Reaction Energy and Reaction Kinetics

1
Chapter 17

• Reaction Energy and Reaction Kinetics

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THERMOCHEMISTRY

• Virtually every chemical reaction is accomplished
  by a change in energy.
• Chemical reactions usually absorb or release
  energy in the form of heat.

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THERMOCHEMISTRY

• Thermochemistry is the study of the changes in
  heat energy that accompany chemical reactions and
  physical changes.
• The heat absorbed or released in a chemical or
  physical change is measured in a calorimeter.

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THERMOCHEMISTRY

• In a calorimeter, known quantities of reactants
  are sealed in a reaction chamber, which is
  immersed in a known quantity of water in an
  insulated vessel.
• The heat given off or absorbed during the
  reaction is equal to the heat absorbed or given
  off by the known quantity of water.

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THERMOCHEMISTRY

• The amount of heat is determined from the
  temperature change of the known mass of the
  surrounding water.
• The data collected from calorimetry experiments
  are temperature changes because heat cannot be
  measured directly, but temperature can be.

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THERMOCHEMISTRY

• What is the difference between heat and
  temperature?
• Temperature is the measure of the average kinetic
  energy of the particles in a sample of matter.
• To measure temperature we use the Celsius and
  Kelvin scales.
• Kelvin Celsius 273.15

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THERMOCHEMISTRY

• The ability to measure temperature is based on
  heat transfer.
• The amount of heat transfer is usually measured
  in joules (J).
• A joule is the SI unit of heat energy as well as
  all other forms of energy.

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THERMOCHEMISTRY

• Heat can be thought of as the sum total of the
  kinetic energies of the particles in a sample of
  matter.
• Heat always flows spontaneously from matter at a
  higher temperature to matter at a lower
  temperature.

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THERMOCHEMISTRY

• The quantity of heat transferred during a
  temperature change depends on
• The nature of the material changing temperature.
• The mass of the material changing temperature.
• The size of the temperature change.

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THERMOCHEMISTRY

• A quantity called specific heat can be used to
  compare heat absorption capacities for different
  materials.
• Specific Heat is the amount of heat energy
  required to raise the temperature of one gram of
  a substance by one Celsius degree or one Kelvin.

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THERMOCHEMISTRY

• Specific Heat is measured in units of
  Joules/gramCelsius (J/gC) or
  calories/gramKelvin (cal/gK) or
  calories/gramCelsius (cal/gC).
• Table 17-1, page 513.

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THERMOCHEMISTRY

• Specific Heat is usually measured under constant
  pressure conditions, so its symbol, cp, contains
  a subscripted p as a reminder.
• Specific heat can be found using the following
  equation
• cp q/(m ?T)

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THERMOCHEMISTRY

• cp Specific Heat
• q Heat lost or gained
• m mass of the sample
• ?T Difference between the
• initial and final temperatures.

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THERMOCHEMISTRY

• EXAMPLE
• A 4.0 g sample of glass was heated from 274 K to
  314 K, a temperature increase of 40 K, and was
  found to have absorbed 32 J of heat. What is the
  specific heat of this type of glass? How much
  heat will the same glass sample gain when it is
  heated from 314 K to 344 K?

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THERMOCHEMISTRY

• EXAMPLE
• Determine the specific heat of a material is a 35
  g sample absorbed 48 J as it was heated from 293
  K to 313 K.

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THERMOCHEMISTRY

• EXAMPLE
• A piece of copper alloy with a mass of 85.0 g is
  heated from 30 C to 45 C. In the process, it
  absorbs 523 J of heat. What is the specific heat
  of this copper alloy? How much heat will the
  sample lose if it is cooled to 25 C?

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THERMOCHEMISTRY

• EXAMPLE
• The temperature of a 74 g sample of material
  increases from 15 C to 45 C when it absorbs 2.0
  kJ of heat. What is the specific heat of this
  material?

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THERMOCHEMISTRY

• EXAMPLE
• How much heat is needed to raise the temperature
  of 5.0 g of gold by 25 C?

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THERMOCHEMISTRY

• EXAMPLE
• What mass of liquid water at room temperature (25
  C) can be raised to its boiling point with the
  addition of 24 kJ of heat energy?

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THERMOCHEMISTRY

• EXAMPLE
• Heat in the amount of 420 J is added to a 35 g
  sample of water at a temperature of 10 C. What
  will be the final temperature of the water?

