CHAPTER 5-ENERGY BALANCEFOR REACTIVE SYSTEM CHE243-MATERIAL AND ENERGY BALANCE AND SIMULATION HEAT OF REACTION HESS’S LAW HEAT OF FORMATION HEAT OF COMBUSTION Consider the reaction between solid calcium carbide and liquid water to form solid calcium hydroxide and gaseous acetylene: CaC 2 s 2H 2Ol CaOH 2 s C 2 H 2 g The heat of the calcium carbide reaction at 25 0C and 1 atm is: H product H reactant ΔHr 125. Refer Felder pp. 442 Stoichiometric quantities of reactions – molar amounts of the reactants numerically equal to their stoichiometric coefficients.HEAT OF REACTION Heat of reaction (or enthalpy of reaction) – Hr (T.4 kJ mol .P) is the enthalpy change for a process in which stoichiometric quantities of reactants at temperature T and pressure P react completely in a single reaction to form products at the same temperature and pressure. or solid) of the reactants and products.P) is negative. Hr (T. .HEAT OF REACTION Several important terms and observations related to heats of reactions: If Hr (T.P) is positive. liquid. The value of heat of reaction depends on how the stoichiometric equation is written. the reaction is endothermic At low and moderate pressures. usually 25 0C and 1 atm. the reaction is exothermic If Hr (T.P) is nearly independent of pressure. Refer Felder pp. 443 The value of a heat of reaction depends on the state of aggregation (gas. H0r is the heat of reaction when both the reactants and products are at specified reference temperature and pressure. The standard heat of reaction. 446 . 3.HESS’S LAW Hess’s Law –If the stoichiometric equation for reaction 1 can be obtained by algebraic equations (multiplication by constants. H0r3……. addition. Refer Felder pp. and subtraction) on stoichiometric equations for reaction 2. …then the heat of reaction H0r1 can be obtained by performing the same operations on the heats of reactions H0r2. CH + 1.Example – Hess’s Law (Felder pp 446) The standard heats of the following combustion reactions have been determined experimentally: . 2 6 → 3.8 kJ/mol Use Hess’s law and the given heats of reaction to determine the standard heat of reaction: 4.6 mol H0r4 = ??? . H2 + 0.5O2 → 2CO2 + CO2 → H2O 3H2O H0r1 = -1559.5 kJ/mol H0r3 = -285. 2C + 3 H2 → C2H6 ^ 0 kJ Δ H r4 84.8 kJ/mol H0r2 = -393. C + O2 3.5O2 2. The standard heat of reaction. etc. H0r is: ^ 0 ^ 0 H r vi H fi i ^ 0 v H i products fi ^ 0 v H i reactan ts fi . 447 Standard heat of formation. O2. N2. H0f – the enthalpy change associated with the formation of 1 mole of the compound at a reference temperature and pressure (usually 25 0C and 1 atm) The H0f for elemental species (eg.. C. Refer Felder pp.) is zero (0).HEAT OF FORMATION A formation reaction – a compound is formed from its elemental constituents as they normally occur in nature. Example – Determination heat of reaction from heats of formation (Felder pp 447) .54 kJ mol .Determine the standard heat of reaction for the combustion of liquid npentane. assuming H2O (l) is a combustion product C5H12(l) + 8O2(g) → 5CO2(g) + 6H2O(l) ^ 0 Δ H r 3509. H0r that involve only combustible substances and combustion products that can be calculated from tabulated standard heats of combustion. H0c– the heat of combustion of that substance with oxygen to yield a specified products.HEAT OF COMBUSTION Standard heat of combustion. Refer Felder pp. with both reactants and products at 25 0C and 1 atm. 448 The standard heat of reaction. ^ 0 ^ 0 H r vi H c i i ^ 0 v H i reactan ts ci ^ 0 v H i products ci . Example – Determination heat of reaction from heats of combustion (Felder pp 449) .93 mol .Determine the standard heat of reaction for the dehydrogenation of ethane: C2H6 → C2H4 + H2 ^ 0 kJ Δ H r 136. PROCEDURE CALCULATION SIMPLE ENERGY BALANCE CALCULATION . HEAT OF REACTION METHOD HEAT OF FORMATION METHOD . 