CHAPTER 3 Volumetric Properties of Pure Fluids: Part 1 Norhaniza binti Yusof Faculty of Chemical Engineering Universiti Teknologi Malaysia, 81310 UTM Johor, Johor Bahru, Malaysia Chemical Reaction Engineering Group, Universiti Teknologi Malaysia

Topic Outcomes Week Topic Topic Outcomes 2-3 Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Topic Outcomes Week Topic Topic Outcomes 2-3 Volumetric Properties of Pure Fluids Introduction to volumetric properties PVT behaviour of pure substances Volumetric properties from equations of state: Ideal gas equation Virial equation Generic cubic equations Volumetric properties from generalized correlations: Gases Liquid Volumetric properties from thermodynamic Tables and Diagrams It is expected that students are able to: Determine the state/phase of a given fluid at given conditions. Calculate the volumetric properties using the equations of state and generalized correlations for a given system. Identify the applicability and limitation of every equation of state. Determine the volumetric properties from thermodynamic tables and diagrams.

Scope of Lecture Introduction to volumetric properties Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Scope of Lecture Introduction to volumetric properties PVT behaviour of pure substances Volumetric properties from equations of state

PVT Behavior of Pure Substances Chemical Reaction Engineering Group, Universiti Teknologi Malaysia

PT Diagram for Pure Substances Chemical Reaction Engineering Group, Universiti Teknologi Malaysia PT Diagram for Pure Substances Ftp = 0 (invariant) Fliq = 2 (divariant) Fvap. curve = 1 (univariant) Pressure Temperature Pc Tc Solid region Fusion curve 2 1 3 A B Vapor region Gas region Fluid region Liquid region Vaporization curve Triple point Sublimation C No. of phases No. of species DOF for the system Independent variables (T, P) F = 2 –  + N Supercritical T > Tc Note: DOF, degree of freedom

PV Diagrams for Pure Substances In a PV diagram, the phase boundaries becomes areas/region Sol., liq. & gas regions Liq., liq./vap. regions & vap. with isotherms Single-phase (sat.) vap. at cond. T Single-phase (sat.) liqs. at boiling T Triple point Subcritical T → consist of 3 segments Note: Sol., solid; liq., liquid; vap., vapor; sat., saturated; cond., condensation; T, temperature

PVT Surface for a Real Substance Chemical Reaction Engineering Group, Universiti Teknologi Malaysia PVT Surface for a Real Substance P T V CP Solid Liquid Triple line Vapor Gas Note: CP., critical point

PVT Surface (Cont.) Constant temperature line Chemical Reaction Engineering Group, Universiti Teknologi Malaysia PVT Surface (Cont.) Constant temperature line

Pure Substances Phase Any fluid could be in one of below conditions : Single-phase liquid Single-phase gas 2-phases, liquid & gas Generally, if the system is at any T or P; Condition T and P Phase T > Tc Gas T < Tc and P > Pc Liquid T < Tc and P < Pc See boiling point T > Tbpt T < Tbpt T = Tbpt 2-phase (saturated) *For H2O, Tc = 374 oC and Pc = 220 bar Note: Tc, critical temperature, Pc, critical pressure, Tbpt, biling point temperature

Determination of Pure Substances Phase Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Determination of Pure Substances Phase Boiling point and vapor pressure could be obtained from : Antoine equation Cox Chart E.g.: Antoine equation for H2O; log10 P (mmHg) = 7.96681 – 1668.21 / (T oC + 228) Liquid phase: V is almost stable and not depend on P and T. Gas phase: V of pure substance is depend on T and P. Mathematic relations between P, V, T of pure substance is called as EQUATION OF STATE

Single-Phase Region f (P, V, T ) = 0 PV = RT Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Single-Phase Region From the regions of the diagram (PV) where a single phase exists, implies a relation connecting P, V & T →express by function equation f (P, V, T ) = 0 PVT equation of state (EoS) Simplest EoS → ideal gas law Valid for low P Will be discussed later PV = RT To solve the equation, V = f (P , T ) or P = f (V , T) or T= f (P , V) Note: P, pressure; EoS; equation of state

Example V = f (P, T) V = V (P, T) Hence, Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Example V = f (P, T) V = V (P, T) Hence, For liquid phase incompressible fluid  and  are very small ( ≈ 0). Partial derivative in the equation Integration Volume expansivity,  Isothermal compressibility,  Divide by V

Notes Gas Ideal gas Non-ideal gas PV = ZRT Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Notes Gas Ideal gas Non-ideal gas PV = ZRT Valid at low pressure Z = 1 Equations of state (from PVT data). Generalized correlations Equations of state Theorem of corresponding states

