Colligative Properties of Solutions

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FST 151 FOOD FREEZING FOOD SCIENCE AND TECHNOLOGY
151 Food Freezing (Basic concepts) Lecture
Notes Prof. Vinod K. Jindal (Formerly
Professor, Asian Institute of Technology) Visiting
Professor Chemical Engineering
Department Mahidol University Salaya,
Nakornpathom Thailand
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Definitions Chilling Temperatures between
15oC and slightly above freezing point.
Freezing From slightly below freezing point to
-18oC.
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Purpose Freezing stops / retards - Growth
of microorganisms - Rate of chemical
reactions - Enzyme activity - Moisture loss, if
properly packaged
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Advantages of freezing Preservation of
color, flavor and nutritive value.
Microorganisms do not grow and multiply during
frozen storage. Freezing kills some
vegetative cells. Spores survive, and may grow
when the food is thawed.
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Disadvantages of freezing Deterioration of
texture depending on the nature of food and the
freezing process Minor losses in nutritive
value and quality Expensive preservation
operation, and requires energy even after the
operation is complete Depending on the
storage conditions, frozen foods may also lose
water
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• The engineering aspects of the freezing
• process deal with the following
• Computing the refrigeration requirements needed
  to accomplish the desired reductions in product
  temperature
• Determining the freezing time needed to reduce
  product temperature to desired levels
• Understanding the changes occurring within the
  food product during frozen food storage.

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A matter can exist in three states or phases
by changing the temperature and/or pressure
- Gas - Liquid - Solid
Some basic concepts related to freezing
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PHASE TRANSISTIONS

• SOLID TO LIQUID MELTING
• LIQUID TO SOLID FREEZING
• GAS TO LIQUID CONDENSATION
• LIQUID TO GAS EVAPORATION
• SOLID TO GAS SUBLIMATION
• GAS TO SOLID DEPOSITION

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PHASE CHANGES
Sublimation
Melting
Boiling
Solid
Liquid
Gas
Freezing
Condensation
Deposition
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PHASE CHANGES

• Freezing point (FP) the temperature where
  liquids change into solids
• Melting point (MP) the temperature where
  solids change into liquids
• Boiling point (BP) - the temperature where
  liquids change into gases

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HEAT TRANSFER

• Exothermic heat is removed from the system
• Endothermic heat is added to the system

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EXOTHERMIC

• Freezing
• Condensation
• Deposition

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ENDOTHERMIC

• Melting
• Boiling
• Sublimating

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SPECIFIC HEAT CAPACITY

• A substances resistance to temperature change
  when heat is added or removed. Symbol is c.
• Measured in J/gC
• Joules are a measurement of energy
• 4.184 J 1 calorie 1000 calorie 1 k calorie
• Specific heat is a physical property.
• High specific heat requires more heat to change
  the temperature.
• Water has a very high specific heat.
• cwater 4.184 J/gC
• cice 2.05 J/gC
• cwater vapor 2.08 J/gC

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PHASE CHANGE HEAT CHANGE

• Heat of vaporization (Hvap) the amount of heat
  required to change 1 g of a substance from liquid
  to gas or gas to liquid.
• q mHvap
• Heat of fusion (Hf) the amount of heat required
  to change 1 g of a substance from liquid to
  solid or solid to liquid
• q mHf
• Hvap for water 2260 J/g
• Hf for water 334 J/g
• Does it take more energy to boil 100 g of water
  or freeze 100 g of water?