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THERMOCHEMISTRY

• The heat of reaction is the quantity of heat
  released or absorbed during a chemical reaction.
• You can think of heat of reaction as the
  difference between the stored energy of the
  reactants and the products.

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THERMOCHEMISTRY

• EXAMPLE
• 2H2(g) O2(g) --gt 2H2O(g)
• If a mixture of hydrogen and oxygen is ignited,
  water will form and heat energy will be released.
• The heat released comes from the formation of the
  product (water).

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THERMOCHEMISTRY

• Chemical equations do not tell you that heat is
  evolved during the reaction.
• Experiments show that 483.6 kJ of heat are
  evolved when 2 mol of gaseous water are formed at
  298.15 K from its elements.

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THERMOCHEMISTRY

• Thermochemical equations include the quantity of
  heat released or absorbed during the reaction.
• 2H2(g) O2(g) --gt 2H2O(g) 483.6 kJ
• The quantity of heat for any reaction depends on
  the amounts of reactants and products.

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THERMOCHEMISTRY

• Producing twice as much water vapor would require
  twice as many moles of reactants, and would
  release twice as much heat.
• 4H2(g) 2O2(g) --gt 4H2O(g) 967.2 kJ

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THERMOCHEMISTRY

• Producing one-half as much water would require
  one-half as many moles of reactants and would
  release only one-half as much heat.
• H2(g) 1/2O2(g) --gt H2O(g) 241.8 kJ

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THERMOCHEMISTRY

• Fractional coefficients are sometimes used in
  thermochemical equations.
• In chemical reactions, heat can either be
  released or absorbed.
• Exothermic release of heat
• Endothermic absorption of heat

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THERMOCHEMISTRY

• In writing thermochemical equations for
  endothermic reactions, the situation is reversed
  because the products have a higher heat content
  than the reactants.
• Decomposition of water
• 2H2O(g) 483.6 kJ --gt 2H2(g) O2(g)

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THERMOCHEMISTRY

• The physical states of the reactants and products
  must always be included in thermochemical
  equations because they influence the overall
  amount of heat exchanged (Ex Ice).

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THERMOCHEMISTRY

• The heat absorbed or released during a chemical
  reaction at constant pressure is represented by
  the symbol H.
• The H is the symbol for a quantity called
  enthalpy.
• Enthalpy is the heat content of a system at
  constant pressure.

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THERMOCHEMISTRY

• Most chemical reactions are run in open vessels,
  so the pressure is constant and equal to
  atmospheric pressure.
• Only changes in enthalpy can be measured (?H
  Enthalpy change).

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THERMOCHEMISTRY

• Enthalpy change is the amount of heat absorbed or
  lost by a system during a process at constant
  pressure.
• ?H Hproducts - Hreactants

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THERMOCHEMISTRY

• Thermochemical equations are usually written by
  designating the value for ?H rather than writing
  the heat as a reactant or product.
• Exothermic reactions have a ?H that is always
  negative, because the system loses energy.
• 2H2(g) O2(g) --gt 2H2O(g) ?H -483.6 kJ

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THERMOCHEMISTRY

• The ?H for endothermic reactions is always
  positive, because the system gains energy.
• 2H2O(g) --gt 2H2(g) O2(g) ?H 483.6 kJ

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THERMOCHEMISTRY

• Keep in mind the following concepts when using
  thermochemical equations
• 1. The coefficients in a balanced thermochemical
  equation represent the number of moles, not
  molecules, which allows us to write these as
  fractions.

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THERMOCHEMISTRY

• 2. The physical state of the product/reactant
  involved in a reaction is an important factor and
  must be included in the thermochemical equation.

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THERMOCHEMISTRY

• 3. The change of energy represented by a
  thermochemical equation is directly proportional
  to the number of moles of substances undergoing a
  change.

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THERMOCHEMISTRY

• 4. The value of the energy change, ?H, is usually
  not significantly influenced by changing
  temperature.

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THERMOCHEMISTRY

• The formation of water from hydrogen and oxygen
  is a composition reaction - the formation of a
  compound from its elements.
• The amount of heat released or absorbed when one
  mole of a compound is formed from its elements is
  called the molar heat of formation.

