The most commonly used derived units are those of volume. As we have already seen, calculation of the volume of an object requires that a length be cubed or that three lengths be multiplied together. Thus the SI unit of volume is the cubic meterThe SI unit for distance or length. (m3). This is rather large for use in the chemical laboratory, and so the cubic decimeter (dm3) or cubic centimeter (cm3, formerly cc) are more commonly used. The relationship between these units and the cubic meter is easily shown:
1 dm = 0.1 m 1 cm = 0.01 m
Cubing both sides of each equation, we have
1 dm3 = 0.1 3 m3 = 0.001 m3 = 10–3 m3
1 cm3 = 0.013 m3 = 0.000 001 m3 = 10–6 m3
Note that in the expression dm3 the exponent includes the prefix as well as the baseIn Arrhenius theory, a substance that increases the concentration of hydroxide ions in an aqueous solution. In Bronsted-Lowry theory, a hydrogen-ion (proton) acceptor. In Lewis theory, a species that donates a pair of electrons to form a covalent bond. unit. A cubic decimeter is one-thousandth of a cubic meter, not one-tenth of a cubic meter.
Two other units of volume are commonly encountered in the chemical laboratory — the literA unit of volume equal to a cubic decimeter. (l) and the milliliter (ml — one-thousandth of a liter). The liter was originally defined as the volume of one kilogramThe SI unit for mass. of pure water at the temperatureA physical property that indicates whether one object can transfer thermal energy to another object. of its maximum densityThe ratio of the mass of a sample of a material to its volume. (3.98°C) but in 1964 the definition was changed. The liter is now exactly one-thousandth of a cubic meter, that is, 1 dm3. A milliliter is therefore exactly 1cm3. Because the new definition of liter altered its volume slightly, it is recommended that the results of highly accurate measurements be reported in the SI unitsThe international system of units (Système International d'Unité) based on seven fundamental units: meter, kilogram, second, ampere, kelvin, candela, mole. cubic decimeters or cubic centimeters, rather than in liters or milliliters. For most situations discussed in this online textbook, however, the units cubic decimeter and liter, and cubic centimeter and milliliter may be used interchangeably. Thus when recording a volume obtained from laboratory glassware calibrated in milliliters, you can just as well write 24.7 cm3 as 24.7 ml.