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PHASE CHANGE PROBLEM

• How much energy is required to boil 250 g of
  water that is at 100C?
• q mHvap
• q heat energy
• m mass in grams
• Hvap heat of vaporization of water

q mHvap q 250g x 2260 J/g q 565,000 J
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THREE STEP PROBLEM

• How much energy is released when 500 g of liquid
  water at 25C is cooled to -15C?
• First calculate 25C to 0C
• Next, calculate freezing
• Next, calculate 0C to -15 C
• Finally, add them together

q mc?T q 500g x 4.184 J/gC x 25C q
52,300 J
q mHf q 500g x 334J/g q 167,000J
q mc?T q 500g x 2.03 J/gC x 15C q
15,225 J
52,300J 167,000J 15,225 234,525 J
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PHASE CHANGE DIAGRAM

• Things to notice
• Pressure and temperature both affect the phase of
  matter.
• All three phases of matter exist at the triple
  point

Melting/Freezing
Boiling/Condensating
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In the phase diagram for pure water, three lines
indicate the phase transition between solid,
liquid and gas. All three lines meet at the
triple point where all three phases are in
equilibrium. If the pressure is lowered, we note
that the boiling point will be lowered and the
melting point raised (very slightly).
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Now look at the following diagram indicating the
phase transitions for pure water and for water
with some solute dissolved in it (not to scale).
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Freezing Point Depression
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Phase Change Freezing/Melting

• Liquid cools at constant rate

Temperature

• Liquid starts freezing

• More more liquid freezes

FP
Time
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Actual Freezing

• Rounded T not uniform throughout

Temperature
FP
Time
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Freezing Freezing Point

• A pure liquid will freeze when enough internal
  energy is removed from the system to the
  surroundings, this is usually initiated by a
  decrease in the surroundings temperature (an
  exothermic process).
• The exact temperature at which the solid phase is
  in equilibrium with the liquid phase is referred
  to as the Freezing or Melting Point and if the
  pressure is 1 atm (760 mmHg) then that
  temperature is called the normal
  Freezing/Melting Point.

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Freezing Point Depression in Solutions The
freezing point of pure water is 0C, but that
melting point can be depressed by the adding of a
solvent such as a salt. A solution typically has
a measurably lower melting point than the pure
solvent. A 10 salt solution may lower the
melting point to -6C (20F) and a 20 salt
solution to to -16C (2F).
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GENERAL PROPERTIES OF SOLUTIONS

• 1. A solution is a homogeneous mixture of two or
  more components.
• 2. The dissolved solute is molecular or ionic in
  size.
• 3. The solute remains uniformly distributed
  throughout the solution and will not settle out
  through time.
• 4. The solute can be separated from the solvent
  by physical methods.

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• Colligative Properties of Solutions
• Colligative properties of solutions are
  properties that depend upon the
  concentration of solute molecules or ions,
  but not upon the identity of the solute.
• Colligative properties include freezing point
  depression, boiling point elevation, vapor
  pressure lowering, and osmotic pressure.

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Colligative Properties

• Solution properties differ from those of pure
  solvent
• Proportional to molality (concentration) of
  solute
• Vapor pressure reduction
• Freezing point depression
• Boiling point elevation
• Osmotic pressure

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Colligative Property

• Magnitude of freezing point depression

Depends on concentration of solute (not identity)
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Freezing Point Depression

• Relationship for freezing point depression
  is

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Freezing point depression

• Kf molal freezing point constant
• specific to solvent
• Units C
• molal
• What is molal?

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Molality

• Concentration in molality, m

• Independent of solution volume (V varies with T)

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Freezing point depression

• Using

• and

• Substitution gives

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Kf and Kb for some solvents

• Freezing point is lower
• Boiling point is higher

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Freezing Point DepressionDTf - kf m

• Q. Estimate the freezing point of a 2.00 L
  sample of seawater (kf 1.86 oC kg / mol), which
  has the following composition
• 0.458 mol of Na 0.052 mol of Mg2 0.010 mol
  Ca2
• 0.010 mol K 0.533 mol Cl- 0.002 mol HCO3-
• 0.001 mol Br- 0.001 mol neutral species.
• Since colligative properties are dependent on the
  NUMBER of particles and not the character of the
  particles, you must first add up all the moles of
  solute in the solution.
• Total moles 1.067 moles of
  solute
• Now calculate the molality of the solution
• m moles of solute / kg of
  solvent 1.067 mol / 2.00 kg
• 0.5335 mol/kg
• Last calculate the temperature change
• DTf - kf m -(1.86 oC
  kg/mol) (0.5335 mol/kg) 0.992 oC
• The freezing point of seawater is Tsolvent - DT
  0 oC - 0.992 oC
• - 0.992 oC

