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_ strengthing dose of 1 part(by weight) fluorine per million parts water? The density of water is 1000g/cm^3, or 1000kg/L
To find the amount of sodium fluoride required per year to give the water a tooth-strengthening dose of 1 part fluorine per million parts water, we need to calculate the total amount of water consumed per year and then determine the amount of sodium fluoride needed to achieve the desired concentration.
Step 1: Calculate the total amount of water consumed per year.
Given:
- New York City's population in 1978: 7.9 million people
- Daily per capita consumption of water: 656 liters
Total water consumed per year = (Daily per capita consumption) * (Number of people) * (Days in a year)
Total water consumed per year = 656 liters * 7.9 million * 365 days
Step 2: Calculate the amount of sodium fluoride needed to achieve the desired fluorine concentration.
Given:
- Sodium fluoride contains 45% fluorine by weight.
- Desired fluorine concentration: 1 part per million parts water.
To convert the desired concentration to a weight ratio, we use the density of water:
1 part per million parts water = 1 gram per 1 million grams water = 1 gram per 1 million milliliters water = 1 gram per 1 million liters water.
Weight of sodium fluoride needed per year = Total water consumed per year * (Desired fluorine concentration / 1 million)
Weight of sodium fluoride needed per year = (Total water consumed per year) * (1 / 1 million)
Step 3: Convert the calculated weight to metric tons.
Weight of sodium fluoride needed per year = Weight of sodium fluoride needed per year / (1000 kg/ton) = Weight of sodium fluoride needed per year / 1000 metric tons/kg
Combining the steps and given information, we can calculate the amount of sodium fluoride needed per year:
Total water consumed per year = 656 liters * 7.9 million * 365 days
Total water consumed per year = 1,750,668,000,000 liters
Weight of sodium fluoride needed per year = (Total water consumed per year) * (1 / 1 million)
Weight of sodium fluoride needed per year = 1,750,668,000,000 * (1 / 1,000,000) grams
Converting grams to metric tons:
Weight of sodium fluoride needed per year = 1,750,668,000,000 / 1,000,000 metric tons
Weight of sodium fluoride needed per year = 1,750.668 metric tons
Therefore, approximately 1,750.668 metric tons of sodium fluoride would be required per year to give New York City's 7.9 million people in 1978 a tooth-strengthening dose of 1 part fluorine per million parts water.
To find out how many metric tons of sodium fluoride would be required per year, we can follow these steps:
Step 1: Calculate the total water consumption in liters per year.
Given that the population of New York City in 1978 was 7.9 million people, and the daily per capita consumption of water was 656 liters, we can calculate the total water consumption per year.
Total Water Consumption = Daily Per Capita Consumption * Population * 365
Total Water Consumption = 656 liters * 7.9 million * 365
Total Water Consumption = 186,116,400,000 liters
Step 2: Calculate the total weight of water consumed in kilograms per year.
Total Water Weight = Total Water Consumption * Density of Water
Total Water Weight = 186,116,400,000 liters * 1000 kg/L
Total Water Weight = 186,116,400,000,000 kg
Step 3: Calculate the weight of fluorine needed per year.
To achieve a tooth-strengthening dose of 1 part fluorine per million parts water, we need to find the weight of fluorine required for 1 million parts water.
Weight of Fluorine = Total Water Weight / 1 million
Step 4: Calculate the weight of sodium fluoride needed per year.
As stated, sodium fluoride contains 45% fluorine by weight. So, we can calculate the weight of sodium fluoride required.
Weight of Sodium Fluoride = Weight of Fluorine / (Fluorine % in Sodium Fluoride)
Weight of Sodium Fluoride = Weight of Fluorine / (45/100)
Weight of Sodium Fluoride = Weight of Fluorine / 0.45
Step 5: Convert the weight of sodium fluoride to metric tons.
Since 1 metric ton is equal to 1000 kilograms, we can calculate the amount of sodium fluoride required in metric tons.
Weight of Sodium Fluoride (in metric tons) = Weight of Sodium Fluoride / 1000
By following these steps, you can find the required amount of sodium fluoride in metric tons per year to achieve the desired tooth-strengthening dose of 1 part fluorine per million parts water.