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THERMOCHEMISTRY

• To make comparisons, heats of formations are
  given for the standard states of reactants and
  products.
• These states are found at atmospheric pressure
  and room temperature (298.15 K).
• Example Water is a liquid at room temperature,
  not a solid.

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THERMOCHEMISTRY

• To signify that a value represents measurements
  on substances in their standard states, a 0 sign
  is added to the enthalpy symbol (?H0).
• Adding the subscript f, further indicates a
  standard heat of formation (?H0f).

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THERMOCHEMISTRY

• Heats of Formation, Appendix Table A-14.
• Each entry in the table is the heat of formation
  for the synthesis of one mole of the compound
  listed from its elements in their standard states.

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THERMOCHEMISTRY

• Elements in their standard states are defined as
  having a ?H0f 0.
• Compounds with a high negative heat of formation
  are very stable, which means that they will not
  decompose back into their respective elements.

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THERMOCHEMISTRY

• Compounds with relatively positive values, or
  slightly negative values, are relatively unstable
  and will spontaneously decompose into their
  elements if the conditions are appropriate.
• Ex Hydrogen Iodide (HI), ethyne (C2H2), and
  Mercury Fulminate (HgC2N2O2).

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THERMOCHEMISTRY

• Combustion reactions produce a considerable
  amount of energy in the form of light and heat
  when a substance is combined with oxygen.
• The heat released by the complete combustion of
  one mole of a substance is called the heat of
  combustion of the substance.

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THERMOCHEMISTRY

• Heat of combustion is defined in terms of one
  mole of reactant (opposite of the heat of
  formation one mole of product).
• Heat of combustion is given the notation ?Hc.
• Heats of Combustion, Appendix Table A-5.

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THERMOCHEMISTRY

• Remember that CO2 and H2O are the products of the
  complete combustion of organic compounds.
• Example
• Combustion of propane.
• C3H8(g) 5O2(g) --gt 3CO2 4 H2O(l)
• ?H0c -2219.2 kJ/mol

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THERMOCHEMISTRY

• Thermochemical equations can be rearranged, terms
  can be canceled, and the equations can be added
  to give enthalpy changes for reactions not
  included in the data tables.
• The basis for calculating heats of reaction is
  known as Hesss Law.

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THERMOCHEMISTRY

• Hesss Law
• The overall enthalpy change in a reaction is
  equal to the sum of the enthalpy changes for the
  individual steps in the process.
• Measured heats of reaction can be combined to
  calculate heats of reaction that are difficult or
  impossible to actually measure.

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THERMOCHEMISTRY

• Calculating Heats of Reaction
• Suppose you want to know the heat of reaction for
  the decomposition of ice to give oxygen and
  hydrogen gases. Given the information below
• ?H0f (liquid water) -285.83 kJ
• Heat of Fusion (melting of ice) 6.0 kJ/mol

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THERMOCHEMISTRY

• Given
• H2(g) 1/2O2(g) --gt H2O(l) ?H0f -285.83
• H2O(s) --gt H2O(l) ?H 6.0 kJ
• Want
• H2O(s) --gt H2(g) 1/2O2(g) ?H ?????

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THERMOCHEMISTRY

• General Principles for combining thermochemical
  equations
• 1. Reverse the direction of the known equations
  so that when added together they give the desired
  thermochemical equation.
• When reversing equations, the sign of ?H is also
  reversed.

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THERMOCHEMISTRY

• 2. Multiply the coefficients of the known
  equations so that when added together they give
  the desired thermochemical equation.
• When multiplying the coefficients, you must also
  multiply the value for ?H.

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THERMOCHEMISTRY

• To solve this example, we must reverse the
  direction of the equation for the formation of
  H2O as a liquid, then add the equations and heats
  together.
• H2O(l) --gt H2(g) 1/2O2(g) ?H0f 285.83
• H2O(s) --gt H20(l) ?H 6.0
• H2O(s) --gt H2(g) 1/2O2(g) ?H 291.83

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THERMOCHEMISTRY

• Example
• What is the heat of reaction used to prepare
  ultra-pure silicon for the electronics industry?
• Given
• Si(s) 2Cl2(g) --gt SiCl4(l) ?H -687.01
• Mg(s) Cl2(g) --gt MgCl2(s) ?H -641.32

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THERMOCHEMISTRY

• Want
• 2Mg(s) SiCl4(l) --gt Si(s) 2MgCl2(s) ?H
  ?
• In this example we must reverse the first
  equation and multiply the second equation by 2,
  then add them together.