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MOLALITY

• Molality moles of solute per kg of solvent
• m nsolute / kg solvent
• If the concentration of a solution is given in
  terms of molality, it is referred to as a molal
  solution.
• Q. Calculate the molality of a solution
  consisting of 25 g of KCl in 250.0 mL of pure
  water at 20oC?
• First calculate the mass in kilograms of solvent
  using the density of solvent
• 250.0 mL of H2O (1 g/ 1 mL) 250.0 g of H2O (1
  kg / 1000 g) 0.2500 kg of H2O
• Next calculate the moles of solute using the
  molar mass
• 25 g KCl (1 mol / 54.5 g) 0.46 moles of
  solute
• Lastly calculate the molality
• m n / kg 0.46 mol / 0.2500 kg 1.8 m
  (molal) solution

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Molality and Mole Fraction

• Two important concentration units are
• by mass of solute

1. Molarity

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Molality and Mole Fraction (contd)

• Molality is a concentration unit based on the
  number of moles of solute per kilogram of solvent.

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Food Freezing Theory

• During freezing, sensible heat is first removed
  to lower the temperature of a food to the
  freezing point. In fresh foods, heat produced by
  respiration is also removed. This is termed the
  heat load, and is important in determining the
  correct size of freezing equipment for a
  particular production rate.

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• A substantial amount of energy is therefore
  needed to remove latent heat, form ice crystals
  and hence to freeze foods.
• The latent heat of other components of the food
  (for example fats) must also be removed before
  they can solidify but in most foods these other
  components are present in smaller amounts and
  removal of a relatively small amount of heat is
  needed for crystallization to take place.

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FOOD FREEZING

• Temperature lowered
• Most water transformed into ice crystals
• Liquid phase concentrated
• As volume of ice 10 larger than volume of water,
  internal pressure in the food rised to 10 bar or
  more

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Freezing Curve A typical freezing curve of a
food consists of the following regions The
initial sensible heat removal section To bring
it to the freezing point. the temperature
changes but without change in phase.
Supercooling In slow freezing, food temperature
may drop temporarily below the freezing point,
without phase change. Latent heat When ice
crystals form, they release heat of fusion, and
temperature increases to the freezing point.
Final sensible heat removal Frozen foods are
kept at or below -18oC. Since the freezing
points of most foods is above that, we need to
cool the frozen food.
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Figure 1. Typical freezing curve of foods
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Typical Freezing Curve (food)
3-21
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SUPERCOOLING
A
Removal of sensible heat
Temperature
Removal of latent heat
Removal of sensible heat
Cooling time
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• During freezing the product temperature decreases
  gradually as the latent heat of fusion is removed
  from water within the product.
• In foods the equilibrium temperature for initial
  formation of ice crystals is lower than the
  equilibrium temperature for ice crystal formation
  in pure water.
• The magnitude of the depression in equilibrium
  freezing temperature is a function of product
  composition.

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• After the formation of initial ice crystals in
  the food product, the removal of phase change
  energy occurs gradually over a range of
  decreasing product temperatures.
• The temperaturetime relationship during phase
  change is a function of the percent water frozen
  at any time during the freezing process.
• The shape of the temperaturetime curve during
  the freezing process will vary with product
  composition and with the location within the
  product structure.

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• The gradual decrease in temperature with time
  will continue until reaching the eutectic
  temperatures for major product components. In
  practice, food products are not frozen to
  sufficiently low temperatures to reach these
  eutectic temperatures.

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Timetemperature data during freezing.
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• AS The food is cooled to below its freezing point
  f which, with the exception of pure water, is
  always below 0ºC . At point S the water remains
  liquid, although the temperature is below the
  freezing point. This phenomenon is known as
  supercooling and may be as much as 10ºC below the
  freezing point.
• SB The temperature rises rapidly to the freezing
  point as ice crystals begin to form and latent
  heat of crystallisation is released.

