Chapter 8. Chemical and Physical Change:  Energy, Rate, and Equilibrium

Energy

Thermodynamics

Two laws of thermodynamics, the science involved with energy flow in physical and chemical change, are of particular importance to us. The first law, the law of conservation of energy, and the second law, entropy or disorder, can provide us with basic information regarding the spontaneity of chemical or physical processes as well as the amount of energy absorbed or released by the reaction. Exothermic reactions release energy; endothermic reactions require energy input. The practical side of the thermodynamics is presented through discussion of enthalpy, entropy, and free energy.

Universe, System and Surrounding

The basic abstraction of thermodynamics is the division of the world into systems delimited by real or ideal boundaries. The systems not directly under consideration are lumped into the surrounding. Usually systems can be assigned a well-defined state solid/liquid or a gas which can be summarized by a small number of parameters. The flow of between the system and surrounding is measured.

First law of thermodynamics

Energy may exist in a variety of forms and may be transformed from one type of energy to another. However, these energy transformations are constrained by a fundamental principle, the Conservation of Energy principle: Energy can neither be created nor destroyed.  Heat is the main form of energy involved with chemical reactions.

Enthalpy change (DH): Heat given our in a chemical reaction. Enthalpy is measured in kJ or calories.

Exothermic.  As the dissolution reaction proceeds, the solution gets hotter because heat  is produced.  Enthalpy change,  D  is negative, meaning that energy is released by the reaction.

Endothermic.  As the dissolution reaction proceeds, the solution gets colder because heat  is absorbed.  Enthalpy change,  D  is positive, meaning that energy is absorbed during the reaction.

Second law of thermodynamics

Disorder (measured as entropy) of the Universe (defined as system + surrounding) increases during a spontaneous process.

Entropy (S): Measure of disorder is measured in J/K.

Entropy increases during these processes:

i) Solid ---> liquid (melting)

ii) Liquid ---> gas (boiling)

iii) Solid ----> gas (sublimation)

iv) Increase in temperature (increase in kinetic energy)

v) Decomposition reactions

vi) Anything that breaks up in to smaller particles

v) Mixing: Diffusion, solution process

Example:   Conversion of a single solid object, the log, into carbon monoxide, carbon dioxide, and water (all gases) and ashes (disordered solid) increases the disorder of the substance.

Entropy decreases. A gas (more disordered) is converted to a liquid  or solid (less disordered). Upon freezing the randomness of the water molecules has decreased.

Third law of thermodynamics

All substances have zero S at 0 K.

A chemical reaction could be exothermic or endothermic

Experimental Determination of Energy Change in Reactions

A calorimeter measures heat changes (in calories or joules) that occur in chemical reactions. The specific heat of substances is the number of calories of heat needed to raise the temperature of one gram of the substance by one degree Celsius.

The amount of energy per gram of food is its fuel value, commonly reported in units of nutritional Calories (1 nutritional Calorie = 1 kcal). A bomb calorimeter is useful for measurement of the fuel value of foods.

Measuring Heat: Calorimetry

A calorimeter is a device that is used to measure the quantity of heat flow in a chemical reaction. Two common types of calorimeters are the coffee cup calorimeter and the bomb calorimeter.

Coffee Cup Calorimeter

A coffee cup calorimeter is essentially a polystyrene (Styrofoam) cup with a lid. Really, any well-insulated container will work. The cup is partially filled with a known volume of water and a thermometer is inserted through the lid of the cup so that the thermometer bulb is below the water surface. The water absorbs the heat of any chemical reaction taking place in the calorimeter.

Bomb Calorimeter

A coffee cup calorimeter is great for measuring heat flow in a solution, but it can't be used for reactions which involve gases, since they would escape from the cup. Also, a coffee cup calorimeter can't be used for high temperature reactions, since high heat would melt the cup. A bomb calorimeter is used to measure heat flows for gases and high temperature reactions like combustion reactions.