Cubic Equation of State Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Equation of State Equation of State Ideal Gas Equation Virial Equation Cubic Equation of State Van Der Waals Redlich/ Kwong Kwong/ Soave Peng/ Robinson Generic Vapor & Vapor-Like Roots Liquid & Liquid-Like

Virial Equations of State Chemical Reaction Engineering Group, Universiti Teknologi Malaysia

Virial Equations (Gas Phase) Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Virial Equations (Gas Phase) A useful auxiliary thermodynamic property is defined by the equation Compressibility factor There are 2 types of virial equations / virial expansions : B’, C’, D’, B, C, D etc. →virial coefficients Only depend on T. Obtained from PVT data. Note: T, temperature

Application of the Virial Equations Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Application of the Virial Equations CH4 Low to moderate P (P < 15 bar) 2 terms High P up to ≈50 bar (below the Pc) Truncated to 3 terms Note: P, pressure; Pc, critical pressure

Chemical Reaction Engineering Group, Universiti Teknologi Malaysia The Ideal Gas Virial expansion arise on account of molecular interaction. Term B/V arises on account of interactions between pairs of molecules The C/V2 term, on account of 3-body interactions. For ideal gas interaction molecular is assume not existed. As the P of real gas is reduced at constant T → V  & the contribution of the terms B/V, C/V2, etc.,  . As P → 0, V becomes , then Z approaches unity, = 1 PV = ZRT (low P only)

Internal energy U = U(T) Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Internal energy Internal energy of a REAL GAS is a function of P & T P dependency is the result of forces between the molecules. If such forces did not exist (IDEAL GAS behavior) → the internal energy of gas depends on T only U = U(T) (Ideal gas)

Property Relations for an Ideal Gas Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Property Relations for an Ideal Gas Heat capacity at constant V (CV) is a func. of T only Enthalpy (H) is a func. of T only Heat capacity at constant P (CP) is a func. of T only Relation between CP and CV This equation does not imply that CP and CV are themselves constant for an ideal gas, but only that they vary with T in such a way that their difference is equal to R.

Equations for Process Calculations Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Equations for Process Calculations For a unit mass or a mole of IDEAL GAS in any mechanically reversible closed-system process: These equations may be applied to the following processes

Adiabatic Process Isothermal process: Isobaric process: Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Adiabatic Process Isothermal process: Isobaric process: Isochoric process:

Adiabatic Process (Const. Heat Capacities) Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Adiabatic Process (Const. Heat Capacities) Equations Other expressions Work The process should be mechanically reversible! Alternative forms

Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Example 1 (Ideal gas) One mol of an ideal gas with Cp = (7/2)R and Cv = (5/2)R expands from P1 = 8 bar and T1 = 600 K to P2 = 1 bar by each of the following paths: Constant volume Constant temperature Adiabatically Assuming mechanical reversibility, calculate W, Q, U, and H for each process.

Example 2 (Virial Equation) Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Example 2 (Virial Equation) Reported values for the virial coefficients of isopropanol vapor at 200 C are: B = – 388 cm3 mol–1 C = – 26000 cm6 mol–2 Calculate V and Z for isopropanol at 200 C and 10 bar by: The ideal-gas equation Truncated virial equation to 3 terms

Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Tutorial 1 For methyl chloride at 100 C the 2nd and 3rd virial coefficients are: B = – 242.5 m3 mol –1 C = 25, 200 cm6 mol –2 Calculate the work of mechanically reversible, isothermal compression of 1 mol of methyl chloride from 1 bar to 55 bar at 100 C. Base calculations on the following forms of the virial equations: Where

CHAPTER 3 Volumetric Properties of Pure Fluids: Part 2 N02 1-310 12.00 – 1.00 P.M Feb 21, 2013 (Thu) CHAPTER 3 Volumetric Properties of Pure Fluids: Part 2 Mohd Asmadi Bin Mohammed Yussuf Faculty of Chemical Engineering Universiti Teknologi Malaysia, 81310 UTM Johor, Johor Bahru, Malaysia Chemical Reaction Engineering Group, Universiti Teknologi Malaysia

Scope of Lecture Cubic equation of state Generic cubic Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Scope of Lecture Cubic equation of state Generic cubic Example & Tutorial

Cubic Equation of State Chemical Reaction Engineering Group, Universiti Teknologi Malaysia

Generic Cubic Equation of State The simplest equations capable of representing both liquid and vapor behavior but not for dual-phase condition. More accurate for a wide range of T and P Where b , θ , κ , λ and η are parameters which is general depend on T and (for mixture) composition . Note: T, temperature; P, pressure; cubic equation of state ,15 < p < 50 bar

Equation of State Parameters Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Equation of State Parameters When in polynomial form : Where Pc and Tc → pressure and temperature in critical point a and b → +ve constants.