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THERMOCHEMISTRY

• SiCl4(l) --gt Si(s) 2Cl2(g) ?H 687.01
• 2Mg(s) 2Cl2(g) --gt 2MgCl2(s) ?H
  -1282.64
• 2Mg(s) SiCl4(l) --gt Si(s) 2MgCl2(s) ?H
  -595.63

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THERMOCHEMISTRY

• Example
• Calculate the heat of reaction for the combustion
  of of methane gas, CH4, to form CO2(g) and
  H2O(l). Write all equations involved.

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THERMOCHEMISTRY

• To find the heat of formation of a compound, you
  would use the same method as finding the heat of
  reaction.

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THERMOCHEMISTRY

• Example
• When carbon is burned in a limited supply of
  oxygen, carbon monoxide and is produced. In this
  reaction, carbon is probably first oxidized to
  carbon dioxide. Then part of the carbon dioxide
  is reduced with carbon to give some carbon
  monoxide.Find the heat of formation of carbon
  monoxide.

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THERMOCHEMISTRY

• We know the heat of formation of carbon dioxide
  and the heat of combustion of carbon monoxide
  from the tables in the book.
• C(s) O2(g) --gt CO2(g) ?H0f -393.5 kJ/mol
• CO(g) 1/2O2(g) --gt CO2(g) ?H0c -283.0
  kJ/mol

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THERMOCHEMISTRY

• We want to find the heat of formation of carbon
  monoxide.
• C(s) 1/2O2(g) --gt CO(g) ?H0f ?
• From the information given we should now be able
  to solve this problem by rearranging and
  combining equations.

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THERMOCHEMISTRY

• Example
• Calculate the heat of formation of pentane,
  C5H12, using the information on heats of
  formation in Appendix Table A-14 and the
  information of heats of combustion in Appendix
  Table A-5. Solve by combining known
  thermochemical equaitons.

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THERMOCHEMISTRY

• Given
• C(s) O2(g) --gt CO2(g) ?H0f -393.5 kJ/mol
• H2(g) ?O2(g) --gt H2O(l) ?H0f -285.8
  kJ/mol
• C5H12(g) 8O2(g) --gt 5CO2(g) 6H2O(l)
• ?H0c -3535.6 kJ/mol
• Want
• 5C(s) 6H2(g) --gt C5H12(g) ?H0f ?

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THERMOCHEMISTRY

• Practice Problems, pg. 524, 1-3.

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THERMOCHEMISTRY

• The change in heat content of a reaction system
  is one of two factors that allow chemists to
  predict whether a reaction will occur
  spontaneously and to explain how it occurs.
• The randomness of the particles in a system is
  the second factor affecting spontaneity.

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THERMOCHEMISTRY

• A great majority of chemical reactions in nature
  are exothermic.
• As these reactions proceed, energy is liberated
  and the products have less energy than the
  original reactants.
• The products are also more resistant to change,
  more stable, than the original reactants.

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THERMOCHEMISTRY

• The tendency throughout nature is for a reaction
  to proceed in a direction that leads to a lower
  energy state.
• In endothermic reactions, energy is absorbed and
  the products are at a higher potential energy and
  are less stable than the original reactants.

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THERMOCHEMISTRY

• So one might think that endothermic reactions do
  not take place spontaneously, but they do.

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THERMOCHEMISTRY

• Consider the melting of ice.
• An ice cube melts spontaneously as heat is
  transferred from the warm air to the ice.
• Well-ordered crystal arrangement to a less
  orderly liquid phase.
• A system that can go from one state to another
  without an enthalpy change does so by becoming
  more disordered.

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THERMOCHEMISTRY

• A disordered system is one that lacks a regular
  arrangement of its parts.
• This factor is called Entropy.
• Entropy (S)
• A measure of the degree of randomness of the
  particles, such as molecules.

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THERMOCHEMISTRY

• The more disordered or the more random a system,
  the higher its entropy.
• Entropy increases when a gas expands, a solid or
  liquid dissolves, or the number of particles in a
  system increases.

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THERMOCHEMISTRY

• Processes in nature are driven in two directions
• Towards lowest enthalpy.
• Towards highest entropy.
• When these two oppose each other, the dominant
  factor determines the direction of change.

