New York city's has 7.9million people in 1978 had a daily per Capita consumption of 656 liter's of water.How many metric tonnes (103) of sodium fluoride (45% fluorine by weight) would be required per year to give this water a fluorine per million parts water? The density of water is 1.000g/cm^3,or 1.000kg/l.
To calculate the amount of sodium fluoride required to give the water a fluorine concentration per million parts water (ppm), we need to consider the daily per capita consumption of water and the population of New York City.
Step 1: Calculate the total water consumption per day in liters:
Total Water Consumption = Daily per Capita Consumption * Population
Total Water Consumption = 656 liters/person/day * 7.9 million people
Step 2: Calculate the total water consumption per year in liters:
Total Water Consumption per Year = Total Water Consumption * 365 days
Step 3: Convert water consumption to kilograms:
Total Water Consumption (kg) = Total Water Consumption (liters) * Density of Water
Total Water Consumption (kg) = Total Water Consumption (liters) * 1.000 kg/l
Step 4: Calculate the amount of fluorine required in metric tonnes:
Fluorine (kg) = Total Water Consumption (kg) * Fluorine concentration (ppm) / 1,000,000
Fluorine (kg) = Total Water Consumption (kg) * 1 ppm / 1,000,000
Step 5: Convert fluorine to metric tonnes:
Fluorine (metric tonnes) = Fluorine (kg) / 1000
Now we can calculate the amount of sodium fluoride needed:
Step 6: Calculate the required amount of sodium fluoride (in metric tonnes) at 45% fluorine by weight:
Sodium Fluoride (metric tonnes) = Fluorine (metric tonnes) / (Fluorine content in sodium fluoride)
Since sodium fluoride is 45% fluorine by weight, we need to account for the difference when calculating the required amount of sodium fluoride:
Sodium Fluoride (metric tonnes) = Fluorine (metric tonnes) / (0.45)
Note: Make sure to multiply the population number by 1,000,000 since it is given in millions.
Let's calculate:
Total Water Consumption = 656 liters/person/day * 7.9 million people
Total Water Consumption = 5,182,400,000 liters/day
Total Water Consumption per Year = 5,182,400,000 liters/day * 365 days
Total Water Consumption per Year = 1,890,016,000,000 liters/year
Total Water Consumption (kg) = 1,890,016,000,000 liters/year * 1.000 kg/l
Total Water Consumption (kg) = 1,890,016,000,000 kg/year
Fluorine (kg) = 1,890,016,000,000 kg/year * 1 ppm / 1,000,000
Fluorine (kg) = 1,890,016 kg/year
Fluorine (metric tonnes) = 1,890,016 kg/year / 1000
Fluorine (metric tonnes) = 1890.016 metric tonnes/year
Sodium Fluoride (metric tonnes) = 1890.016 metric tonnes/year / 0.45
Sodium Fluoride (metric tonnes) ≈ 4,200.04 metric tonnes/year
Therefore, approximately 4,200.04 metric tonnes of sodium fluoride would be required per year to give the water a fluorine concentration per million parts water.
To calculate the amount of sodium fluoride required per year, we can follow these steps:
Step 1: Calculate the total water consumption per year in liters.
Given:
- Daily per capita consumption of water = 656 liters
- Population of New York City in 1978 = 7.9 million
Total water consumption per year = Daily consumption per capita * Population * 365 days
Total water consumption per year = 656 liters * 7.9 million * 365 days
Step 2: Convert the total water consumption into kilograms.
Given:
- Density of water = 1.000 kg/liter
Total water consumption per year in kilograms = Total water consumption per year * Density of water
Total water consumption per year in kilograms = (656 liters * 7.9 million * 365 days) * 1.000 kg/liter
Step 3: Calculate the amount of fluorine required per year.
Given:
- Sodium fluoride contains 45% fluorine by weight
Amount of fluorine required per year = Total water consumption per year in kilograms * (Fluorine % / 100)
Amount of fluorine required per year = Total water consumption per year in kilograms * (45% / 100)
Step 4: Convert the amount of fluorine required into metric tonnes (103).
1 metric tonne = 1000 kilograms
Amount of sodium fluoride required per year in metric tonnes = Amount of fluorine required per year / 1000
By following these steps, you should be able to calculate the required amount of sodium fluoride per year to give the water a fluorine concentration in parts per million.