Cubic Equation of State Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Cubic Equation of State Cubic Equation of State Van Der Waals Redlich/ Kwong Redlich/ Kwong/ Soave Peng/ Robinson Generic Vapor & Vapor-Like Roots Liquid & Liquid-Like Roots

van der Waals θ = a η = b κ = λ = 0 Chemical Reaction Engineering Group, Universiti Teknologi Malaysia van der Waals θ = a η = b A Generic Cubic EoS (previous slide) κ = λ = 0 Reduces to van der Waals EoS Will be discussed later Note: EoS; equation of state

Redlich/Kwong Equation, Solve by cubic equation solver. Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Redlich/Kwong Equation, Solve by cubic equation solver.

V for Gas & Liquid Phases (RK) Chemical Reaction Engineering Group, Universiti Teknologi Malaysia V for Gas & Liquid Phases (RK) V for gas phase V for liquid phase Multiple & rearrange Solve by iteration method, use b as an initial Vo. Note: RK, Redlich/Kwong

Redlich-Kwong-Soave & Peng-Robinson Acentric factor (App. B) Chemical Reaction Engineering Group, Universiti Teknologi Malaysia

Parameters for all Cubic Equation of State EoS a( Tr) σ ε Ω Ψ Zc van der Waals 1 1/8 27/64 3/8 Redlich/ Kwong 0.08664 0.42748 1/3 Redlich-Kwong-Soave 0008664 Peng-Robinson 0.07779 0.45724 0.30740 Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Note: Please text book p. 98

Generic Cubic Vapor & Vapor-Like Roots of the Generic Cubic EoS Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Generic Cubic Vapor & Vapor-Like Roots of the Generic Cubic EoS Solution for V may be by Trial Iteration With the solve routine of a software package Initial estimate for V is the ideal-gas value →

Dimensionless Quantities Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Dimensionless Quantities An equation for Z equivalent to equation above is obtained through substitute 2 dimensionless quantities leads to simplification

Process continues to convergence Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Determination of Z Therefore, Iteration Start with Z = 1 → Substituted on the right side. Calculated Z → Returned to the right side Process continues to convergence Final Z → yields the volume root through V = ZRT/P

Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Generic Cubic (Cont.) Liquid & Liquid-Like Roots of the Generic Cubic EoS V in the numerator of the final fraction to give : Starting value V = b. An equation for Z equivalent to the equation above :

Iteration For iteration Z = β. Once Z is known, the volume root is Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Iteration For iteration Z = β. Once Z is known, the volume root is EoS which express Z as a function of Tr & Pr Called generalized Their general applicability to all gases & liquids. Note: EoS; equation of state

A Generic Cubic Equation of State Chemical Reaction Engineering Group, Universiti Teknologi Malaysia A Generic Cubic Equation of State An important class of cubic equations results from the preceding equation with the assignments η = b θ = a ( T ) κ = ( є + σ ) b λ = є σ b2 ε & σ are pure numbers →same for all substances a(T) is specific to each EoS Note: EoS; equation of state

Determination of EoS Parameters Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Determination of EoS Parameters Suitable estimates of EoS parameters are usually found from values for the critical constants Tc and Pc → critical isotherm exhibits a horizontal inflection at the critical point! At critical point ( Pc, Tc, Vc & Zc ) : Replace Pc, Tc and Vc From van der Waals equation : Then, Note: EoS; equation of state

Chemical Reaction Engineering Group, Universiti Teknologi Malaysia EoS Parameters (Cont.) An analogous procedure may be applied to the generic cubic equation Previous slide Yielding expressions for parameters Ω and Ψ Pure numbers, Independent of substance Determined for a particular EoS from the values assigned to ε & σ

EoS Parameters (Cont.) unity at the Tc Chemical Reaction Engineering Group, Universiti Teknologi Malaysia EoS Parameters (Cont.) This result may be extended to T other than the critical by Introduction of a dimensionless function unity at the Tc Function α(Tr) : an empirical expression specific to a particular equation of state. Note: Tc; critical temperature