Heat flow is calculated in Calorimeters:

Q = m (mass)  x DT(temperature change) x SH (specific heat)

where Q is heat flow, m is mass in grams, and DT is the change in temperature. The specific heat is the amount of heat required to raise the temperature of 1 gram of a substance 1 degree Celsius. The specific heat of (pure) water is 4.18 J/(g·°C).

Calorie:  Amount of heat required to raise the temperature of 1 gram of a substance 1 degree Celsius.

Nutritional (dietary) calorie = 1 k cal = 1000 cal

How many Joules of heat energy is in 7.0 x 102 cal?

7.0 x 102 cal x  = 2.9 x 103 J

Specific Heat

The specific heat of a substance is the number of calories of heat needed to raise the temperature of one gram of substance by one degree Celsius.

 Substance kJ/ g·°C cal/ g·°C Copper 0.386 0.0923 Brass 0.380 0.092 Gold 0.126 0.0301 Lead 0.128 0.0305 Silver 0.233 0.0558 Alcohol(ethyl) 2.4 0.58 Water 4.184 1.00

Heat Calculations

For example, consider a chemical reaction which occurs in 200 grams of water with an initial temperature of 25.0°C. The reaction is allowed to proceed in the coffee cup calorimeter. As a result of the reaction, the temperature of the water changes to 31.0°C. The heat flow is calculated:

Q water = m water x DT water x SH water

Q water = 200 g x (31.0°C - 25.0°C) x 4.18 J/(g·°C)

Q water = +5.0 x 103 J

In other words, the products of the reaction evolved 5000 J of heat, which was lost to the water. The enthalpy change, DH, for the reaction is equal in magnitude but opposite in sign to the heat flow for the water:

DHreaction = -( Q water)= - 5.0 x 103 J

What would be the temperature change if 200g of another liquid with a specific heat of 0.800 cal/(g°C  is in the calorimeter and absorb 6.5 x 102 cal of heat?

Q = mliquid x DTliquid x SHliquid

Solving for DTl,            DT l =

Substituting,

DT l =  = 8.1˚C

What is the mass of water that absorb 3.00 nutritional calories to yield a temperature change of 5.00˚C?

Q = mw x DTw x SHw

Solving for mw, mw =

Substituting,

mw =  = 6.0 x 102 g

The fuel value

The fuel value of a substance is the amount of energy, in units of nutritional Calories, derived from one gram of that substance.

The Chemical Reaction and Energy

Chemical reactions are also known as chemical changes. This refers to the changes in the structure of molecules. Such reactions can result in molecules attaching to each other to form larger molecules, molecules breaking apart to form two or more smaller molecules, or rearrangements of atoms within molecules. Chemical reactions usually involve the making or breaking of chemical bonds.

Enthalpy

By calculating the amounts of energy required to break all the bonds on the left ("before") and right ("after") sides of the equation, we can calculate the energy difference between the reactants and the products. This is referred to as ΔH, where Δ (Delta) means difference, and H stands for enthalpy, a measure of energy which is equal to the heat transferred at constant pressure. ΔH is usually given in units of kJ (thousands of joules) or in kcal (kilocalories). ΔH˚ is the enthalpy measure at standard thermodynamic temprearture and pressure: 25˚C (298 K) and 1 atm (760 torr).

If ΔH is negative for the reaction, then energy has been released. This type of reaction is referred to as exothermic (literally, outside heat, or throwing off heat). An exothermic reaction is more favourable and thus more likely to occur. Our example reaction is exothermic, which we already know from everyday experience, since burning gas in air gives off heat.

Exothermic Reactions

A reaction may have a negative ΔH. This means that, to proceed, the reaction does not require energy from outside. This type of reaction is called exothermic (literally, outide heat, or releasing  heat).

Endothermic Reactions

A reaction may have a positive ΔH. This means that, to proceed, the reaction requires an input of energy from outside. This type of reaction is called endothermic (literally, inside heat, or absorbing heat).

Spontaneous and Nonspontaneous Reactions

The spontaneity of a reaction is favored if it is exothermic, but endothermic reactions are possible too. Why? The other factor that affects the direction of spontaneous change may dominate.

