Post on 04-Jun-2018
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PEME2210
Energy Balances
Dr Bao H. Xu
Institute of Particle Science and Engineering
School of Process, Environmental and Materials Engineering
Room 2.30; Phone: 0113 343 2423; Email: b.h.xu@leeds.ac.uk
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Mixing and solution:
When two different liquids are mixed or when a gas or solid isdissolved in a liquid, bonds are broken between neighbouring
molecules (and possibly atoms) of the feed materials, and new
bonds are formed between neighbouring molecules or ions in the
product solution.
If less energy is required to break the bonds in the feed materials
than is released when the solution bonds form, a net release of
energy results.
Unless this energy is transferred from the solution to its surroundingsas heat, it goes into raising the solution temperature.
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Suppose we mix 1mol of pure liquid sulphuric acid with water at aspecified temperature and pressure and then cool the mixture at
constant pressure to bring it back to the initial temperature.
The energy balance for this constant-pressure process is:
where H is the difference between the enthalpy of the solution at
the specified temperature and pressure and the total enthalpy of the
pure solute and solvent at the same temperature and pressure, or
heat of solutionat that temperature and pressure.
For this process, the container must be cooled to keep the solution
temperature from rising, so that Q < 0and H< 0.
OHlSOHaqSOH 24242HHHHQ
Heats of solution and mixing:
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Heats of solution and mixing:
The heat of solution, , is defined as the change in enthalpyfor a process in which 1mol of a solute (gas or solid) is dissolved in r
moles of a liquid solvent at a constant temperature T.
As rbecomes large, the heat of solution approaches a limiting value
known as the heat of solution at infinite dilution.
The heat of mixinghas the same meaning as the heat of solution
when the process involves mixing two fluids rather than dissolving a
gas or solid in a liquid.
PerrysChemical EngineersHandbook(pp. 2.201-204) gives heats
of solution of various substances in water at either 18C or 25C.
r,THs
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Reference states:
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Reference states:
From Table B.11, the specific enthalpy of hydrochloric acid solution (r= 10moles H2O/mole HCl and T = 25C), relative to pure HCl(g) and
H2O(l) is -69.49kJ/mol HCl.
Now the enthalpy of the solution relative to H2O(l) and a highly dilute
solution of HCl is the enthalpy change for the isothermal process
If taking pure HCl(g) and H2O(l) at 25C as references, the enthalpychange is
HClkJ/molrHrHHss
65.514.7549.69,2510,25
lOHmol10-10OHmol10
HClmol1
OHmol10
HClmol12
6
2
C25
26
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Test yourself:
The heat of solution of a solute A in water at 25C is -40 kJ/mol A forr = 10 mol H2O/mol A and -60 kJ/mol A for infinite dilution.
1. What is the specific enthalpy (kJ/mol A) of an aqueous solution
of A for which r = 10 mol H2O/mol A relative to (a) pure H
2O and
A at 25C and (b) pure H2O and infinitely dilute aqueous
solution of A?
2. If 5.0 mol of A is dissolved in 50.0 mol of H2O at 25C, how
much heat is evolved or absorbed?
3. How much heat is evolved or absorbed if the solution prepared
in question 2 is poured into a large tank of water at 25C .
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Procedures:
When setting up an energy balance on a process that involvesforming, concentrating, or diluting a solution for which the heat of
solution or mixing cannot be neglected, prepare an inlet-outlet
enthalpy table considering the solution as a single substance and
pure components at 25C as reference states.
To calculate the enthalpy of the solution at a temperature T(25C),
first calculate its enthalpy at 25C from tabulated heat of solution
data, then add the enthalpy change for the heating or cooling of the
solution from 25C to T from tabulated solution heat capacities if
they are available; otherwise use the average heat capacitydetermined from
for liquid mixture or heat capacity of the pure solvent for dilute
solutions.
i
piimixpTCyTC
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Example 8.5-1:
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Enthalpy-concentration chart:
Energy balance calculations onliquid-phase systems can be
simplified for binary (two-
component) systems by using
an enthalpy-concentration
chart, a plot of specificenthalpy versus mole/mass
fraction of one component.
Figure right shows the
enthalpy-concentration chart
for H2SO4 - H2O. The reference
conditions are pure liquid
H2SO4at 77F and liquid water
at 32F.
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Example 8.5-2: