Hardness of Water
Types, Degree of Hardness & Calculations | Chemistry
1. What is Hard Water?
Water that does not produce lather easily with soap is called Hard Water. This hardness is caused by the presence of dissolved bicarbonates, chlorides, and sulfates of Calcium ($Ca^{2+}$) and Magnesium ($Mg^{2+}$).
Soap Reaction: Hard water forms a white precipitate ("scum") with soap (Sodium Stearate), wasting soap.
$2C_{17}H_{35}COONa + M^{2+} \rightarrow (C_{17}H_{35}COO)_2M \downarrow + 2Na^+$
$2C_{17}H_{35}COONa + M^{2+} \rightarrow (C_{17}H_{35}COO)_2M \downarrow + 2Na^+$
2. Types of Hardness
| Type | Caused By | Removal |
|---|---|---|
| Temporary Hardness | Dissolved Bicarbonates of Ca & Mg: $Ca(HCO_3)_2$, $Mg(HCO_3)_2$ |
Simple Boiling or Clark's Method (adding Lime). |
| Permanent Hardness | Dissolved Chlorides & Sulfates of Ca & Mg: $CaCl_2, CaSO_4, MgCl_2, MgSO_4$ |
Treatment with Washing Soda, Calgon's method, or Ion Exchange method. |
3. Degree of Hardness
The degree of hardness is defined as the number of parts by mass of calcium carbonate ($\text{CaCO}_3$) equivalent to the hardness-causing salts present in one million ($10^6$) parts of water.
Why $\text{CaCO}_3$?
- Its Molecular Weight is exactly 100, making calculations easy.
- It is the most common insoluble precipitate formed in water treatment.
$$ \text{Mass of } CaCO_3 \text{ Eq} = \frac{\text{Mass of Salt} \times 100}{\text{Molar Mass of Salt}} $$
Common Units of Hardness
- ppm (parts per million): Parts of $\text{CaCO}_3$ eq per $10^6$ parts water.
- Degree Clark ($^\circ\text{Cl}$): Parts of $\text{CaCO}_3$ eq per 70,000 parts water.
- Degree French ($^\circ\text{Fr}$): Parts of $\text{CaCO}_3$ eq per $10^5$ parts water.
Relation: $1 \text{ ppm} = 1 \text{ mg/L} = 0.1 ^\circ\text{Fr} = 0.07 ^\circ\text{Cl}$
4. Calculation Example
Problem: Water contains 11.1 mg of $\text{CaCl}_2$ per liter. Calculate hardness in ppm.
Solution:
- Molar Mass of $\text{CaCl}_2$ = $40 + 2(35.5) = 111$.
- Convert to $\text{CaCO}_3$ Equivalent: $$ \text{Eq Mass} = 11.1 \times \frac{100}{111} = 10 \text{ mg} $$
- Hardness = 10 mg/L = 10 ppm.
Practice Quiz
Test your stoichiometry skills on Water Hardness.
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