AE 205 Materials and Energy Balances Asst. Prof. Dr. Tippabust Eksangsri Chapter 4 Stoichiometry and MB with Reactions
Stoichiometry Stoichiometry provides a quantitative means of relating the amount of products produced by chemical reactions to the amount of reactants. The stoichiometric equation of a chemical reaction is a statement of a relative numbers of molecules or moles of reactants and products that participate in the reaction. The stoichiometric coefficients of a balanced equation tell us the mole ratios among substances that reacted and produced by the reaction. The stoichiometric ratio is the ratio of stoichiometric coefficients in the balanced reaction equation.
Sulfur Trioxide (SO 3 ) Production During combustion of sulfur bearing fuels, such as coal, sulfur oxides are produced. While most of the sulfur forms sulfur dioxide (SO 2 ), a small amount is further oxidized to sulfur trioxide (SO 3 ) due to the oxidation of SO 2. The stoichiometric equation for this reaction is written as: 2SO 2 + O 2 2SO 3 Let i = stoichiometric coefficient of substance i in the reaction, then SO2 = (-) 2 O2 = (-) 1 SO3 = (+) 2 The stoichiometric ratios from this reaction can be; 2 moles of SO 3 produced 2 mole ofso 2 reacted or 2 moles of SO 3 produced 1 mole ofo 2 reacted or 2 moles of SO 3 reacted 1 mole ofo 2 reacted
Example 1: Combustion of heptane (C 7 H 16 ) In the combustion of heptane, carbon dioxide is produced. Assume you want to produce 500 kg of dry ice per hour, and that 50% of the CO 2 can be convert into dry ice. How many kilograms of heptane must be burned per hour? Other gases C 7 H 16 O 2 Combustion Chamber CO 2
Example 2: Application of Stoichiometry when more than one reaction occurs By heating limestone we can recover oxides known as Lime. A limestone composition is analyzed as Component % wt CaCO 3 92.89 MgCO 3 5.41 Inert 1.70 (1) How many pounds of CaO can be made from 1 ton of limestone? (2) How many pounds of CO 2 can be recovered per pound of limestone? (3) How many pounds of limestone are needed to produce 1 ton of lime?
Limiting and Excess Reactants In industrial reactors, it is very rare to find exact stoichiometric amounts of materials used. Some reactants are costly that we need to use it up. However, there will always be excess materials come out of the reactor together with the products. The limiting reactant is the specie in a chemical reaction that would theoretically run out first if the reaction proceeds to completion according to the chemical reaction. The reactant is limiting since it presents in less than its stoichiometric proportion relative to every other reactants. The other species of reactants are, then, called excess reactants. % excess reactant = 100[ amount of excess reactant fed stoichiometric amount stoichiometric amount ]
Example 3: Hydrogenation of Acetylene The hydrogenation of acetylene will form ethane as shown below: C 2 H 2 + 2H 2 C 2 H 6 Suppose that 20 kmol/h of acetylene and 50kmol/h of hydrogen are fed to a reactor. Therefore, the ratio of H 2 to C 2 H 2 in the reactor is 50:20, or 2.5:1. However, the stoichiometric ratio of H 2 to C 2 H 2 is 2:1. Hydrogen is fed in a greater than stoichiometric proportion to acetylene. Therefore, acetylene is the limiting reactant. With 20 kmol/h of C 2 H 2 fed, we will need 40 kmol/h of H 2 to do the reaction. %excess of H 2 = (50 40) kmol/h 40 kmol/h x 100 = 25%
Extent of Reaction ( ) Extent of reaction denotes how much reaction occurs, mostly reflecting by the consumption of limiting reactants. The unit of extent of reaction is presented as mole reacting. When, Or, = n i n io i n i and n io are moles of specie i present in the system after reaction and when reaction starts, respectively. i = stoichiometric coefficient of specie I n i = n io + i
Example 4: Calculation of the Extent of Reaction Determine the extent of reaction for the following chemical reaction N 2 + 3H 2 2NH 3 Given the following analysis of feed and product: Specie Amount in Feed (g) Amount in Product (g) N 2 100 na. H 2 50 na. NH 3 5 90
Maximum Extent of Reaction ( Max ) The maximum extent of reaction is the of each reactant, based on the complete reaction. The amount of products produced would be controlled by the amount of limiting reactant. Max = 0 n io i The amount of n i will always be zero for the complete reaction. The reactant with the smallest Max is the limiting reactant.
Example 5: Determination of limiting reactant using Max Consider the combustion of heptane; C 7 H 16 + 11O 2 7CO 2 + 8H 2 O If 1 gmol of heptane and 12 gmol of oxygen are mixed, which specie will be considered a limiting reactant? Using maximum extent of reaction to answer this problem.