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THERMOCHEMISTRY

• To predict which will dominate for a given
  system, a function has been defined to relate the
  enthalpy and entropy factors at a given
  temperature.
• Free Energy (G)
• The combined enthalpy-entropy function of a
  system.

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THERMOCHEMISTRY

• Natural processes proceed in the direction that
  lowers the free energy of a system.
• Only the change in free energy can be measured.
• The change in free energy can be defined in terms
  of the changes in enthalpy and entropy.

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THERMOCHEMISTRY

• Free-Energy Change (?G)
• The difference between the change in enthalpy,
  ?H, and the product of the Kelvin temperature and
  the entropy change, which is defined as T?S.
• Equation for Free Energy Change
• ?G0 ?H0 - T ?S0

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THERMOCHEMISTRY

• Each of the variables in the equation can have
  positive or negative values, this leads to four
  possible combinations of terms.
• The more negative ?H is, the more negative ?G is
  likely to be.
• The more positive ?S is, the more negative ?G is
  likely to be.

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THERMOCHEMISTRY

• Reactions systems that change from a high
  enthalpy state to a low one tend to proceed
  spontaneously.
• Also, systems that change from a well-ordered
  state to a highly disordered state also tend to
  proceed spontaneously.

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THERMOCHEMISTRY

• ?G can either be positive or negative, depending
  on the temperature (T).
• If the temperature of the system is the dominant
  factor that determines the relative importance of
  the tendencies toward lower energy and higher
  entropy.

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THERMOCHEMISTRY

• EXAMPLE
• Consider the reaction between water and carbon to
  produce carbon monoxide and hydrogen.
• H2O(g) C(s) --gt CO(g) H2(g)
• ?H 131.3 kJ
• ?S 0.134 kJ/(molK)
• T 298 K

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THERMOCHEMISTRY

• Calculate free energy change and tell whether or
  not this reaction is spontaneous or not.
• ?G 131.3 - (298)(0.134)
• ?G 131.4 - 39.9
• ?G 91.4 kJ/mol

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THERMOCHEMISTRY

• Since ?G has a positive value, the reaction that
  produces produces hydrogen gas is not spontaneous
  at a relatively low temperature of 298 K.

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THERMOCHEMISTRY

• Increases in temperature tend to favor increases
  in entropy.

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THERMOCHEMISTRY

• EXAMPLE
• For the reaction NH4Cl(s) --gt NH3(g) HCl(g), at
  25C, ?H 176 kJ/mol and ?S 0.285 kJ/(molK).
  Calculate ?G and decide if this reaction will be
  spontaneous in the forward direction.

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THERMOCHEMISTRY

• ?G 176 - (298)(0.285)
• ?G 176 - 84.9
• ?G 91 kJ/mol
• The positive value of ?G shows that this reaction
  is not spontaneous at 25C.

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THERMOCHEMISTRY

• EXAMPLE
• For the vaporization reaction Br2(l) --gt Br2(g),
  ?H 31.0 kJ/mol and ?S 93.0 kJ/(molK). At
  what temperature will this process be spontaneous?

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THERMOCHEMISTRY

• No matter how simple a balanced equation, the
  reaction pathway may be complicated and difficult
  to determine.
• Chemists believe that simple, one step reaction
  mechanisms are unlikely, and that nearly all
  reactions are complicated.

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THERMOCHEMISTRY

• EXAMPLE
• A reaction between colorless H2 gas and violet
  colored I2 gas at elevated temperatures produces
  hydrogen iodide, a colorless gas. HI molecules,
  in turn, tend to decompose and re-form hydrogen
  and iodine.

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THERMOCHEMISTRY

• H2(g) I2(g) --gt 2HI(g)
• 2HI(g) --gt H2(g) I2(g)
• These types of reactions do not show the reaction
  pathway by which either reaction proceeds.

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THERMOCHEMISTRY

• Reaction Mechanism
• The step-by-step sequence of reactions by which
  the overall chemical change occurs.
• Most reactions take place in a sequence of simple
  steps.

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THERMOCHEMISTRY

• This reaction is also a Homogenous reaction.
• Homogenous Reaction
• A reaction whose reactants and products exist in
  a single phase.
• In such a reaction, all reactants and products in
  intermediate steps are in the same phase.

