Calculating Daily Bleaching Powder for Water Disinfection

This solution explains the step-by-step calculation to determine the amount of bleaching powder needed for disinfecting a specific volume of water daily, given the chlorine dosage and the strength of the bleaching powder.

Understanding the Problem Parameters

• Water Volume: The total amount of water to be disinfected per day is 2 million liters. This can be written as $2 \times 10^6$ liters.
• Chlorine Dosage: The required concentration of chlorine in the water is 1 part per million (ppm). This means 1 mg of chlorine is needed for every liter of water.
• Bleaching Powder Strength: The bleaching powder available contains only 40% of available chlorine. The rest is inert material.

Step 1: Calculate the Total Chlorine Required

First, we need to find out how much pure chlorine is needed for the given volume of water.

• Since the dosage is 1 ppm, this translates to 1 mg of chlorine per liter of water.
• Total chlorine required = Dosage $\times$ Volume of water
• Total chlorine required = $1 \frac{\text{mg chlorine}}{\text{L water}} \times (2 \times 10^6 \text{ L water})$
• Total chlorine required = $2 \times 10^6$ mg of chlorine.

Step 2: Convert Chlorine Requirement to Kilograms

The requirement is currently in milligrams, which we need to convert to kilograms for practical measurement.

• We know that 1 kg = 1,000 grams, and 1 gram = 1,000 milligrams.
• Therefore, 1 kg = $1,000 \times 1,000$ mg = $10^6$ mg.
• So, the total chlorine required in kg is:
• Chlorine required (kg) = $\frac{2 \times 10^6 \text{ mg}}{10^6 \text{ mg/kg}}$
• Chlorine required (kg) = 2 kg.

This means we need 2 kg of pure (available) chlorine per day.

Step 3: Calculate the Amount of Bleaching Powder Needed

Bleaching powder is not pure chlorine; it only has 40% available chlorine. We need to calculate how much bleaching powder contains the required 2 kg of available chlorine.

• Let 'X' be the quantity of bleaching powder in kg required per day.
• The amount of available chlorine in 'X' kg of bleaching powder is $X \times 40\%$.
• We need this amount to be equal to the required 2 kg of pure chlorine.
• So, $X \times 40\% = 2$ kg
• $X \times \frac{40}{100} = 2$ kg
• $X \times 0.40 = 2$ kg
• To find X, we rearrange the equation:
• $X = \frac{2 \text{ kg}}{0.40}$
• $X = \frac{2}{0.4}$ kg
• $X = 5$ kg.

Conclusion

Therefore, 5 kg of bleaching powder is required per day to disinfect 2 million liters of water at a dosage of 1 ppm chlorine, considering the bleaching powder has 40% available chlorine.