Theorem of Corresponding States All fluids, when compared at the same Tr & Pr, have approximately the same Z, and all deviate from ideal-gas behavior to about the same degree . This theorem is very nearly exact for the simple fluids (Ar, Kr, Xe). However, systematic deviations are observed for more complex fluids. Note: Z; compressibility factor ; Tr, reduce temperature; Pr, reduced pressure

Acentric Factor (Cont.) Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Acentric Factor (Cont.) Approximate T dependence of the reduced vapor pressure

Acentric Factor (Cont.) Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Acentric Factor (Cont.) Therefore, an acentric factor is introduced as follow: Acentric factor At Tr = 0.7 → = 0 (Ar, Kr & Xe) This value of  can be determined for any fluid from Tc, Pc and a single vapor-pressure measurement made at Tr = 0.7 App. B lists the values of ω and the critical constants Tc, Pc, and Vc for a number of fluids.

Acentric Factor (Cont.) Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Acentric Factor (Cont.) All fluids having the same value of ω, when compared at the same Tr & Pr, have about the same value of Z, and all deviate from ideal-gas behavior to about the same degree. w

Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Example 3 Given that the vapor pressure of n-butane at 350 K is 9.4573 bar, find the volumes of (a) saturated-vapor and (b) saturated-liquid n-butane at these conditions as given by the Redlich/Kwong equation.

Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Example 4 Calculate Z and V for ethylene at 25 C and 12 bar by the following equations: The Redlick/Kwong equation The Soave/Redlich/Kwong equation The Peng/Robinson equation

Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Tutorial 2 Calculate Z and V for ethylene at 50 C and 15 bar by the following equations: The Redlick/Kwong equation The Soave/Redlich/Kwong equation The Peng/Robinson equation

CHAPTER 3 Volumetric Properties of Pure Fluids: Part 3 N02 2-6, 11.00 –1.00P.M Feb 17, 2013 (Mon) CHAPTER 3 Volumetric Properties of Pure Fluids: Part 3 Mohd Asmadi Bin Mohammed Yussuf Faculty of Chemical Engineering Universiti Teknologi Malaysia, 81310 UTM Johor, Johor Bahru, Malaysia Chemical Reaction Engineering Group, Universiti Teknologi Malaysia

Scope of Lecture Generalized Correlations for Gases Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Scope of Lecture Generalized Correlations for Gases Compressibility factor, Z 2nd virial coefficient, B Generalized Correlations for Liquids Examples & Tutorials

Generalized Correlations for Gases Chemical Reaction Engineering Group, Universiti Teknologi Malaysia

Pitzer Correlations for the Z Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Pitzer Correlations for the Z The correlation for Z takes form : Equally suitable for gases & liquids Where Z0 and Z1 are functions of both Tr and Pr . From Table E1–E4, require interpolation, see App. F Error Non-polar/slightly polar < 2-3% Highly polar larger error When ω = 0 →simple fluids. Ar, Kr, Xe

Lee/ Kesler Correlation for Z0 = F0 (Tr, Pr) Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Lee/ Kesler Correlation for Z0 = F0 (Tr, Pr) Pr 1.2 1.0 0.8 0.6 Z0 0.4 0.05 0.1 0.2 0.5 1.4 2.0 5.0 10.0 Two-phase region Compressed liquids (Tr < 1.0) Gases Tr = 0.7 0.9 4.0 1.5 C

Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Quantum Gases (H2, He, Ne) Do not conform to the same corresponding-states behavior as do normal fluids The correlation is accommodated by use of T-dependent effective critical parameters. E.g. Hydrogen T = absolute temperature in K

Pitzer Correlations for B Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Pitzer Correlations for B Correlations for 2nd Virial Coefficientn(comb Eq 3.61 and 3.63) Validity at low to moderate P Simple and recommended Tr > Tr ≈ 3, there appears to be no limitation on the P Most accurate for non-polar species

Virial Correlations (Cont.) Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Virial Correlations (Cont.) The simplest form of the virial equation : Compare 2nd correlations, yields 2nd virial coefficients = f(T) only B0 & B1 = f(Tr) only Note: f, function

Comparison of Correlation for Z0 Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Comparison of Correlation for Z0 Region above the dashed line the 2-correlations differ by <2% Points: Lee/ Kesler correlation 0.0 0.5 1.0 1.5 2.0 2.5 Pr 0.9 0.8 0.7 Z0 Tr = 0.8 1.1 1.3 1.8 2.4 4.0 Straight lines: virial-coefficient correlation