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THERMOCHEMISTRY

• The real reaction has 2 possible mechanisms
• First Reaction Mechanism
• I2 lt--gt 2I
• 2I H2 lt--gt 2HI
• I2 H2 lt--gt 2HI

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THERMOCHEMISTRY

• Second Reaction Mechanism
• I2 lt--gt 2I
• I H2 lt--gt H2I
• H2I I lt--gt 2HI
• I2 H2 lt--gt 2HI
• Some species that appear in some steps, but not
  in the net equation are known as intermediates.

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THERMOCHEMISTRY

• Collision Theory
• A set of assumptions regarding collisions and
  reactions.
• In order for reactions to occur between
  substances, their particles (molecules, atoms, or
  ions) must collide.

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THERMOCHEMISTRY

• EXAMPLE
• HI HI --gt H2 2I
• According to the collision theory, 2 HI molecules
  must collide in order to react.

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THERMOCHEMISTRY

• The HI molecules must collide while favorably
  orientated and with enough energy to disrupt the
  bonds of the molecules.

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THERMOCHEMISTRY

• If the collision is too gentle, the old bonds are
  not disrupted and new ones are not formed. They
  simply bounce off each other.

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THERMOCHEMISTRY

• If the reactant molecules are poorly orientated,
  the collision has little effect.

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THERMOCHEMISTRY

• If the reactants collide with enough energy and
  proper orientation, a reshuffling of bonds leads
  to the formation of 1 H2 molecule and 2 I atoms.

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THERMOCHEMISTRY

• The collision theory provides two reasons why a
  collision between reactants molecules may fail to
  produce a new chemical species
• Collision is not energetic enough.
• Colliding molecules are not orientated properly.

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THERMOCHEMISTRY

• Activation Energy (Ea)
• Energy required to transform the reactants into
  the activated complex.
• Activated Complex
• A transitional structure that results from an
  effective collision and that persists while old
  bonds are breaking and new bonds are forming.

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THERMOCHEMISTRY

• Reading Energy Diagrams
• Symbols
• ?H Change in Enthalpy (Heat)
• ?H HPRODUCTS - HREACTANTS
• Ea Activation Energy of the
• forward reaction.
• Ea Activation Energy of the
• reverse reaction.

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THERMOCHEMISTRY

• Reaction Rate
• The change in concentration of reactants per unit
  time as a reaction proceeds.
• Chemical Kinetics
• The area of chemistry that is concerned with
  reaction rates and reaction mechanisms.

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THERMOCHEMISTRY

• There are 5 important factors that influence the
  rate of a chemical reaction
• 1. Nature of Reactants
• Substances vary greatly in their tendencies to
  react.
• The rate of reaction depends on the particular
  reactants and bonds involved.

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THERMOCHEMISTRY

• 2. Surface Area
• The more surface area an object has the faster
  the reaction will occur.

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THERMOCHEMISTRY

• 3. Concentration
• Increasing the concentration of a substance could
  increase the rate of reaction or it could have no
  effect on the reaction. The effect depends on the
  particular reaction.

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THERMOCHEMISTRY

• Reactions take place in a series of steps. The
  step that proceeds the slowest determines the
  overall rate of reaction.
• The slowest step is called the Rate-Determining
  Step.

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THERMOCHEMISTRY

• 4. Temperature
• The rates of many reactions roughly double or
  triple with a 10 C rise in temperature.
• The increase in temperature increases the energy
  of the particles in the reaction, thus increasing
  the number of collisions between those particles.

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THERMOCHEMISTRY

• 5. Presence of a Catalyst
• A substance that changes the rate of a chemical
  reaction without itself being permanently
  consumed.
• The action of a catalyst is called catalysis.
• Catalysts do not appear among the final products
  of reactions the accelerate.

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THERMOCHEMISTRY

• A catalyst may be effective in forming an
  alternative activated complex that requires a
  lower activation energy.

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THERMOCHEMISTRY

• A catalyst that is in the same phase as all the
  reactants and products in a reaction system is
  called a homogeneous catalyst.
• When its phase is different from that of the
  reactants, it is called a heterogeneous catalyst.

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THERMOCHEMISTRY

• Sometimes chemists need to slow down the rate of
  reaction, to do so they add an inhibitor.
• Inhibitor
• A substance that slows down a process.
• A negative catalyst.