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• BC Heat is removed from the food at the same rate
  as before, but it is latent heat being removed as
  ice forms and the temperature therefore remains
  almost constant. The freezing point is gradually
  depressed by the increase in solute concentration
  in the unfrozen liquor, and the temperature
  therefore falls slightly. It is during this stage
  that the major part of the ice is formed .
• CD One of the solutes becomes supersaturated and
  crystallizes out. The latent heat of
  crystallization is released

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• DE Crystallization of water and solutes
  continues. The total time tf taken (the freezing
  plateau) is determined by the rate at which heat
  is removed.
• EF The temperature of the icewater mixture falls
  to the temperature of the freezer. A proportion
  of the water remains unfrozen at the temperatures
  used in commercial freezing the amount depends
  on the type and composition of the food and the
  temperature of storage. For example at a storage
  temperature of -20ºC the percentage of water
  frozen is 88 in lamb, 91 in fish and 93 in egg
  albumin.

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INITIAL FREEZING POINT OF DIFFERENT FOODS (OC)

• Beef -1.1
• Common fruits - 0. to 2.7
• Common vegetables - 0.8 to 2.8
• Eggs - 0.5
• Milk - 0.5

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Effects of Freezing The goal of freezing is
to reduce the temperature of the food below
-18oC This results in the crystallization of
part of the water and some of the solutes
in the food Water in the frozen state does
not act as a solvent, can not enter into
chemical reactions, and is not available
to microorganisms.
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Effect of water Water has a major impact on
the freezing behavior of foods. Most foods
contain large amounts of water
(fruits/vegetables up to 90 wt water, meats
65 - 75 water). Freezing point, the heat
capacity above and below freezing, and the
latent heat of freezing are strongly affected by
the moisture content.
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Freezing point Pure water freezes at 00C
under 1 atm. The freezing point of foods will
be close to 00C depending on the amount of water
present. In general, the higher the moisture
content, the closer the freezing point to 00C.
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Water binding The degree of binding of water
by the food is also important. Water that
is tightly bound will not freeze as readily as
"free water". In foods, there are inorganic
and organic substances such as sugars, acids,
salts, colloids, etc. dissolved in water.
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Supercooling It is possible to reduce the
temperature of water below 00C, and still have
liquid water at 1 atm. This is called
supercooling. If we cool a solution with no
ice crystals, the temperature can be lowered
below the freezing point. Supercooling is an
unstable and temporary state. It occurs because
there is no "nucleus" for the crystals to form
around. Occurrence of supercooling depends on
the rate of freezing.
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Crystallization of Water Formation of a
regularly organized solid phase from a
solution. There are two steps in the
process Nucleation Crystal growth
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Nucleation When the first ice crystal forms,
it starts nucleation and the solidification
process. The nucleus occurs homogeneously or
heterogeneously. In very pure water,
nucleation is homogeneous, the "nucleus" is
water molecules orienting as crystals.
Homogeneous nucleation does not occur in
foods. In heterogeneous nucleation, crystals
form around foreign particles, surface films,
container walls. Ice crystal formation is easier
in this case.
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• Crystal growth
• The rate of crystal growth depends on
• - How fast water molecules get to the
  nucleus.
• - How fast heat is removed from the system
  to favor orientation and ordering of the
  water molecule.

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• Crystal growth
• If a material is cooled rapidly, the rate of
• nucleation is greater than the rate of crystal
  growth, and many small crystals
• will form.
• These crystals have no time to attract
• more water molecules and grow because new
  crystal formation is faster, and it consumes the
  available water.