450 • Complete the material balance calculations on the reactor to the greatest extent possible. • Choose reference states for specific enthalpies calculation – the best choice is 25 0C and 1 atm. .HEAT OF REACTION METHOD 100 mol C3H8 (g)/s T=250C 600 mol O2 (g)/s 2256 mol N2 (g)/s T=3000C 100 mol O2 (g)/s 2256 mol N2 (g)/s Q (kJ/s) 300 mol CO2 (g)/s 400 mol H2O (g)/s T=10000C For single reaction where H0r is known. Refer Felder pp. ξ Prepare inlet – outlet enthalpy table. O2 (g). References: C3H8 (g). calculate the extent of reaction. CO2 (g).For a single reaction in a continuous process. H2 O (l). 1 atm Substances min ( mol/s) Hin (kJ/mol) mout ( mol/s) Hout (kJ/mol) C3H8 100 0 0 0 O2 600 H2 100 H4 N2 2256 H3 2256 H5 CO2 - - 300 H6 H2O - - 400 H7 . N2 (g). at 250C. H2 8. calculate Q in (for multiple reaction) . ^ 0 ^ ^ H H r n H n H out .Calculate the unknown stream component enthalpy H 2 ΔH for O2 (250 C 3000 C) From Table B.47 kJ mol Calculate H for the reactor. H in ^ 0 H j reaction (for single reaction) rj ^ ^ n H n H out From energy balance. Use one of the following formula: .8. Refer Felder pp. .HEAT OF FORMATION METHOD 100 mol C3H8 (g)/s T=250C 600 mol O2 (g)/s 2256 mol N2 (g)/s T=3000C 100 mol O2 (g)/s 2256 mol N2 (g)/s Q (kJ/s) 300 mol CO2 (g)/s 400 mol H2O (g)/s T=10000C Preferably for multiple reactions and single reactions where H0r is not available. Choose reference states for specific enthalpies calculation – the best choice is 25 0C and 1 atm. 451 Complete the material balance calculations on the reactor to the greatest extent possible. N2 (g). at 250C. H2 O (l). CO2 (g). O2 (g). 1 atm Substances nin ( mol/s) Hin (kJ/mol) nout ( mol/s) Hout (kJ/mol) C3H8 100 H1 0 0 O2 600 H2 100 H4 N2 2256 H3 2256 H5 CO2 - - 300 H6 H2O - - 400 H7 . References: C3H8 (g).Prepare inlet – outlet enthalpy table. Use one of the following formula: .8 mol 25 Calculate H for the reactor.8 Cp(T)dT 103. calculate Q in . ^ ^ H n H n H out From energy balance.Calculate the unknown stream component enthalpy H 1 ΔH for C 2 H 8 (at 250 C) T H 1 ΔH 0f Cp(T)dT 25 25 kJ H 1 103. assuming operation at approximately 1 atm.Example – Energy Balance About an Ammonia Oxidizer (Felder pp 453) The standard heat of reaction for the oxidation of ammonia is given below: 0 . The product gas emerges at 300 0C.45kW . 4NH3 (g) + 5O2 (g) → 4NO (g) + 6H2O(v) : H r=-904. Calculate the rate at which heat must be transferred to or from the reactor.7 kJ/mol 100 mol NH3 /s and 200 mol O2 /s at 25 0C are fed into a reactor in which the ammonia is completely consumed.701. Q 19. CH4 (g) + 2O2 (g) → CO2 (g) + 2H2O(v) A flow chart of the process for an assumed basis of 100 mol methane fed to the reactor is shown in Figure 1. Calculate the rate at which heat must be transferred to or from the reactor. Q 15.382 kJ . A competing reaction is the combustion of methane to form CO2 . CH4 (g) + O2 (g) → HCHO (g) + H2O(v) 2.1.Example – Energy Balance About a Methane Oxidizer (Felder pp 454) Methane is oxidized with air to produce formaldehyde in a continuous reactor. assuming operation at approximately 1 atm. decreasing the reaction rate to an unacceptably low level. To keep the temperature from dropping too much and thereby . heat is transferred to the reactor.0 mol% ethanol and the balance acetaldehyde and enters the reactor at a rate of 150 mol/s.313 n feed . the outlet temperature is 2530C. When the heat addition rate is 2440 kW. The feed contains 90. Calculate the fractional conversion of ethanol achieved in the reactor. The reaction of dehydrogenation of ethanol to form acetaldehyde is stated as: C2H5 OH (v) → CH3 CHO (v) + H2(g) The fractional conversion of ethanol: n feed n unreacted 0.Example – Simultaneous Material and Energy Balance (Felder pp 458) The ethanol (C2H5 OH) dehydrogenation reaction is to be carried out with the feed entering at 3000C.