Example 6: Calculation of the Ammonia Production If we feed 10 g of N 2 and 10 g of H 2 into a reactor; (A) What is the maximum amount of NH3 that can be produced? (B) Which specie is a limiting reactant? (C) What is the %excess of an excess reactant? Knowing that MW. of N 2 =28 MW. of H 2 = 2 MW. of NH 3 = 17 N 2 + 3H 2 2NH 3
Conversion Conversion is the fraction of the feed that is converted into products; amount of feed that reacted %conversion = 100 x [ amount of feed introduced ] Or, Conversion = extent of reaction that occurs extent of reaction for complete reaction = Max = n i n io 0 n io
Yield 1. Yield based on feed: Yield 1 = amount of desired product obtained amount of the limiting reactant fed 2. Yield based on reactant consumed: Yield 2 = amount of desired product obtained amount of the limiting reactant consumed 1. Yield based on theoretical consumption of the limiting reactant: Yield 3 = amount of desired product obtained amount of that product that would be obtained theoretically
Selectivity Selectivity is the ratio of desired product produced to the amount of other products co-produced. In most chemical processes, reactants are bought together with the object of producing a desired production, Unfortunately, reactants can usually combine in more than one way, and the product once formed may react to yield something less desirable. The result of these side reactions is an economic loss. Take an example on ethylene production by dehydrogenation of ethane; C 2 H 6 H 2 + C 2 H 4 Once hydrogen is produced, it can react with ethane and form methane; C 2 H 6 + H 2 2CH 4 Ethylene can also react with ethane to form propylene and methane; C 2 H 6 + C 2 H 4 C 3 H 6 + CH 4
Example 7: Production of Ethanol from Sugar Yeasts are living organisms that consume sugars and produce a variety of products. For example, yeasts are used to convert malt to beer, and convert corn to ethanol. The growth of S. cerevisiae on glucose under anaerobic conditions proceeds by the following reaction to produce biomass, glycerol, and ethanol. C 6 H 12 O 6 + 0.118NH 3 0.59CH 1.74 N 0.2 O 0.45 + 0.43C 3 H 8 O 3 + 1.54CO 2 + 1.3C 2 H 5 OH + 0.03H 2 O Calculate the theoretical yield of biomass (in g. biomass per g. glucose) and yield of ethanol (in g. ethanol per g. glucose).
Example 8: Selectivity in the Production of Nanotubes A carbon nanotube may consist of a single wall tube or a number of concentric tubes. A single wall tube may be produced as unaligned structures or bundles of ropes packed together in an orderly manner. The structure of the carbon nanotubes influences its properties, such as conductance. In nanotechnology, numerous methods exist to produce nanotubes. For example, large amount of single wall carbon nanotubes can be produced by the catalytic decomposition of ethane over Co and Fe catalysts supported on silica. C 2 H 6 2C + 3H 2 C 2 H 6 C 2 H 4 + H 2 (a) (b) If you collect 3 gmol of H 2 and 0.5 gmol of C 2 H 4 in the products, what is the selectivity of C relative to C 2 H 4?
Carbon Nanotubes Structures Conceptual diagram of single-walled carbon nanotube (SWCNT) (A) and multi-walled carbon nanotube (MWCNT) (B) delivery systems showing typical dimensions of length, width, and separation distance between graphene layers in MWCNTs. THE JOURNAL OF NUCLEAR MEDICINE Vol. 48 No. 7 July 2007
Example 9: Determination of limiting reactant when there are more than two reactants involved Acrylonitrile (C 3 H 3 N) is produced in the reaction of propylene (C 3 H 6 ), ammonia (NH 3 ), and oxygen (O 2 ): C 3 H 6 + NH 3 + 1.5O 2 C 3 H 3 N + 3H 2 O The feed contains 10%mol propylene, 12%mol ammonia and 78%mol air. A fractional conversion of 30% of the limiting reactant is achieved. Taking 100 gmol of feed as a basis, determine (A) Which reactant is limiting? (B) %excess of the excess reactants (C) Molar amount of all products
Review of Mass Balance Equation Let m 0 = initial mass of the system m t = mass of the system at time t m i = mass of inlet stream(s) m e = mass of exit stream(s) m gen = mass of generated material(s) m con = mass of consumed material(s) m t m 0 = m i m e + m gen m con
Species Mole Balance When reaction occurs, equation of mass balance can be modified for each specie, replacing mass by mole. Let n A,0 = initial mass of specie A in the system n A,t = mass of specie A in the system at time t n A,i = mass of specie A in inlet stream(s) n e = mass of specie A in exit stream(s) n gen = mass of specie A generated n con = mass of specie A consumed n A,t n A, 0 = n A, i n A,e + n A,gen n A,con
The use of For an open and steady-state process n A,t na, 0 = 0 From the definition of extent of the reaction ( ), = n A,out n A,in A For reacting species (reactants); n A,con = n A,out n A,in = A For producing species (products); n A,gen = n A,out n A,in = A
Example of ammonia production (open, steady state process): N 2 + 3H 2 2NH 3 6 gmol NH 3 18 gmol H 2 15 gmol N 2 Reactor 9 gmol H 2 12 gmol N 2 Species mole balance can be written as follow; For H 2 ; n H2,con = n H2,out n H2,in = 9 18 = 9 gmol reacted For N 2 ; n N2,con = n N2,out n N2,in = 12 15 = 3 gmol reacted For NH 3 ; n NH3,gen = n NH3,out n NH3,in = 6 0 = 6 gmol produced
Example 10: Reaction in which the fraction conversion is specified The chlorination of methane occurs by the following reaction: CH 4 + Cl 2 CH 3 Cl + HCl Determine the product composition if the conversion of the limiting reactant is 67%, and the feed composition in mole percent is 40% methane, 50% chlorine gas, and 10% nitrogen gas.
