Units Volume and Density

There are many quantities, snch as volume and density, that require units not included in the base SI units. In these cases, we must combine base units to derive appropriate units for the quantity. 

Density is the ratio of mass to volume. Oil floats on water, for example, because, in addition to not mixing with water, oil has a lower density than water. That is, given equal volumes of the two liquids, the oil will have a smaller mass than the water. Density is calculated using the following equation  

Ice cubes float in a glass of water because solid water is less dense than liquid water, (a) Calculate the density of ice given that, at 0°C, a cube that is 2.0 cm on each side has a mass of 7.36 g, and (b) determine the volume occupied by 23 g of ice at 0°C. 

Strategy (a) Determine density by dividing mass by volume (Equation 1.4), and (b) use the calculated density to determine the volume occupied by the given mass. 

Setup (a) We are given the mass of the ice cube, but we must calculate its volume from the dimensions given. The volume of the ice cube is (2.0 cm), or 8.0 cm. (b) Rearranging Equation 1.4 to solve for volume gives V = mid. 

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Fluids on the Earth s surface that are in hydrostatic equilibrium may be stable or unstable depending on their thermal structure. In the case of freshwater (an incompressible fluid), density decreases with temperature above ca. 4°C. Warm water lying over cold water is said to be stable. If warm water underlies cold, it is buoyant it rises and is unstable. The buoyant force, F, on the parcel of fluid of unit volume and density p is ... 

The SI unit of speed is meters per second (that is, meters divided by seconds). The unit is symbohzed m/s or m s The unit of speed is an example of an SI derived unit, which is a unit derived by combining SI base units. Table 1.4 defines a number of derived units. Volume and density are discussed in this section pressure and energy are discussed later (in Sections 5.1 and 6.1, respectively). 

The quantity AU JV° is the internal energy of vaporization per unit volume and is called the cohesive energy density (CED) of component i. The square root of the CED is generally given the symbol 6j for component i. 

Density and Relative Density. Density is mass per unit volume and in SI is normally expressed as kilograms per cubic meter (density of water = 1000 kg/m or 1 g/cm ). The term specific gravity was formerly the accepted dimensionless value describing the ratio of the density of sohds and Hquids to the density of water at 4°C or for gases to the density of ak at standard conditions. The term specific gravity is being replaced by relative mass density, a more descriptive term. 

Density The measure of the amount of mass in a unit volume. The density of a gas is a function of its pressure and temperature, It can be determined by using the ideal gas laws. 

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. 

Single crystal x-ray diffraction studies showed that the crystals of halcinonide recrystallized from tz-propyl alcohol-water azeotrope (79 22) are orthorhombic and belong to the gpace group P2 2 2, with unit ell constants of a = 10.007 A, = 11.875 A ana Q = 19.460 A. Density is 1.330 gm/cm2 3, as measured by flotation in a hexane-carbon tetrachloride gradient. The molecular weight calculated from the unit cell volume and density is 461 daltons (theoretical is 455 daltons). 

The three most important characteristics of an individual particle are its composition, its size and its shape. Composition determines such properties as density and conductivity, provided that the particle is completely uniform. In many cases, however, the particle is porous or it may consist of a continuous matrix in which small particles of a second material are distributed. Particle size is important in that this affects properties such as the surface per unit volume and the rate at which a particle will settle in a fluid. A particle shape may be regular, such as spherical or cubic, or it may be irregular as, for example, with a piece of broken glass. Regular shapes are capable of precise definition by mathematical equations. Irregular shapes are not and the properties of irregular particles are usually expressed in terms of some particular characteristics of a regular shaped particle. 

The close packing of the molecules of a substance in the liquid state results in a density much higher than in the gaseous state and approaching that in the solid state. The density, p, is the mass per unit volume, and can be expressed as the ratio of the molar mass M to the molar volume V of a liquid. Table 2.1 lists the values of the properties M and V of representative liquids that are important in the field of solution chemistry and solvent extraction. The densities and molar volumes depend on the temperature, and the latter are given for 25°C. (For a discussion of industrial solvents, see Chapter 12.)... 

We now constmct a mass balance on the total amount of Bg in the film The volume of solid is A t (area x length) with Ag the area of the film If the density of the solid is Pb (mass of Bg per unit volume) and the molecular weight of is Mb, then the number of moles of solid is given by... 

Consider the equilibrium in a vertical cylinder of suspension of density pi in a suspension medium of density of unit cross-section and height. o o. If at a height x there are n particles per unit volume and at a height xJr x,n->cM particles per unit volume the difference in osmotic pressures due to the particles on the assumption that the suspension conforms to the laws of an ideal solution will be... 

The original densities, heat capacities per unit volume and enthalpies of mixing from which the various thermodynamic functions are calculated for the ternary systems are given elsewhere. ... 

It should be noted, however, that some extensive properties become intensive properties, in case their specific values - that is, their values for unit mass or unit volume - are considered. For example, specific heat (i.e., heat capacity per unit mass) and density (i.e., mass per unit volume) are intensive properties. 

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