Mass and Volume

After completing this chapter, you should be able to do the following  

The density of a substance is the mass per unit volume of the substance (kg/m, g/cm Ibm/ft, etc.) The specific volume of a substance is the volume occupied by a unit mass of the substance it is the inverse of density. Densities of pure solids and liquids are essentially independent of pressure and vary relatively slightly with temperature. Hie temperature variation may be in either direction the density of liquid water, for example, increases from 0.999868 g/cm at 0°C to 1.00000 g/cm at 3.98°C, and then decreases to 0.95838 g/cm at 100°C. Densities of many pure compounds, solutions, and mixtures may be found in standard references (such as Perry s Chemical Engineers Handbook pp. 2-7 through 2-47 and 2-91 through 2-120). Methods of estimating densities of gases and mixtures of liquids are given in Chapter 5 of this book. 

The density of a substance can be used as a conversion factor to relate the mass and the volume of a quantity of the substance. For example, the density of carbon tetrachloride is 1.595 g/cm the mass of 20.0 cm of CCLt is therefore 

The specific gravity of a substance is the ratio of the density p of the substance to the density Pref of a reference substance at a specific condition  

The reference most commonly used for solids and liquids is water at 4.0 C. which has the following density  

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A general prerequisite for the existence of a stable interface between two phases is that the free energy of formation of the interface be positive were it negative or zero, fluctuations would lead to complete dispersion of one phase in another. As implied, thermodynamics constitutes an important discipline within the general subject. It is one in which surface area joins the usual extensive quantities of mass and volume and in which surface tension and surface composition join the usual intensive quantities of pressure, temperature, and bulk composition. The thermodynamic functions of free energy, enthalpy and entropy can be defined for an interface as well as for a bulk portion of matter. Chapters II and ni are based on a rich history of thermodynamic studies of the liquid interface. The phase behavior of liquid films enters in Chapter IV, and the electrical potential and charge are added as thermodynamic variables in Chapter V. 

There are a few basic numerical and experimental tools with which you must be familiar. Fundamental measurements in analytical chemistry, such as mass and volume, use base SI units, such as the kilogram (kg) and the liter (L). Other units, such as power, are defined in terms of these base units. When reporting measurements, we must be careful to include only those digits that are significant and to maintain the uncertainty implied by these significant figures when transforming measurements into results. 

Commercially available concentrated hydrochloric acid is 37.0% w/w HCl. Its density is 1.18 g/mL. Using this information calculate (a) the molarity of concentrated HCl, and (b) the mass and volume (in milliliters) of solution containing 0.315 mol of HCl. 

In steady-state conditions, the mass and volume flow are constant through the fan and duct. If the duct consists of branches of different cross-sectional area A then... 

The properties used to identify a substance must be intensive that is, they must be independent of amount The fact that a sample weighs 4.02 g or has a volume of 229 mL tells us nothing about its identity mass and volume are extensive properties that is, they depend on amount. Beyond that substances may be identified on the basis of their—... 

Note that even though mass and volume are extensive properties, the ratio of mass to volume is intensive. Samples of copper weighing 1.00 g, 10.5 g, 264 g,... all have the same density, 8.94 g/mL at 25°C. 

Density can be found in a straightforward way by measuring, independently, the mass and volume of a sample (Example 1.5). 

In a practical sense, density can be treated as a conversion factor to relate mass and volume. Knowing that mercury has a density of 13.6 g/mL, we can calculate the mass of 2.6 mL of mercury ... 

Unlike mass and volume, density does not vary with the amount of a substance. Notice in Figure 1-20 that all the corks float, regardless of their sizes. Notice also that all the pieces of lead sink, regardless of their sizes. Dividing a sample into portions changes the mass and volume of each portion but leaves the density unchanged. A property that depends on amount is called extensive. Mass and volume are two examples of extensive properties. A property that is independent of amount is called intensive. Density and temperature are intensive properties. 

Mass and volume often can be measured easily, and density is then calculated using Equation. The equation can also be rearranged to find an objects volume or mass, as Example illustrates. 

Identify a process to solve the problem. The question asks about the volume of one silver atom. Mass and volume are related through density p — mj V. From this equation, we can calculate the total volume of the silver atoms. The problem also gives the total number of silver atoms transferred from the wire to the spoon. The volume of a single atom is the total volume divided by the number of atoms. Oftentimes, a flow chart helps to summarize the process ... 

The chemicai formuia identifies the ions that are present in the finai soiution. The formula also tells us how many moles of each ion are present in one moie of the sait. Use mass, molar mass, and volume to calculate molarity. 

We have mass and volume information for the stock solution, so we use Equations and ... 

First, we must identify the chemistry. This is an acid-base titration in which hydrogen phthalate anions (the acid) react with OH (the base). We use the molar equality of acid and base at the stoichiometric point together with the equations that link moles with mass and volume. 

The overall molarity of NaOH can be calculated from mass, molar mass, and volume ... 

Measure the mass and volume of several different objects. 

Calculate the density of objects by using their measured mass and volume. 

Using Numbers Use the mass and volume data to calculate the densities of water,... 

By measuring the mass and volume of blocks of wood, can the identity of the wood be determined ... 

On the following day, record the mass and volume of the ice as soon as it is removed from the freezer. 

Avogadro s number is the number of particles (atoms, molecules,. or formula units) that are in a mole of a substance. In this lab, you will relate a common object to the concept of Avogadro s number by finding the mass and volume of one mole of the object. 

Compare the mass and volume of a mole of split peas to the masses and volumes of atoms and compounds. 

In the lab, you changed units of mass and volume to moles. Think of the world s monetary systems. Why is it important to be able to change from one unit to another if you are traveling in a foreign country ... 

The state (or behaviour) of a system is described by variables or properties which may be classified as (a) extensive properties such as mass, volume, kinetic energy and (b) intensive properties which are independent of system size, e.g., pressure, temperature, concentration. An extensive property can be treated like an intensive property by specifying that it refers to a unit amount of the substance concerned. Thus, mass and volume are extensive properties, but density, which is mass per unit volume, and specific volume, which is volume per unit mass, are intensive properties. In a similar way, specific heat is an intensive property, whereas heat capacity is an extensive property. 

It is common to achieve accuracies of 1 part in 105 in using equation (1.1) with pycnometers as small as 5 cm3 and routine measurements can achieve 1 part in 104. However the main sources of error in assigning density to a particular compound in a particular state arise from factors other than the measurment of mass and volume. See Section 1.4.1... 

In doing numerical density problems, you may always use the equation d = m/V or the same equation rearranged into the forms V = m/d or m = dV. You are often given two of these quantities and asked for the third. You will use the equation d = m/V if you are given mass and volume, but if you are given density and either of the others, you probably should use the factor-label method. That way, you need not manipulate the equation and then substitute you can solve immediately. 

The three states are alike in that they all exhibit definite mass and volume under a given set of conditions. All consist of some combination of atoms, molecules or ions. The differences are stated above. Additional differences occur in their relative densities ... 

Mass and volume relations with emphasis on the mole concept, including empirical formulas and limiting reactants... 

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