Processes involving multiple reactions For open, steady-state processes with multiple reactions, R n A,e n A,i = ij j Where ij = j = R = j=1 Stoichiometric coefficient of specie i in the reaction j in the minimal reaction set extent of reaction for the j th reaction, in which component i is present in the minimal set number of independent chemical reactions
The Minimal Set The minimal set is the set of independent chemical reactions among all the multiple chemical reactions occur in the process of interest. Consider the carbon dioxide (CO 2 ) generation; C + O 2 CO 2 (1) C + ½ O 2 CO (2) CO + ½ O 2 CO 2 (3) The independent reactions are (1) and (2), since reaction (3) is the operation of (1) and (2).
Example 11: Material balances involving two ongoing reactions Formaldehyde is produced by catalytic oxidation of methanol by the following reaction, CH 3 OH + ½ O 2 CH 2 O + H 2 O (A) Unfortunately, under the conditions used, a significant portion of formaldehyde can react with oxygen to produce carbon monoxide. CH 2 O + ½ O 2 CO + H 2 O (B) Methanol and twice the stoichiometric amount of air needed for complete oxidation of methanol are fed to the reactor. This results 90% conversion of methanol, and 75% yield of formaldehyde (based on reaction A). Determine the composition of product leaving the reactor.
Analysis of Bioreactor (unsteady-state process) In the anaerobic fermentation of grain, the yeast Saccharomyces cerevisiae digests glucose from plants to form ethanol (C 2 H 5 OH) and propenoic acid (C 2 H 3 CO 2 H) by the following reactions: Reaction 1: C 6 H 12 O 6 C 2 H 5 OH + 2CO 2 Reaction 2: C 6 H 12 O 6 C 2 H 3 CO 2 H + 2H 2 O In a process, a tank is initially charged with 4,000 kg of a 12% glucose solution (in water). After fermentation, 120 kg of CO 2 have been produced and 90 kg of unreacted glucose remain the the broth. What are the weight percent of ethanol and propenoic acic in the broth at the end of the process?
Combustion Process Combustion is a reaction of substance with oxygen, with the association of energy released and generation of product gases such as H 2 O, CO 2, CO and SO 2. Most combustion uses air as a source of oxygen. We usually approximate the composition of air as it contains 79%mol N 2 and 21%mol O 2, with MW =29 O entering - O required O required 2 2 %Excess Air = x 100 2
Example 12: Excess Air Calculation Fuels other than gasoline are being used for motor vehicles because the create lower levels of pollutants than gasoline does. Compressed propane (C 3 H 8 ) is one such proposed fuel. Suppose that 20 kg of C 3 H 8 is burned with 400 kg of air to produce 44 kg of CO 2 and 12 kg of CO. What is the percent excess air? C 3 H 8 + 5O 2 3 CO 2 + 4H 2 O
Element Balance Element balance is useful when the exact stoichiometric equations are not known. For element balance, there will be no generation nor consumption terms in the material balance equations. All elements are conserved through out the reactions. Example 13: Octane cracking process produces the cracked products with the following composition. C 3 H 8 19.5 %mol C 4 H 10 59.4 %mol C 5 H 12 21.1 %mol Determine the molar ratio of hydrogen to octane reacted for this process.
Example 14: Combustion of Fuel Component of coal (Fuel) %wt C 83.05 H 4.45 O 3.36 N 1.08 S 0.70 Ash 7.36 Total 100.0 Component of Stack gas (Product) %mol CO2 + SO2 15.4 O2 4.0 N2 80.6 Total 100.0 A local utility burns coal and report the gas product as tabulated. Moisture in the fuel was 3.9%wt and the air contains 0.0048 lb water/lb dry air. The refuse showed 14% unburned coal, with remainder being ash. You are asked to check the consistency of the report, and find the percent excess of air used.