The density of a substance is a physical constant at a given temperature. The density of water changes as temperature changes. Water is more dense at 4°C and 1 atmosphere of pressure and becomes less dense as it freezes. This property of water is important to life on earth. If water became denser as it froze, as most substances do, lakes would freeze from the bottom up and life in would die. Also, as water changes density as its temperature changes, it essentially churns up the water and aids in the movement of oxygen, carbon dioxide, food, and materials in the oceans. Temperature (°C/°F)
Density (g/cm3)
100/212
0.9584
60/140
0.9832
25/77
0.9970
4/39.2
1.000
0/32
0.9998
−10/14
0.9981
−30/−22
0.9839 Conversion using density is an important
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What is the mass of a 22.3 cm3 sample? Let’s rearrange the density equation to solve for mass: d= mass volume
⇒d×volume=mass⇒22.59 g c m 3
×22.3
c m 3
=504g d=massvolume⇒d×volume=mass⇒22.59gcm3×22.3cm3=504g By rearranging the equation, cm3 gets cancelled out, leaving g as a result.
Quick Check: 2.8.b
What is the volume of a 5.98 g sample of sodium chloride? Sodium chloride has a density of 2.16 g/cm3.
3.00 g of a sample was placed in a graduated cylinder with 10.0 mL of water. The volume of the water increased to 12.4 mL. What is the density of the sample?
Challenge question:
The nucleus of a carbon-12 atom is 2.7 x 10−3 pm and has a mass of 1.99 x 10−23 g. What is the density of the nucleus in g/cm3? Assume the nucleus is the shape of the sphere and use the formula v= 4
3
π r 3 v=43 π r3 First let’s find the volume. It will be easier to convert pm to cm before we calculate volume: 2.7×
10
−3 pm×
1×
10
−12
m
1 pm
×
1 cm
1×
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The conversions are simple because they are based on orders of 10. The standard system does not have simple conversions between units. There are exactly 1000 m in 1 km and 1000 L in 1 kL, but if we use the standard conversions, we would need to know there are 1760 yards in one mile and there are 128 fl oz in a gallon. The conversion between units allows us to express the same measurement in any unit we want without changing the amount measured and the certainty of the measurement. You will use this same process when we start dealing with chemical reactions. This skill is translatable in any science and engineering class you may