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Crystal growth If the rate of cooling is
slow, the rate of crystal growth is faster than
the formation of new crystals, and there will
be a smaller number of large crystals. At
temperature near the melting point, water
molecules add to the mass of the nucleus rather
than forming new nuclei.
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Freezing point In foods, there are solutes,
suspended matter, and cellular material in
solution. Ice crystals "squeeze" other
molecules out. Solutes get concentrated.
This reduces the freezing point. In most
foods, there is a narrow range of temperature at
which freezing occurs.
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Ice crystals The number and shape of ice
crystals has a major effect on the quality of
frozen foods. Large crystals damage the
tissue. Meat, poultry, fish, shellfish, fruit
and vegetable cells contain jelly-like
protoplasm. Large ice crystals puncture cells.
After thawing, they cannot reach their former
state. Small crystals do not injure the
tissue as much. When thawed, they can be
re-absorbed into the protoplasm. Thaw-drip is
minimized.
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The location of ice crystals in food tissues
depends on freezing rate, temperature, nature of
the cells. Slow freezing (less than 10C/min)
causes the crystals to form exclusively in the
extracellular spaces. This shrinks the cells,
disrupts tissues and results in lower quality.
Freezing starts at extracellular space. Inside
the cell is a supercooled solution. Its water
vapor pressure is higher than that of
extracellular ice. This difference in vapor
pressure causes water to migrate from inside the
cell to extracellular space.
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Re-crystallization Largest possible size, and
no defects in the crystal lattice is the
thermodynamically stable form of a crystal.
Small crystals try to coalesce into bigger
ones. The number, size, shape and
orientation of crystals change during storage.
The rate of re-crystallization depends on
temperature.
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Re-crystallization Lower temperature implies
slower re- crystallization. Keep foods at as
low a temperature as possible. Fluctuations in
temperature help re-crystallization. Pure
ice re-crystallizes at a significant rate at
-70oC. In regular tissue food, the rate is very
slow at -28oC.
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Eutectic Each solute has a solubility limit in
water. As more water is removed by freezing, a
point is reached where the solute is saturated
in the remaining solution at that
temperature. Further freezing of water
results in crystallization of solute together
with water. Such simultaneous crystallization
is called a eutectic and the temperature is
known as the eutectic point of the solute.
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Examples For example, a NaCl solution in water
has a eutectic point of -21oC. When this
temperature is reached, water and salt
crystallize together. Since the concentration
of the remaining solution does not change after
this point, temperature is constant until all
water and salt crystallize. Sucrose
solutions have a eutectic point of -14oC.
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Eutectic Point Temperature where there is no
further concentration of solutes due to
freezing, thus the solution freezes. Temperatur
e at which a crystals of individual solute
exists in equilibrium with the unfrozen liquor
and ice. Difficult to determine individual
eutectic points in the complex mixtures of
solutes in foods so the term Final Eutectic
Point is used This represents lowest Eutectic
temperature of the solutes in the food.
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Eutectic temperatures Ice Cream -55oC Meat
-50 to -60oC Bread -70oC MAXIMUM ICE
CRYSTALS FORMATION IS NOT POSSIBLE UNTIL THIS
TEMPERATURE IS REACHED
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Effects of Freezing Volume change Most
substances shrink when going from the liquid to
the solid state. Water is anomalous its volume
increases as it freezes. Conversion of water
to ice causes about 9 volume increase. Volume
change in food during freezing depends on its
composition. Concentrated sugar solutions do not
expand when frozen, they may even shrink.
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Volume change The change in volume depends
on Percent water. More water larger
expansion. Air pockets. They absorb the growth
of crystals. Unfreezable water. If there are
many solutes present, water is bound, and will
not freeze. Temperature. Before the freezing
point of water is reached, its volume decreases.
Maximum density is around 4oC. Below that
temperature, it will expand.
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• Effects of volume change
• During freezing some parts of food contract, and
  some expand. This causes mechanical stresses. If
  these stresses are allowed enough time to
  dissipate, there will be mo major mechanical
  damage to the material.
• If the rate of freezing is very fast (cryogenic
  freezing) the material cracks.

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Concentration Effects Freezing removes water
from the food, and the solute concentration
increases. Changes in electrolytes may
cause irreversible changes in colloidal
structures. Milk proteins may coagulate. Changes
in pH, ionic strength, viscosity, surface
tension, redox potential, freezing point, etc.
may result.