Answer:
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Step-by-step explanation:
Substance Density (g/mL or g/cm3)
water 1.0
gold 19.3
mercury 13.6
air 0.0012
cork 0.22–0.26
aluminum 2.7
iron 7.87
Because of how it is defined, density can act as a conversion factor for switching between units of mass and volume. For example, suppose you have a sample of aluminum that has a volume of 7.88 cm3. How can you determine what mass of aluminum you have without measuring it? You can use the volume to calculate it. If you multiply the given volume by the known density (from Table 1 “Densities of Some Common Substances”), the volume units will cancel and leave you with mass units, telling you the mass of the sample:
7.88 cm3 × 2.7 g/cm3 = 21 g of aluminum
where we have limited our answer to two significant figures.
Example 1
What is the mass of 44.6 mL of mercury?
Solution
Use the density from Table 1 “Densities of Some Common Substances” as a conversion factor to go from volume to mass:
44.6 mL × 13.6 g/mL = 607 g
The mass of the mercury is 607 g.
Test Yourself
What is the mass of 25.0 cm3 of iron?
Answer
197 g
Density can also be used as a conversion factor to convert mass to volume—but care must be taken. We have already demonstrated that the number that goes with density normally goes in the numerator when density is written as a fraction. Take the density of gold, for example:
d = 19.3 g/1 mL
Although this was not previously pointed out, it can be assumed that there is a 1 in the denominator:
That is, the density value tells us that we have 19.3 grams for every 1 milliliter of volume, and the 1 is an exact number. When we want to use density to convert from mass to volume, the numerator and denominator of density need to be switched—that is, we must take the reciprocal of the density. In so doing, we move not only the units but also the numbers:
1/d = 1mL/19.3g
This reciprocal density is still a useful conversion factor, but now the mass unit will cancel and the volume unit will be introduced. Thus, if we want to know the volume of 45.9 g of gold, we would set up the conversion as follows:
45.9 g x 1mL/19.3g = 2.38 mL
1. Give at least three possible units for density.
2. A sample of iron has a volume of 48.2 cm3. What is its mass?
3. The volume of hydrogen used by the Hindenburg, the German airship that exploded in New Jersey in 1937, was 2.000 × 108 L. If hydrogen gas has a density of 0.0899 g/L, what mass of hydrogen was used by the airship?
4. A typical engagement ring has 0.77 cm3 of gold. What mass of gold is present?
5. What is the volume of 100.0 g of lead if lead has a density of 11.34 g/cm3?
6. What is the volume in liters of 222 g of neon if neon has a density of 0.900 g/L?
7. Which has the greater volume, 100.0 g of iron (d = 7.87 g/cm3) or 75.0 g of gold (d = 19.3 g/cm3)?
Answers
1. g/mL, g/L, and kg/L (answers will vary)
2. 379 g
3. 1.80 × 107 g
4. 15 g
5. 8.818 cm3
6. 247 L
7. The 100.0 g of iron has the greater volume.
