MEB - Reactions & Energy Balance
Nomenclature - Reaction types
Combustion
Neutralization: combine an acid and a base
Saponification: caustic (base) plus fats into soap and alcohol
Hydration: react with water
Dehydration: remove water
Hydrogenation: add hydrogen (H2)
Dehydrogenation: remove hydrogen (H2)
Fermentation: transform sugar into alcohol plus carbon dioxide
Named reaction: Ostwald, Haber, Claus, photosynthesis
Stoichiometry
Use proper methods to balance a reaction from the word statement
Keep track of the inert in the mass balance equations and given information, not the reaction (if applicable)
Find the limiting reactant by comparing the mole ratios of the reactants used in the balanced equation to the initial amounts of each reactant present
A reaction is aA + bB —> cC + dD, you must determine a, b, c, d by balancing the equation, ensuring that the number of atoms for each element is equal on both sides of the equation
Then determine the amount of every reactant by taking the moles of the reactant divided by the stoichiometric coefficients, the smallest one is the limiting reactant.
Calculations
%A Excess = (moles of A initial) - (moles of A stoich) / (moles of A stoich) *100%
Can exceed 100% but cannot be negative
Conversion = fA = (moles of A reacted) / (moles of A fed) = (moles of A fed) - (moles of A unreacted) / (moles of A fed)
Most useful on limiting reactant
fA does not need to be the same as fB
fA does not need to go to 1 (only true if reaction goes to completion)
Reactions usually start at fA = 0.0, but not always true
Extent Notation
u = ‘upsilon’
Let:
uA = -a
uB = -b
uC = c
uD = d
Reactants have a negative sign
Products have a positive sign
Overall change in moles due to reaction is the summation of ‘upsilon’ for A, B, C, D
This is helpful for writing generalized mole balances for reactors
Extent = E = (moles of i exiting) - (moles of i fed) / u of i [=] no units
E of i = (E of i)*(u of i) = (moles of i) - (moles of i initially) [=] moles of i
Note that E has no units, E of A has unites of moles of A
Single pass conversion of A = f of A = -E of A / moles of A initially = (-u of A)*(E) / moles of A initially
Single pass conversion of B = f of B = -u of B / moles of B initially = (-u of B)*(E) / moles of B initially = (-u of B / u of A)*(E of A) / moles of B initially
Words for Describing Feed
Stoichiometric [n of A initially = a, n of B initially = b, . . .]
Equi-molar [n of A initially = n of B initially = . . .]
Equi-mass [m of A initially = m of B initially = . . . need MWs to convert to moles]
Specified amount(s) [n of A initially = 100 mol/min, n of B initially = 75 mol/min]
Limiting and excess [A is limiting, B is added at 50% excess]
You choose a basis [You pick 100 mol/min of limiting or A]
Three Methods
Mass/Mole balance with the reactor unit operation
Species Balance (straight forward extrapolation on methods we already use)
Extent (very similar to species balance, less writing)
Atom Balance (works even if stoichiometry is unknown, may have complex algebra sets such as solving four equation - for unknowns simultaneously)
When writing equations for species balance you need to include the generation and consumption terms now and recall the u sign convention based on the reaction
When writing equations for the extent method you need to define and add the extent value
When writing equations for atom balance you do not use the reaction or stoichiometry, the DOF changes, you count atoms and not moles, the equations are atom balances and not mole balances, and you need a list of all molecules and atom types participating
Multiple Reactions
The general mole balance: n of i out = n of i in + the summation of (u of i of j / u of LR j of j)*(E of LR j of j) where i = species and j = reaction
i ranges over all the species and j over the reactions
Choose a limiting reactant for each reaction, do not need to be the same species between reactions (will be - for reactant or + for product)
n of i out = n of i in + (u of i of 1 / u of LR 1 of 1)*(E of LR 1 of 1) + (u of i of 2 / u of LR 2 of 2)*(E of LR 2 of 2) + (u of i of 3 / u of LR 3 of 3)*(E of LR 3 of 3) + (u of i of 4 / u of LR 4 of 4)*(E of LR 4 of 4)
How to Decide Which Method to Use
Do you know all the entering and exiting species? —> all methods are good
Do you know (or can you figure out) the actual reactions? —> species of extent are easier to solve
Given information —> conversions = use extent, molar flows of reactants in and products out = use species if know the reactions, use atom if you do not know the reactions
If i ee that my basis is in outside/overall equations, but the reaction info is inside the recycle loop I can move my basis by looking at all the equations, see if there is a set of equations where if I knew one thing it would help me find lots of things
Energy Balance Start
New ways to specify mass balance information
Basic information on a few ways to describe separations, based on phase change
Determine the energy associated with mass balances (air conditioning, boiler operation (reaction), distillation, condensation/evaporation)
Learn new types of unit operations that include energy changes, phase changes, and combined mass and energy changes
Specify inputs: volume of given concentration (molarity, molality)
Energy characteristics: temperature, pressure (total, partial, vapor), volume, phase
Describe the complex relationship between pressure, temperature, volume, amount (moles) with an Equation of State
Useful Properties to Describe Energy/Mass Balance Terms
Density: mass / volume or mole / volume
Specific Volume: volume / mass
Pressure, Partial: P of A
Pressure, Vapor: VP of A
Solubility: how much of A dissolves into B, single phase (solvent = more of, solute = less of)
Heat Capacity: energy needed to increase temperature of something
How to find these property values? look it up, estimate with an equation, or from an experiment
Density
Liquids and Solids, V increases as T increases or P decreases
Change is often very small, assume negligible for small to meduym change in T (delta-T of 100 oC) and very large change in P (several hundred atm)
How to find density of a mixture?
