
Q4: Ion exchange in water softening works by passing hard water through a resin bed containing sodium ions. The resin captures calcium and magnesium ions and releases sodium ions in return, softening the water. This process effectively removes hardness without significantly changing the volume or pH of the water. The resin is regenerated periodically with a salt (NaCl) solution, which restores its sodium content by displacing the accumulated calcium and magnesium ions.
Lime-Soda and Zeolite Process
Q5: Advantages and disadvantages of using the lime-soda process for water softening:
Advantages:
Effective in reducing both temporary and permanent hardness.
Can also remove iron and manganese.
Cost-effective for large-scale operations.
Disadvantages:
Requires precise control of pH and dosage of chemicals.
Produces a large amount of sludge that needs disposal.
Not suitable for small-scale applications due to operational complexity.
Q6: Calculate the amount of lime and soda required for the treatment of 60,000 liters of water with the following analysis:
Given:
Mg(HCO₃)₂ = 39 ppm
Ca(HCO₃)₂ = 46 ppm
MgSO₄ = 70 ppm
CaSO₄ = 74 ppm
CaCl₂ = 49 ppm
NaCl = 90 ppm
Temporary hardness: Temporary Hardness = (Mg(HCO₃)₂ + Ca(HCO₃)₂) = 39 + 46 = 85 ppm
Non-carbonate hardness: Non-carbonate Hardness = (MgSO₄ + CaSO₄ + CaCl₂) = 70 + 74 + 49 = 193 ppm
Amount of lime (Ca(OH)₂) required: Lime required = Temporary hardness + 2 × Non-carbonate hardness = 85 + 2 × 193 = 85 + 386 = 471 ppm
Amount of soda (Na₂CO₃) required: Soda required = 1.25 × Non-carbonate hardness = 1.25 × 193 = 241.25 ppm
For 60,000 liters: Lime required = 471 × 60,000 / 1,000,000 = 28.26 kg Soda required = 241.25 × 60,000 / 1,000,000 = 14.48 kg
Q7: The zeolite method for water softening involves passing hard water through a bed of synthetic resin (zeolite) that contains sodium ions. As the water flows through the resin, calcium and magnesium ions are exchanged with sodium ions. This exchange effectively removes the hardness ions from the water. The resin is regenerated periodically with a sodium chloride (salt) solution, which replenishes the sodium ions and restores the resin’s softening capacity.
Classification and Analysis of Coal
Q8: Ultimate analysis of coal determines the elemental composition, including carbon (C), hydrogen (H), sulfur (S), nitrogen (N), and oxygen (O). This analysis provides detailed information about the fuel’s chemistry, which is essential for understanding its combustion properties and environmental impact.
Proximate analysis measures the moisture content, volatile matter, ash content, and fixed carbon in coal. This analysis provides a quick assessment of coal quality and is used for routine classification and control. It is less detailed than ultimate analysis but is useful for general characterization of coal.
Q6: Calculate the amount of lime and soda required for the treatment of 60,000 liters of water with the following analysis:
Given:
Mg(HCO₃)₂ = 39 ppm
Ca(HCO₃)₂ = 46 ppm
MgSO₄ = 70 ppm
CaSO₄ = 74 ppm
CaCl₂ = 49 ppm
NaCl = 90 ppm
Temporary hardness: Temporary Hardness = (Mg(HCO₃)₂ + Ca(HCO₃)₂) = 39 + 46 = 85 ppm
Non-carbonate hardness: Non-carbonate Hardness = (MgSO₄ + CaSO₄ + CaCl₂) = 70 + 74 + 49 = 193 ppm
Amount of lime (Ca(OH)₂) required: Lime required = Temporary hardness + 2 × Non-carbonate hardness = 85 + 2 × 193 = 85 + 386 = 471 ppm
Amount of soda (Na₂CO₃) required: Soda required = 1.25 × Non-carbonate hardness = 1.25 × 193 = 241.25 ppm
For 60,000 liters: Lime required = 471 × 60,000 / 1,000,000 = 28.26 kg Soda required = 241.25 × 60,000 / 1,000,000 = 14.48 kg
Q7: The zeolite method for water softening involves passing hard water through a bed of synthetic resin (zeolite) that contains sodium ions. As the water flows through the resin, calcium and magnesium ions are exchanged with sodium ions. This exchange effectively removes the hardness ions from the water. The resin is regenerated periodically with a sodium chloride (salt) solution, which replenishes the sodium ions and restores the resin’s softening capacity.
Classification and Analysis of Coal
Q8: Ultimate analysis of coal determines the elemental composition, including carbon (C), hydrogen (H), sulfur (S), nitrogen (N), and oxygen (O). This analysis provides detailed information about the fuel’s chemistry, which is essential for understanding its combustion properties and environmental impact.
Proximate analysis measures the moisture content, volatile matter, ash content, and fixed carbon in coal. This analysis provides a quick assessment of coal quality and is used for routine classification and control. It is less detailed than ultimate analysis but is useful for general characterization of coal.
Determination of Calorific Value
Q9: Calculate the GCV and NCV of coal having the following composition: C = 82%, H = 5%, O = 4%, S = 3%, N = 3%, and ash = 3%.
Using Dulong’s formula for Gross Calorific Value (GCV):
GCV (kcal/kg) = 0.338 × %C + 1.428 × (%H – %O / 8) + 0.095 × %S
Plugging in the values:
GCV = 0.338 × 82 + 1.428 × (5 – 4 / 8) + 0.095 × 3
GCV = 27.716 + 1.428 × (5 – 0.5) + 0.285
GCV = 27.716 + 1.428 × 4.5 + 0.285
GCV = 27.716 + 6.426 + 0.285
GCV = 34.427 kcal/kg
Now, calculate the Net Calorific Value (NCV):
NCV = GCV – 0.2122 × %H × 9
Assuming the latent heat of vaporization for the moisture produced by hydrogen combustion (approximately 9 times the hydrogen content):
NCV = 34.427 – 0.2122 × 5 × 9
NCV = 34.427 – 0.2122 × 45
NCV = 34.427 – 9.549
NCV = 24.878 kcal/kg
Explain the Definition of Calorific Value of a Fuel
Calorific value is the amount of heat energy produced by the complete combustion of a unit quantity of fuel. It is an important measure of the energy content of fuel.
Gross Calorific Value (GCV), also known as the Higher Heating Value (HHV), is the total heat produced when a fuel is completely burned, including the latent heat of vaporization of water produced during combustion. GCV is calculated assuming that all water vapor produced during combustion is condensed to liquid form, thus releasing its latent heat.Net Calorific Value (NCV), also known as the Lower Heating Value (LHV), is the heat produced excluding the latent heat of vaporization of water. NCV is calculated assuming that the water produced during combustion remains as vapor and does not condense. As a result, NCV is typically lower than GCV because it accounts for the energy lost in vaporizing the water content in the fuel.
NCV = GCV – (Latent Heat of Vaporization × Mass of Water Vapor)