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• The relationship between rate of reaction and the
  concentration of one reactant is determined
  experimentally by first keeping the
  concentrations of other reactants and the
  temperature of the system constant.

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• Then the reaction rate is measured for various
  concentrations of the reactant in question.
• A series of such experiments reveals how the
  concentration for each reactant affects the
  reaction rate.

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• EXAMPLE
• Hydrogen gas reacts with nitrogen monoxide gas at
  constant volume and at an elevated constant
  temperature, according to the following equation
• 2H2(g) 2NO(g) --gt N2(g) 2 H2O(g)

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• Four moles of reactant gases produce three moles
  of product gases thus, the pressure of the
  system diminishes as the reaction proceeds.
• The rate of reaction can, therefore, be
  determined by measuring the change of pressure in
  the vessel with time.

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• Suppose a series of experiments is conducted
  using the same initial concentration of NO but
  different initial concentrations of H2.

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• The initial reaction rate is found to vary
  directly with H2 concentration
• Doubling the concentration of H2 doubles the
  rate.
• Tripling the concentration of H2 triples the rate.

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• If R represents the reaction rate and H2 is the
  concentration of hydrogen in moles per liter, the
  mathematical relationship between rate and
  concentration can be written as
• R ? H2
• ? is proportional to

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• Now suppose the same initial concentration of H2
  is used but the initial concentration of NO is
  varied.
• The initial reaction rate is found to increase
  fourfold when the NO concentration is doubled and
  ninefold when the concentration of NO is tripled.

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• Thus, the reaction rate varies directly with the
  square of the NO concentration.
• R ? NO2

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• Because R is proportional to H2 and to NO2,
  it is proportional to their product
• R ? H2NO2

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• By introduction of an appropriate
  proportionality constant, k, the expression
  becomes an equality
• R k H2NO2

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• An equation that relates reaction rate and
  concentration of reactants is called the rate
  law.
• It is applicable for a specific reaction at a
  given temperature.
• A rise in temperature increases the reaction
  rates of most reactions.

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• The value of k usually increases as the
  temperature increases, but the relationship
  between reaction rate and concentration almost
  always remains unchanged.

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• The form of rate law depends on the reaction
  mechanism.
• For a reaction that occurs in a single step, the
  reaction rate of that step is proportional to the
  product of the reactant concentrations, each of
  which is raised to its stoichiometric coefficient.

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• EXAMPLE
• Suppose one molecule of a gas A collides with one
  molecule of gas B to form two molecules of
  substance C.
• A B --gt 2C

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• One particle of each reactant is involved in each
  collision. Thus, doubling the concentration of
  either reactant will double the collision
  frequency.
• It also will double the reaction rate for this
  step.

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• Therefore, the rate for this step is directly
  proportional to the concentration of A and B.
• The rate law for this one-step reaction follows
• R kAB

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• Now suppose the reaction is reversible.
• In the reverse step, 2 molecules of C must
  decompose to form one molecule of A and one of B.
• 2C --gt A B

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• Thus, the reaction rate for this reverse step is
  directly proportional to C C.
• The rate law for this step is
• R kC2

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• The power to which the molar concentration of
  each reactant is raised in the rate laws above
  corresponds to the coefficient for the reactant
  in the balanced chemical equation.

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• Such a relationship holds only if the reaction
  follows a simple one-step path.
• If a chemical reaction proceeds in a series of
  steps, the rate law is determined from the
  slowest step because it has the lowest rate.
• Rate Determining Step.

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• EXAMPLE
• Consider the following reaction
• NO2(g) CO(g) --gt NO(g) CO2(g)

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• The reaction is believed to be a two step process
  represented by the following mechanism
• Step 1 NO2 NO2 --gt NO3 NO slow
• Step 2 NO3 CO --gt NO2 CO2 fast

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• The first step is the slower of the two and is
  therefore the rate-determining step.
• We can write the rate law from this
  rate-determining step
• R kNO22

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• CO does not appear in the rate law because it
  reacts after the rate-determining step, so the
  reaction rate will not depend on CO.

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• The general form for the rate law is given by the
  following equation
• R kAnBm.

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• The reaction rate is represented by R, k is the
  rate constant, and A and B represent the
  molar concentrations of reactants.
• The n and m are the respective powers to which
  the concentrations are raised. They must be
  determined from experimental data.