How many milligrams of sodium fluoride must be dissolved in 500 mL of water to make 0.05 %(w /

How many milligrams of sodium fluoride must be dissolved in...

Key Concepts

Unit Conversion

Unit conversion is essential in these calculations to ensure consistency across all measurements. This includes converting between mass units such as grams and milligrams, which is particularly important when the final answer is required in a different unit of measure than that initially used in the calculation.

Weight Percent Concentration

This concept defines the ratio of the mass of the solute to the total mass of the solution, expressed as a percentage. It is crucial in determining how much of a substance must be added to a solvent to achieve a desired concentration, and it emphasizes that the concentration is based on mass rather than volume.

Density of Solvent

In many solution preparation problems, particularly those involving water, it's assumed that the density is approximately 1 gram per milliliter. This assumption simplifies the conversion from volume (mL) to mass (g) when calculating the total mass of the solvent, which is needed to accurately determine the mass of the solute for a given weight percent solution.

Transcript

00:01 So for this question, we're told that our target concentration of fluorine in the water is one hearts per million.

00:10 So that would be one gram of fluorine per one million grams of water.

00:15 So we can write one gram fluorine over 10 to 6 grams of water.

00:18 So one gram of pure water is equal to 1 millimeter since the density of water is 1 grams per millimeter.

00:25 So we can write that our target concentration is 1 gram of fluorine per 10.

00:32 10 to the 6 milliliters of water.

00:34 So that's what we want to get.

00:37 So we're told that each day, one person drinks 150 gallons of water.

00:45 There are 50 ,000 people in the city.

00:49 So we get set of dimensional analysis using the conversion factors we're given.

00:54 We want to find the mass in kilograms of sodium fluoride that this city consumes in a year.

01:02 So therefore, you write 150 gallons of water per day per person, multiply by 50 ,000 people.

01:12 And then we cancel out the units for people on top and bottom.

01:16 And then we convert gallons to liters using one gallon to go to 3 .79 liters.

01:22 So gallons cancel.

01:25 And then convert liters to milliliters.

01:28 And then we use the target concentration to convert from miller's water to mass of the fluorine.

01:39 And then the mass fluorine is in grams.

01:42 So we also have to convert from grams to kilograms.

01:47 And we have the same units on top and bottom and they cancel.

01:50 So this is the daily consumption per person and we want the yearly consumption.

01:55 So this is our 365 days in a year...

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