Energy balance lecture

8/13/2019 Energy balance lecture

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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: [email protected]


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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:

Energy balance lecture

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