Mass fraction weighted density is the summation of (x of i)8(specific p of i)
Mass fraction weighted specific volume is the summation of (x of i)*(specific V of i)
Overbar = average
Caret = specific or unit basis (ex. volume per unit mass)
Ideal Gas Law
The IGL is an equation of state that relates the three fundamental properties of a material with the amount of material (P, T, V)
Amount of material: n = moles, m = mass, recall n*MW = m
PV = nRT
Conditions for ideal gas
no molecular scale interaction between molecules
simple molecules (contain few atoms)
low pressure (compared to critical pressure)
high temperature (compared to critical temperature)
Ideal gas can be pure substance or mixture as long as all conditions are met
A vapor will not behave as an ideal gas
Mixtures
Can be considered ideal if most of the components are ideal
Air (nitrogen and oxygen) at room conditions
Humid air (nitrogen, oxygen, water vapor <5%) at room conditions
NOT steam with some air
Ideal properties do not change based on composition
P, V, T density can all be calculated using the ideal gas law even for mixtures
Consider the mixing of a liquid and a gas (different species)
Some gas will dissolve into the liquid [absorption]
Some liquid will vaporize (form a vapor in the gas) [evaporation or stripping]
A vapor in the gas may join the liquid [condensing]
Each type is a separation unit operation
Assume that equilibrium happens quickly
All are based on vapor pressure relationship called Vapor-Liquid-Equilibrium
Data is present in P-x-y or T-x-y diagrams, where P = pressure, T = temperature, x = liquid concentrations, and y = vapor concentrations
Gas with one species in vapor phase (single condensable)
Vapor pressure from Antoine relationship
P* = Vapor pressure = saturation pressure, when liquid and vapor coexist
Only true if there is just one condensable
Only true if that vapor species is at a low concentration in the gas
Example: Air with water in it
Gas with more than one species in vapor phase (multi condensable)
Vapor pressure from Raoult’s law
One condensable vapor
A condensable vapor in equilibrium with its liquid must be saturated
The partial pressure of a condensable vapor cannot exceed its vapor pressure for a given T and if it did it would be a super-saturated and some will condense/vaporize
If the partial pressure is less than its vapor pressure, the vapor is superheated (even though it is the pressure that causes it), more liquid could evaporate
When a gas with one condensable is cooled at constant pressure, and the vapor pressure equals the partial pressure, it will start to condense [called the Dew Point]
Definitions For Mixtures of Gas + Vapor
Applies when only one species is vapor
General (water) cases concerning Saturation (Humidity)
T = temperature
P = Total Pressure
Pi = Partial Pressure of species i at given (T,P)
P* = Vapor Pressure of species i at given (T,P) from Antoine equation (look up in steam table)
Relative Saturation, sr (relative humidity, hr)
Ratio of partial pressure to vapor pressure
sr = Pi / P* *100%
Molal Saturation, sm (molal humidity, hm)
Ratio of vapor moles to moles of vapor free gas
sm = Pi / (P - Pi)
Absolute Saturation, sa (absolute humidity, ha)
Mass of vapor to mass of vapor free gas
sa = MWi(Pi) / MWdry (P - Pi)
Percent Saturation sp (percent humidity)
Ratio of (ratio of vapor moles to moles of vapor free gas) to (ratio of vapor moles to moles of vapor free gas) at saturation
sp = Pi (P - P*) / (P - Pi) P*i
If you know any one of these at a given T and P, then you can determine all the others
Partial Pressure
Since all parts act ideal we can sum parts to create the whole
Moles, pressure and volume, not temperature
Only use partial volume if P and T are exactly the same, of not, find moles associated with each set of conditions, add the moles, then convert back to volume
Phase Diagrams
Identify the phase(s) present at a given [T, P] for a particular substance
Inform on how the material may behave when changing [T, P]
Isothermal
Isobaric
Phase diagrams can also use volume in place of T or P, the plots are similar
Isochoric
Isothermal transition - T stays the same, P changes
Transitions take time and energy to complete
Isothermal transitions are the transitions from A to B showing the substance starting as a vapor and becoming a liquid - only P changes
Note how it crosses a line, the line represents the conditions when the transition happens
Distinct change in properties (density, appearance, phase, etc.)
