Chapter 5 Single Phase Systems

Introduction Before carrying out a complete material balance, we usually need to determine various physical properties of materials in order to derive additional relationship among the system variables. As an example we need the density to relate the volumetric flow rate to mass flow rate or vice versa. 3 ways to obtain the values of physical properties (such as density, vapor pressure, solubility, heat capacity, etc) Handbook or database - Perry’s Chemical Handbook, CRC Handbook of Chemistry & Physics, TRC Database in Chemistry & Engineering, etc Estimation using empirical correlations Experimental work

Density of Liquid and Solid Temperature dependence: modest but sometimes important (liquid and solid expanded during heating and density decrease) Pressure dependence: usually negligible (solid and liquid are incompressible with pressure). 2 methods to estimate the density of a mixture of n liquid (n is number of different type of liquid) Method 1: Volume Additivity Work best for mixture of liquid species with similar molecular structure Method 2: Average Pure Component Densities

Ideal Gases Equation of state Relates the molar quantity and volume of a gas to temperature and pressure. Ideal gas equation of state Simplest and most widely used Used for gas a low pressure and high temperature Derived from the kinetic theory of gases by assuming gas molecules have a negligible volume; Exert no forces on one another; Collide elastically with the wall of container or The use of this equation does not require to know the gas species: 1 mol of an ideal gas at 0˚C and 1 atm occupies 22.415 liters, whether the gas is argon, nitrogen, mixture of propane and air, or any other single species or mixture of gases

Ideal Gas Equation of State P = absolute pressure V = volume of the gas n = number of moles of gas R = gas constant which the unit depend on unit of P, V, n, T T = absolute temperature Ideal gas equation of state can also be written as Which ; specific molar volume of gas. Unit for gas constant, R or

Ideal Gas Equation of State Density of ideal gas ( M is average molecular weight-refer back previous chapter Eq. 3.3-7) Rule of thumb for when it is reasonable to assume ideal gas behavior. Let Xideal be a quantity calculated using ideal gas equation of state (X can be pressure, volume, temperature or mole). Error is estimated value is ε Let say quantity to be calculate is ideal specific molar volume, If error calculte is satifies this criterion, the ideal gas equation of state should yield an error less than 1%

Class Discussion Example 5.2-1

Standard Temperature and Pressure (STP) A way to avoid the use of gas constant, R when using ideal gas equation For ideal gas at arbitrary temperature, T and pressure, P For the same ideal gas at standard reference temperature, Ts and standard reference pressure, Ps (refer to STP). Divide eq. 1 to eq. 2 Value of standard conditions (Ps, Ts, Vs) are known, above equation can be used to determine V for a given n or vice versa Standard cubic meters (SCM) : m3 (STP) Standard cubic feet (SCF) : ft3 (STP) Let say 18 SCMH mean 18 m3 (STP)/h

Standard Conditions for Gases System Ts Ps Vs ns Vs SI 273K 1atm 0.022415 m3 1 mol 22.4 m3/kmol cgs 273K 1atm 22.415 L 1 mol 22.4 L/mol English 492˚R 1atm 359.05ft3 1 lb-mole 359.05 ft3/lb-mole

“ Saya pasti akan berjaya kerana saya telah kehabisan benda-benda yang tidak berjaya” Thomas Eddison

Class Discussion Example 5.2-2

Class Discussion Example 5.2-3

Class Discussion Example 5.2-4

Ideal Gas Mixture Suppose nA moles of species A, nB moles of species B, nc moles of species C and so on, contained in a volume, V at temperature, T and pressure, P Partial pressure, pA The pressure that would be exerted by nA moles of species A alone in the same total volume, V at the same temperature, T of the mixture. Pure component volume, vA The volume would be occupied by nA moles of A alone at the same total pressure, P and temperature, T of the mixture. Ideal gas mixture Each of the individual species component and the mixture as whole behave in an ideal manner

Ideal Gas Mixture Dalton’s Law The summation of partial pressure of the component of an ideal gas mixture is equal to total pressure Amagat’s Law Volume fraction = vA/V; percentage by volume (%v/v)= (vA/V )x 100% For an ideal gas mixture, the volume fraction is equal to the mole fraction of the substance: 70% v/v C2H6 = 70 mole% C2H6

Class Discussion Example 5.2-5

Equation of State for Nonideal Gases Critical temperature (Tc)- the highest temperature at which a species can exist in two phases (liquid and vapor), and the corresponding pressure is critical pressure (Pc) Other definition: highest temperature at which isothermal compression of the species vapor results in the formation of a separate liquid phase. Critical state- a substance at their critical temperature and critical pressure. Species below Pc: Species above Tc- gas Species below Tc- vapor Species above Pc and above Tc- supercritical fluids

Virial Equation of State B,C,D- second, third, fourth virial coefficient respectively Truncated virial equation Tr=T/Tc ω – acentric factor from Table 5.3-1 Tc,Pc from Table B.1

Class Discussion Example 5.3-1

Kebebasan tanpa tanggungjawab membawa kehancuran

Cubic Equations of State Refer as cubic equation because when the equation is expanded, it become third order equation for the specific volume To evaluate volume for a given temperature and pressure using cubic equation of state, we need to do trial and error procedure. Two famous cubic equation of state Van der Waals equation of state Soave-Redlich-Kwong (SRK) equation of state

Van der Waals Equation of State (a/V2) - account for attractive force between molecules b - correction accounting for the volume occupied by the molecules themselves

Soave-Redlich-Kwong (SRK) equation of state

Class Discussion Example 5.3-2

Compressibility Factor Equation of State If z=1, equation become ideal gas equation of state Value of z is given in Perry’s Chemical Engineering Handbook pg. 2.140- 2.150. Alternatively; can use generalized compressibility chart Figure 5.4-1 – generalized compressibility chart Fig. 5.4-2 to Fig. 5.4-4 – expansion on various region in Fig. 5.4-1

Steps to Read Compressibility Factor Find Tc and Pc If gas is either Hydrogen or Helium, determine adjusted critical temperature and pressure form Newton’s correction equation Calculate reduced pressure and reduced temperature of the two known variables Read off the compressibility factor from the chart

Class Discussion Example 5.4-2

Nonideal Gas Mixtures Kay’s Rule: estimation of pseudocritical properties of mixture as simple average of pure a component critical constants Pseudocritical temperature (Tc’) Tc’= yATcA + yBTcB +…… Pseudocritical pressure (Pc’) Pc’= yAPcA + yBPcB +…… Pseudocritical reduced temperature (Tr’) Tr’= T/Tc’ Pseudocritical reduce pressure (Pr’) Pr’= P/Pc’ Compressibility factor for gas mixture, Zm

Class Discussion Example 5.4-3

ANY QUESTION?