1.3. METHODS OF EXPRESSING TEMPERATURES AND COMPOSITIONS

1.3A. Temperature

There are two temperature scales in common use in the chemical and biological industries. These are degrees Fahrenheit (abbreviated °F) and Celsius (°C). It is often necessary to convert from one scale to the other. Both use the freezing point and boiling point of water at 1 atmosphere pressure as base points. Often temperatures are expressed as absolute degrees K (SI standard) or degrees Rankine (°R) instead of °C or °F. Table 1.3-1 shows the equivalences of the four temperature scales.

Table 1.3-1. Temperature Scales and Equivalents

	Centigrade	Fahrenheit	Kelvin	Rankine	Celsius
Boiling water	100°C	212°F	373.15 K	671.67°R	100°C
Melting ice	0°C	32°F	273.15 K	491.67°R	0°C
Absolute zero	−273.15°C	−459.67°F	0 K	0°R	−273.15°C

The difference between the boiling point of water and melting point of ice at 1 atm is 100°C or 180°F. Thus, a 1.8°F change is equal to a 1°C change. Usually, the value of −273.15°C is rounded to −273.2°C and −459.67°F to −460°F. The following equations can be used to convert from one scale to another:

Equation 1.3-1

Equation 1.3-2

Equation 1.3-3

Equation 1.3-4

1.3B. Mole Units, and Weight or Mass Units

There are many methods used to express compositions in gases, liquids, and solids. One of the most useful is molar units, since chemical reactions and gas laws are simpler to express in terms of molar units. A mole (mol) of a pure substance is defined as the amount of that substance whose mass is numerically equal to its molecular weight. Hence, 1 kg mol of methane CH₄ contains 16.04 kg. Also, 1.0 lb mol contains 16.04 lb_m.

The mole fraction of a particular substance is simply the moles of this substance divided by the total number of moles. In like manner, the weight or mass fraction is the mass of the substance divided by the total mass. These two compositions, which hold for gases, liquids, and solids, can be expressed as follows for component A in a mixture:

Equation 1.3-5

Equation 1.3-6

EXAMPLE 1.3-1. Mole and Mass or Weight Fraction of a Solution A container holds 50 g of water (B) and 50 g of NaOH (A). Calculate the weight fraction and mole fraction of NaOH. Also, calculate the lbm of NaOH (A) and H2O (B). Solution: Taking as a basis for calculation 50 + 50 or 100 g of solution, the following data are calculated: Component G Wt Fraction Mol Wt G Moles Mole Fraction H2O (B) 50.0 18.02 NaOH (A) 50.0 40.0 Total 100.0 1.000   4.03 1.000 Hence, xA = 0.310 and xB = 0.690 and xA + xB = 0.310 + 0.690 = 1.00. Also, wA + wB = 0.500 + 0.500 = 1.00. To calculate the lbm of each component, Appendix A.1 gives the conversion factor of 453.6 g per 1 lbm. Using this, Note that the g of A in the numerator cancels the g of A in the denominator, leaving lbm of A in the numerator. The reader is cautioned to put all units down in an equation and cancel those appearing in the numerator and denominator. In a similar manner we obtain 0.1102 lbm B (0.0500 kg B).

The analyses of solids and liquids are usually given as weight or mass fraction or weight percent, and gases as mole fraction or percent. Unless otherwise stated, analyses of solids and liquids will be assumed to be weight (mass) fraction or percent, and of gases to be mole fraction or percent.

1.3C. Concentration Units for Liquids

In general, when one liquid is mixed with another miscible liquid, the volumes are not additive. Hence, compositions of liquids are usually not expressed as volume percent of a component but as weight or mole percent. Another convenient way to express concentrations of components in a solution is molarity, which is defined as g mol of a component per liter of solution. Other methods used are kg/m³, g/liter, g/cm³, lb mol/cu ft, lb_m/cu ft, and lb_m/gallon. All these concentrations depend on temperature, so the temperature must be specified.

The most common method of expressing total concentration per unit volume is density, kg/m³, g/cm³, or lb_m/ft³. For example, the density of water at 277.2 K (4°C) is 1000 kg/m³, or 62.43 lb_m/ft³. Sometimes the density of a solution is expressed as specific gravity, which is defined as the density of the solution at its given temperature divided by the density of a reference substance at its temperature. If the reference substance is water at 277.2 K, the specific gravity and density of the substance are numerically equal.