New York city's 7.9 million people in 1978 had a daily per Capita consumption of 656 liters of water. How many metric tons (103 kg) of sodium fluoride (45% fluorine by weight) would be required per year to give this water a tooth strenghting dose of 1 part (by weight) fluorine per million parts water? The density of water is 1000 g/cm3, or 1000 kg/L

1 answer

To find the amount of sodium fluoride required per year, we need to calculate the total consumption of water in liters per year and then convert it to metric tons.

Given:
Population in 1978 = 7.9 million people
Daily per capita consumption of water = 656 liters

Total water consumption per day = Population × Daily per capita consumption
Total water consumption per day = 7.9 million × 656 liters
Total water consumption per day = 5,164,000,000 liters

Total water consumption per year = Total water consumption per day × 365 days
Total water consumption per year = 5,164,000,000 liters × 365
Total water consumption per year = 1,884,760,000,000 liters

Now, we need to calculate the amount of sodium fluoride required to achieve 1 part fluorine per million parts of water.

1 part fluorine per million parts of water means the concentration of fluorine is 1 ppm.
In other words, we need 1 gram of fluorine for every 1 million grams (or liters) of water.

Total amount of fluorine required per year = Total water consumption per year × Fluorine concentration in ppm
Total amount of fluorine required per year = 1,884,760,000,000 liters × 1 ppm (1 gram per million grams)
Total amount of fluorine required per year = 1,884,760,000,000 grams

Since the density of water is 1000 kg/L, we can convert the amount of fluorine required to metric tons.

Total amount of fluorine required per year (in metric tons) = Total amount of fluorine required per year (in grams) / 1,000,000 (conversion factor)
Total amount of fluorine required per year (in metric tons) = 1,884,760,000,000 grams / 1,000,000
Total amount of fluorine required per year (in metric tons) = 1,884,760 metric tons

To calculate the amount of sodium fluoride required, we need to consider that sodium fluoride is 45% fluorine by weight.

Amount of sodium fluoride required per year (in metric tons) = Total amount of fluorine required per year (in metric tons) / Fluorine content in sodium fluoride
Amount of sodium fluoride required per year (in metric tons) = 1,884,760 metric tons / 0.45
Amount of sodium fluoride required per year (in metric tons) = 4,188,244 metric tons

Therefore, approximately 4,188,244 metric tons of sodium fluoride would be required per year to give New York City's 7.9 million people a tooth-strengthening dose of 1 part fluorine per million parts water.