Answer to Question #74785 in General Chemistry for LC

Question

I need helping solving my calculations 1. Nutrition experts recommend that you drink at least 8 cups of water daily. If your local water supply contains 1.00 part fluoride (by mass) per million parts water, how many milligrams of fluoride would you consume daily in your 8 cups of water?
2.Light in a vacuum travels at a speed of 3.00x10^8 m/s. Pluto's average distance from the sun is
3.6 billion miles. How many minutes will it take sunlight to reach Pluto?
3.If the gasoline in a full 20.0-gal tank weighs 116 lb, what is the density of gasoline in g mL^-1?
4. Dry sand has a density of 1.5 g cm^-3. A child's sandbox, measuring 4.0 ft by 5.0 ft, is filled with sand to a depth of 6.0 in. What is the mass of the sand in kg? in lb?

Answer 1

1. Nutrition experts recommend that you drink at least 8 cups of water daily. If your local
water supply contains 1.00 part fluoride (by mass) per million parts water, how many
milligrams of fluoride would you consume daily in your 8 cups of water?
Solution:
The "parts per million" unit is the relative unit of any quantity. In our case, this is a mass.
Therefore, 1.00 parts of fluorine per million parts of water means that 1 mg of fluorine is
contained in 1 kg of water. Next, the average volume of water cups is 250 ml. Since the density
of water is 1 gram per cubic centimeter, one cup holds 250 grams of water, which is four times
less than 1 kg, which means that 250 grams of water will contain and four times less fluorine,
that is 250 g of water will contain 0.25 mg of fluoride. Thus, 1 cup of water contains 0.25 mg of
fluoride. Then 8 cups of water will contain: 0.258=2 mg.
Answer: 2 mg fluoride.
2. Light in a vacuum travels at a speed of 3.00x10^8 m/s. Pluto's average distance from the
sun is 3.6 billion miles. How many minutes will it take sunlight to reach Pluto?
Solution:
First of all, you need to convert miles to meters. 1 mile is 1609.344 m. Then 3.6 billion miles will
be: 3.610 9 1609.344=5793.63810 9 m.
Now we can find the time by dividing the distance in meters by the speed of light:
t=, or 321 minutes 48 seconds, or 5 hours 21 minutes 48 seconds
Answer: 321 minutes 48 seconds
3. If the gasoline in a full 20.0-gal tank weighs 116 lb, what is the density of gasoline in g
mL^-1?
Solution:
The formula for calculating the density is as follows: ρ=
Since we need to get the density in grams per milliliter, it is necessary to translate the units
given in the condition into grams and milliliters. So, 1 gallon is 4.55 liters, then 20 halons will
be: 204.55=91 litres, or 91000 ml.
1 pound is 0.45 kg, then 116 pounds will be: 1160.45=52.2 kg, or 52200 g.
Thus, the density of the liquid is: ρ=
Answer: 0.57
4. Dry sand has a density of 1.5 g cm^-3. A child's sandbox, measuring 4.0 ft by 5.0 ft, is
filled with sand to a depth of 6.0 in. What is the mass of the sand in kg? in lb? 
Solution:
The mass of sand will be according to the formula: m=ρV, where V - the volume of the sandbox,
which is, in turn, according to the formula: V=lengthwidthdepth.

Further, 1 foot is 30.48 centimeters, then 4.0 feet will be: 30.484.0=121.92 cm; 5 feet will be:
530.48=152.4 cm.
Next, 1 inch is 2.54 centimeters, then 6 inches will be: 62.54=15.24 cm.
As a result, the volume of the sandbox will be: V=121.92152.415.24=283168.46 cm 3 .
Given that the density of sand is 1.5 g cm -3 , We find a lot of sand: m=1.5283168.46=424753 g, or
424.753 kg.
1 kg is 2.205 pounds, then the mass found in us in pounds is: 424.7532.205=936.58 lb.
Answer: 424.753 kg; 936.58 lb.