CHAPTER 2 SYSTEMS AND THEIR PROPERTIES
2.3 SOMEBASICPROPERTIES ANDTHEIRMEASUREMENT 37
gravitational force on a weight of known mass. A modern balance (strictly speaking a
scale) incorporates a strain gauge or comparable device to directly measure the gravita-
tional force on the unknown mass; this type must be calibrated with known masses. For the
most accurate measurements, we must take into account the effect of the buoyancy of the
body and the calibration masses in air. The accuracy of the calibration masses should be
traceable to a national standard kilogram (which in the United States is maintained at the
National Institute of Standards and Technology, formerly the National Bureau of Standards,
in Gaithersburg, Maryland) and ultimately to the international prototype of the kilogram
located at the International Bureau of Weights and Measures in S`evres, France.
From the measured mass of a sample of a pure substance, we can calculate the amount
of substance (called simply theamountin this book). The SI base unit for amount is the
mole (Sec.1.1.1). Chemists are familiar with the fact that, although the mole is a counting
unit, an amount in moles is measured not by counting but by weighing. This is possible
because one mole is defined as the amount of atoms in exactly 12 grams of carbon-12, the
most abundant isotope of carbon (AppendixA). One mole of a substance has a mass ofMr
grams, whereMris therelative molecular mass(or molecular weight) of the substance, a
dimensionless quantity.
A quantity related to molecular weight is themolar massof a substance, defined as the
mass divided by the amount:
Molar mass DM
def
Dm
n(2.3.1)
(The symbolMfor molar mass is an exception to the rule given on page 29 that a subscript
m is used to indicate a molar quantity.) The numerical value of the molar mass expressed
in units of g mol ^1 is equal to the relative molecular mass:
M=g mol ^1 DMr (2.3.2)2.3.2 Volume
We commonly measure liquid volumes with precision volumetric glassware such as burets,
pipets, and volumetric flasks. The National Institute of Standards and Technology in the
United States has established specifications for “Class A” glassware; two examples are listed
in Table2.2on the next page. We may accurately determine the volume of a vessel at one
temperature from the mass of a liquid of known density, such as water, that fills the vessel
at this temperature.
The SI unit of volume is the cubic meter, but chemists commonly express volumes in
units of liters and milliliters. Theliteris defined as one cubic decimeter (Table1.3). One
cubic meter is the same as 103 liters and 106 milliliters. Themilliliteris identical to the
cubic centimeter.
Before 1964, the liter had a different definition: it was the volume of 1 kilogram of
water at3:98C, the temperature of maximum density. This definition made one liter
equal to1:000028dm^3. Thus, a numerical value of volume (or density) reported before
1964 and based on the liter as then defined may need a small correction in order to be
consistent with the present definition of the liter.