Basic principle IFirst classDr. Arkan Jasim Hadi

CHAPTER 2

MOLES, DENSITY,

AND CONCENTRATION

2.1 The Mole43

2.2 Density48

2.3 Specific Gravity51

2.4 Flow Rate56

2.5 Mole Fraction and Mass (Weight) Fraction57

2.6 Analyses of Multicomponent Solutions and Mixtures59

2.7 Concentration62

2.1 The Mole

What is a mole? For our purposes we say that a mole is a certain amount of material corresponding to a specified number of molecules, atoms, electrons, or any other specified types of particles.

One important calculation you should become skilled at is to convert the number of moles to mass and the mass to moles. To do this you make use of the molecular weight—the mass per mole:

EXAMPLE 2.2 Use of Molecular Weights to Convert Mass to Moles

If a bucket holds 2.00 lb of NaOH, how many

(a)Pound moles of NaOH does it contain?

(b)Gram moles of NaOH does it contain?

Solution

You want to convert pounds to pound moles, and then convert respective values to the SI system of units.

Look up the molecular weight of NaOH, or calculate it from the atomic weights. It is 40.0.

2.2 Density

Density is the ratio of mass per unit volume, as for example, kg/m3 or lb/ft3. Density has both a numerical value and units. To determine the density of a substance, you must find both its volume and its mass. Densities for liquids and solids do not change significantly at ordinary conditions with pressure, but they do change with temperature, as shown in Figure 2.1. Usually we will ignore the effect of temperature on liquid density. Specific volume is the inverse of density, such as cm3/g or ft3/1b. Molar density is the number of moles divided by the volume.

What can you do with density? You use it to determine the volume of a given mass, or the mass of a given volume of material.

A homogeneous mixture of two or more components, whether solid, liquid, or gaseous, is called a solution. Solutions have variable composition while pure sub-stances do not. That is, the relative amounts of the various components in a solution can vary. Thus, air, salt water, and 16-carat gold each are solutions. For some solutions, to calculate the density of the solution, you can make a linear combination of the individual components by adding the respective masses and volumes, and then dividing:

2.3 Specific Gravity

Specific gravity is commonly thought of as a dimensionless ratio. Actually, it should be considered as the ratio of two densitiesthat of the substance of interest, A, to that of a reference substance- each of which has associated units. In symbols:

The reference substance for liquids and solids normally is water. Thus, the specific gravity is the ratio of the density of the substance in question to the density of water, which is 1.000 g/cm3, 1000 kg/m3, or 62.43 lb/ft3 at 4°C. The specific gravity of gases frequently is referred to air, but may be referred to other gases. We will explain what to do in Chapter 13.

You may be acquainted with the fact that in the petroleum industry the specific gravity of petroleum products is often reported in terms of a hydrometer scale called °API. The equation for the API scale is

The volume and therefore the density of petroleum products vary with temperature, and the petroleum industry has established 60°F as the standard temperature for volume and API gravity.

Many other specialized systems of measuring density and specific gravity such as Baume (°Be) exist.

The Baumé (°Be) scale is a pair of hydrometer scales developed by French pharmacist Antoine Baumé in 1768 to measure density of various liquids.

For liquids more dense than water:

For liquids less dense than water:

2.4 Flow Rate

For continuous processes the flow rate of a process stream is the rate at which material is transported through a pipe. In this book we usually use an overlay dot to denote a rate except for the volumetric flow rate F. The mass flow rate () of a process steam is the mass (m) transported through a line per unit time (t).

The volumetric flow rate (F) of a process stream is the volume (V) transported through a line per unit time.

The molar flow (n) rate of a process stream is the number of moles (n) of a substance transported through a line per unit time.

Use any consistent units in your calculation.

2.5 Mole Fraction and Mass (Weight) Fraction

Mole fraction is simply the number of moles of a particular compound in a mixture or solution divided by the total number of moles in the mixture or solution. This definition holds for gases, liquids, and solids.

Similarly, the mass (weight) fraction is nothing more than the mass (weight) of the compound divided by the total mass (weight) of all of the compounds in the mixture or solution. Although the mass fraction is the correct word, by custom ordinary engineering usage employs the term weight fraction. Mathematically, these ideas can be expressed as

2.6 Analyses of Multicomponent

Solutions and Mixtures

Some confusion often exists when you are presented with an analysis of a solution or mixture because you may be uncertain as to whether the numbers presented represent mass (weight) fraction or mole fraction.

In this book, the composition of gases will always be presumed to be given in mole percent or fraction unless specifically stated otherwise.

In this book the composition of liquids and solids will be given by mass (weight) percent or fraction unless otherwise specifically stated, as is the common practice in industry.

As an example, look at Table 2.1 that lists the detailed composition of dry air. Do the values in the column headed "Perpent" designate mass or mole percent? They are mole percent.

2.7 Concentration

Concentration generally refers to the quantity of some substance per unit volume, but other related measures of the amount of material frequently occur, as indicated by some of the terms in the following list of ways to express concentration:

1. Mass per unit volume (lb of solute/ft3 of solution, g of solute/L, lb of solute/barrel, kg of solute/m3). 1 barrel= 119.240471 liter

1. Moles per unit volume (lbmol of solute/ft3 of solution, gmol of solute/L, gmol of solute/cm3).

1. Parts per million (ppm); parts per billion (ppb), a method of expressing the concentration of extremely dilute solutions; ppm is equivalent to a mass (weight) fraction for solids and liquids because the total amount of material is of a much higher order of magnitude than the amount of solute; it is a mole fraction for gases.

1. Parts per million by volume (ppmv) and parts per billion by volume (ppbv)

1. Other methods of expressing concentration with which you may be familiar are molarity (g mol/L), molality (mole solute/kg solvent), and normality (equivalents/L).

Note that the gas concentrations are mostly mass/volume except for the ppm.

Parts per million is a very small number. One ppm is equivalent to 1 inch in 16 miles, or a 1.0 g needle in a metric ton of hay.

API Scale used to report specific gravity of petroleum compounds.

Average molecular weight A pseudo-molecular weight computed by dividing the mass in a mixture or solution by the number of moles in the mixture or solution.

Atomic weight Mass of an atom based on 12C being exactly 12.

Compound A species composed of more than one element.

Concentration Quantity of a material per unit volume.

Density Mass per unit volume of a compound; molar density is the number of moles divided by the volume.

Flow rate Mass, moles, or volume of a material that is in motion divided by unit time.

.Mass fraction Mass of a particular compound in a mixture or solution divide by the total amount of mass present.

Mole fraction Moles of a particular compound in a mixture or solution divided by the total number of moles present.

Molecular weight Mass of a compound per mole.

Parts per million Concentration expressed in terms of millionths of units (ppm) Solution Homogeneous mixture of two or more compounds.

Specific gravity Ratio of the density of a compound to the density of a reference compound.

Specific volume Inverse of the density (volume per unit mass).

Weight fraction the historical term for mass fraction.