Isobaric transitions are the transitions from A to B having the substance starting as a liquid and becoming a vapor - this time only T changes
The line represents the conditions when the transition happens
Distinct change in properties
During the transition (phase change (all the energy added (removed) goes towards altering the amount of each phase, so the T,P remains constant
If we know the energy content of the mixture, we will be able to determine how much is liquid and how much is vapor
These graphs are general representations of typical features for pure substances
Specific substances will have differences in:
Location of critical and triple point
Shape of saturation curves
Slope of lines
Number of phases (multiple solid phases are typical)
The saturation line becomes an envelope
Boils or condenses over a range, not just a single value of T or P
Dew Point is when the first from of liquid forms from vapor
Bubble Point is when the first bubble of vapor forms from liquid
System never exists in two-phase-region rather than two phases coexist, but each phase will have a different composition
Compositions determined by using a horizontal line
Isothermal for Txy diagram
Isobar for Pxy diagram
Raoult’s Law approximates vapor phase mole fraction of a dilute species in a liquid
Works best when components [A and B] are similar
Error grows as concentration increases
Henry’s Law is a data fit of gas solubility in a liquid
Requires data from direct observation not first principles
Add and isotherm (line of constant temperature)
Reveals compositions of the phases in the two-phase region [vapor and liquid]
Add a line of single-phase composition (either all vapor or all liquid)
Reveals dew and bubble points
Together they provide the amount and composition of the substance at any temperature (single and two phase regions)
Standard Conditions and Vapor Pressure
It is common to report gas flow in units of:
scm [standard cubic meters]
scf [standard cubic feet]
On a dry basis (exclude water from mole fraction calculation)
dscm [dry standard cubic meters]
dscf [dry standard cubic feet]
Convert from actual conditions (a) to standard conditions (s)
Assumes moles remain constant and R values cancel:
PaVa / Ta = PsVs / Ts
Rearrange as needed
Vapor Pressure
Vapor pressure represents the gas phase pressure exerted by a liquid at a given total pressure and temperature
VP exists along entire saturation line of pressures for a given temperature
The saturation line represents all the points where liquid and vapor can coexist in any ratio (the vapor pressures)
Think of it as the boiling or condensing points
If P actual > VP, the substance will be all liquid
If P actual < VP, the substance will be all vapor
If P actual = VP, the substance can convert between liquid and vapor and the phases can coexist - the entire amount of substance can transition between vapor and liquid and the entire range of ratios of liquid-vapor is allowable [0,1]
Behavior will be different when we have mixtures
All pure substances have a unique vapor pressure at a given T and P
VP = P vapor = P sat = P* = f[T,P]
Mixtures will have a range of [T,P] values where the two phases coexist
How to obtain VP
Look up in table of [substance, T, VP] or [substance, P, VP]
Often the table provides data in the form of constants and a temperature dependent function
Antoine Equation - where P* [=] mmHg and T [=] oC
The equation is given by: where A, B, and C are constants unique to a substance
NOTE: Valid only in given range and must be below critical point! Will not work for gas phase - might work for some solids
Steam Tables Provide
Temperature
Pressure
Specific volume
Specific internal energy
Specific enthalpy
Specific entropy
Enthalpy
Very useful description of energy content of a substance in an ‘as-is’ state
H = U + PV
Internal energy is the energy associated with temperature (average of the quantum states of the molecules - electrons, bonds, vibrations, rotations, translations)
PV-hat: flow work, energy needed to arrange substance in its phase - accounts for attraction/repulsion forces between molecules
Quality
Measure of the vapor mass fraction of a two-phase mixture
X = mass of vapor / (mass of vapor + mass of liquid)
X = 0 all liquid
X = 1 all vapor
Anything in between is allowed
May use U or H to determine it, may not use T or P
Raoult’s Law
[Ideal gas in contact with a liquid mixture]
Assumes Ideal Gas and Ideal Liquid Mixture Solution - want to know how much one of the liquids will evaporate into the ideal gas above it
Works for very dilute liquid mixtures (a few percent)
yi = xi (P*i / P)
Where
yi is the vapor phase mole fraction of species i
xi is the vapor phase mole fraction of species i
P* is the vapor pressure of species i at system temperature, obtain from Antoine’s equation
P is total pressure of system
Henry’s Law
One gas, One liquid
Assumes low liquid phase concentration of the gas (it applies to the solubility of the gas in contact with a certain liquid) - it can apply to non-ideal systems
yi = xi (Hi / P)
Where
yi is the vapor phase mole fraction of species i
xi is the vapor phase mole fraction of species i
Hi is the Henry’s Law constant of gas species i in the liquid
P is total pressure of system