Numerical Problems on Water Hardness and Alkalinity

Engineering Chemistry में Water Hardness तथा Alkalinity से संबंधित Numerical Problems परीक्षा की दृष्टि से अत्यंत महत्वपूर्ण हैं। अधिकांश प्रश्न CaCO₃ Equivalence, Hardness Calculation, EDTA Method तथा Alkalinity Determination पर आधारित होते हैं।

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🔹 Basic Concepts

Hardness तथा Alkalinity को सामान्यतः CaCO₃ Equivalent के रूप में व्यक्त किया जाता है।

Molecular Weight of CaCO₃ = 100

Equivalent Weight of CaCO₃ = 50

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🔹 Formula for CaCO₃ Equivalent

CaCO₃ Equivalent = (Amount × 50) / Equivalent Weight

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🔹 Example 1

Calculate the CaCO₃ equivalent of 81 mg/L of NaHCO₃.

Given

• Amount = 81 mg/L
• Molecular Weight of NaHCO₃ = 84
• Equivalent Weight = 84

Solution

CaCO₃ Equivalent = (81 × 50) / 84

= 48.21 mg/L as CaCO₃

Answer = 48.21 ppm

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🔹 Example 2

Calculate the CaCO₃ equivalent of 111 mg/L CaCl₂.

Given

• Amount = 111 mg/L
• Molecular Weight = 111
• Valency = 2
• Equivalent Weight = 55.5

Solution

CaCO₃ Equivalent = (111 × 50) / 55.5

= 100 mg/L as CaCO₃

Answer = 100 ppm

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🔹 Example 3

A water sample contains:

• Ca(HCO₃)₂ = 162 mg/L
• Mg(HCO₃)₂ = 146 mg/L

Calculate Temporary Hardness.

Step 1

Ca(HCO₃)₂ Equivalent

= (162 × 50) / 81

= 100 ppm

Step 2

Mg(HCO₃)₂ Equivalent

= (146 × 50) / 73

= 100 ppm

Total Temporary Hardness

= 100 + 100

= 200 ppm as CaCO₃

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🔹 Example 4

A water sample contains:

• CaSO₄ = 136 mg/L
• MgCl₂ = 95 mg/L

Calculate Permanent Hardness.

CaSO₄ Equivalent

= (136 × 50) / 68

= 100 ppm

MgCl₂ Equivalent

= (95 × 50) / 47.5

= 100 ppm

Total Permanent Hardness

= 100 + 100

= 200 ppm

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🔹 EDTA Numerical

50 mL water sample requires 15 mL EDTA.

1 mL EDTA = 1 mg CaCO₃

Calculation

Hardness = (15 × 1000) / 50

= 300 mg/L

Answer = 300 ppm

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🔹 Alkalinity Numerical

50 mL water sample requires 10 mL N/50 HCl for neutralization.

Formula

Alkalinity = (A × N × 50000) / V

Where:

• A = Acid Volume
• N = Normality
• V = Sample Volume

Calculation

= (10 × 0.02 × 50000) / 50

= 200 ppm as CaCO₃

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🔹 Shortcut Formula Table

Parameter	Formula
CaCO₃ Equivalent	(Amount × 50) / Eq. Wt.
Total Hardness	Sum of all CaCO₃ Equivalents
Temporary Hardness	Bicarbonate Hardness
Permanent Hardness	Total Hardness - Temporary Hardness
Alkalinity	(A × N × 50000)/V

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🔹 Exam Tips

• CaCO₃ Equivalent Formula हमेशा याद रखें।
• Molecular Weight और Equivalent Weight में अंतर समझें।
• Hardness तथा Alkalinity दोनों के Numericals का अभ्यास करें।
• RGPV Exam में 5-10 Marks के Numerical Questions अक्सर पूछे जाते हैं।

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🔹 Frequently Asked Questions

1. CaCO₃ Equivalent क्यों निकाला जाता है?
2. Temporary Hardness कैसे Calculate करते हैं?
3. Permanent Hardness Formula क्या है?
4. EDTA Method में Hardness कैसे निकाली जाती है?
5. Alkalinity का Numerical कैसे Solve करते हैं?

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🔹 Conclusion

Water Hardness तथा Alkalinity के Numerical Problems Engineering Chemistry में अत्यंत महत्वपूर्ण हैं। CaCO₃ Equivalent Method, EDTA Titration तथा Alkalinity Formula के आधार पर अधिकांश समस्याओं का समाधान किया जाता है। इन Numericals का नियमित अभ्यास परीक्षा में अच्छे अंक प्राप्त करने में सहायता करता है।