App. Validity of the Ideal-Gas Eqn. Chemical Reaction Engineering Group, Universiti Teknologi Malaysia App. Validity of the Ideal-Gas Eqn. 10 1 0.1 0.01 Pr 0.001 2 3 4 Tr Z0 = 0.98 Z0 = 1.02 Region where Z0 lines between 0.98 &1.02 Ideal-gas eqn. is a reasonable approximation to reality

Generalized Correlations for Liquid Chemical Reaction Engineering Group, Universiti Teknologi Malaysia

Molar Volume of Sat. Liquids Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Molar Volume of Sat. Liquids The generalized cubic equation of state →low accuray The Lee/Kesler correlation includes data for subcooled liquids Suitable for non-polar & slightly polar fluids Estimation of molar volumes of saturated liquids Data required → crirical conts. (App. B) Results accurate → 1 or 2%

Generalized Density Correlation Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Generalized Density Correlation 2-parameter corresponding-states correlation for estimation of liquid volumes. Density at the critical point Known volume Required volume Reduced densities read from next page Give good results and requires only experimental data (usually available).

Generalized Density Correlation (Cont.) Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Generalized Density Correlation (Cont.) Tr = 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Tr = 0.95 0.97 0.99 Saturated liquid 3.5 3.0 2.5 2.0 r 1.5 1 2 3 4 5 6 7 8 9 10 Pr

Examples & Tutorials Chemical Reaction Engineering Group, Universiti Teknologi Malaysia

Example 4 (Gases) Solution 4: Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Example 4 (Gases) Determine the molar volume of n-butane at 510K and 25 bar by, (a) the ideal-gas equation; (b) the generalized compressibility-factor correlation; (c) the generalized virial-coefficient correlation. Solution 4: The ideal-gas equation The generalized compressibility-factor correlation

Solution 4 (Cont.) The generalized virial-coefficient correlation Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Solution 4 (Cont.) The generalized virial-coefficient correlation

Example 5 (Gases) Solution 5: Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Example 5 (Gases) What pressure is generated when 1 (lb mol) of CH4 is stored in a volume of 2 ft3 at 122 F using (a) the ideal-gas equation; (b) the Redlich/Kwong equation; (c) a generalized correlation. Solution 5: The ideal-gas equation The RK equation

Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Solution 5 (Cont.) The generalized compressibility-factor correlation (high P) Z starts at Z0 = 1 Pr Tr = 1.695 Table E.3 & E.4 Z0 & Z1 Z = Z0 + Z1 Final Z Converges (Z = 0.890) Pr1 = 4.68

Example 6 (Gases) Solution 6: Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Example 6 (Gases) A mass of 500 g of gases ammonia is contained in a 30000 cm3 vessel immersed in a constant-temperature bath at 65 C. Calculate the pressure of the gas by (a) the ideal-gas equation; (b) a generalized correlation . Solution 6: The ideal-gas equation

Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Solution 6 (Cont.) The generalized virial-coefficient correlation (low P, Pr ~ 3 )

Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Tutorial 3 Calculate the molar volume of saturated liquid and the molar volume of saturated vapor by Redlich /Kwong equation fo one of the folowing and compare results with values found by suitable generalized correlations. Propane at 40 C where Psat = 13.71 bar n-Butane at 100 C where Psat = 15.41 bar Tutorial 4 The vapor-phase molar volume of a particular compound is reported as 23,000 cm3mol–1 at 300 K and 1 bar. No other data are available. Without ideal-gas behavior, determine a reasonable estimate of the molar volume of the vapor at 300 K and 5 bar.

Example 7 (Liquid) Solution 7: Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Example 7 (Liquid) For ammonia at 310 K, estimate the density of (a) the saturated liquid; (b) the liquid at 100 bar Solution 7: Apply the Rackett equation at the Tr Exp. = 29.14 cm3 mol–1 → differs = 2.7% Compares

Solution 7 (Cont.) At 100 bar Fig. 3.16 Exp. value Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Solution 7 (Cont.) At 100 bar Fig. 3.16 Exp. = 29.14 cm3 mol–1 → differs = 6.5% Exp. value

Tutorial 5 Tutorial 6 Tutorial 7 Chemical Reaction Engineering Group, Universiti Teknologi Malaysia Tutorial 5 The specific volume of isobutane liquid at 300 K and 4 bar is 1.824 cm3 g–1. Estimate the specific volume at 415 k and 75 bar. Tutorial 6 The density of liquid n-pentane is 0.630 g cm–3 at 18 C and 1 bar. Estimate its density at 140 C and 120 bar. Tutorial 7 Estimate the volume change of vaporization for ammonia at 20 C. At this temperature the vapor pressure of ammonia is 857 kPa.