Disorder - Disorder transitions, regardless of their energetics appear to be favored in the world around us. They point the arrow of time. Humpty Dumpty couldn't be put back together because of the disorder his fall created. A measure of the disorder of a system is called its Entropy, S.  Therefore endothermic reactions could be spontaneous if the disorder or Entropy, S could out weigh the endothermic effect.

Reactions that split molecules up increase the disorder in the universe and have a positive change in entropy and have a positive ΔH (endothermic but still spontaneous reaction).

How can one tell whether a reaction is spontaneous, if both entropy and enthalpy affect spontaneity?

Free Energy

We can combine entropy and enthalpy together to make a new quantity, the Free Energy which, under conditions of constant temperature and pressure, will determine the direction of spontaneous change

How is free energy (DG) related to enthalpy and entropy?

Rates  of  Reactions

Kinetics

Chemical kinetics is the study of the rate of a chemical reaction. Recognizing that chemical reactions result from effective collisions between potentially reacting particles, we show that factors such as the structure of the reactant, its concentration, reaction temperature, and the presence or absence of a catalyst influence reaction rates. The role of the activation energy in chemical processes determines reaction rates, for we view the formation of the activated complex as an energy barrier to be overcome.

Mathematical Representation of Reaction Rate

The reaction rate of a chemical reaction is the speed of production of products from reactants. The rate value is always positive. Reaction rates are expressed by the formula:   A  à  B

$Rate = k \times [A]^n$

In this equation, [A] is the molar concentration of the reactant (there may be several) A, n is the order of the reaction, and k is the rate constant. Order establishes the mathematical relation of concentration to rate. For instance, in a second-order reaction, if the concentration doubles, the rate quadruples.

When there is more than one reactant involved in a reaction, the rate is simply the product of all of the reactants and their orders:

A + B + C à D + E

$Rate = k \times {[A]^n} \times {[B]^m} \times {[C]^p}\, \dots$

Rate is often expressed in the units mol/Ls.

Write the general form of the rate equation for the following reactions:

a) CH4(g)  + 2 O2   à   CO2 (g)   +  2 H2O(g)

b)  2NO2(g)  à  2NO(g) +  O2 (g)

a.   rate = k[CH4]n[O2]n'

b.   rate = k [NO2]n

If the rate equation for the follwing reactions is given what are the orders with respect to each reactant?

C2H5OH(l)  +  3O2(g) à   2CO2 (g)   +  3H2O(g)

Rate equation =  k[C2H5OH] [O2]2

Order with respect to C2H5OH =  1 (first order)

Order with respect to C2H5OH =  2 (second order)

Activation energy

Net energy is the difference in energy between products and reactants. Activation energy is the threshold energy that must be overcome in order to cause a chemical reaction.

Activation Energy and the Activated Complex

This is the energy that must be reached by 2 colliding molecules before a reaction can take place.

Factors that Affect Reaction Rate:

Temperature: Conducting a reaction at a higher temperature puts more energy into the system and increases the reaction rate. The influence of temperature is described by the Arrhenius equation. As a rule of the thumb, the reaction rate doubles for every 10 degrees Celsius increase in temperature.

Why is growth of bacteria slowed down in a refrigerator?

The rate of chemical reactions critical to the growth process decreases at the lower temperature of the refrigerator.

Order: Clearly the order of the reaction has a major effect on its rate. The order of a reaction is found experimentally, and, for most basic reactions, is an integer value.

A catalyst: The presence of a catalyst increases the reaction rate in both the forward and reverse reactions by lowering the activation energy of the reaction.

·        Catalysts increase the rate of reaction.

·        Catalysts are not consumed by the reaction.

·        A small quantity of catalyst should be able to affect the rate of reaction for a large amount of reactant.

·        Catalysts do not change the equilibrium constant for the reaction.

Particle size or the state of sub-division of reactants: The larger the surface area compared to the volume, the faster a reaction can take place, as more simultaneous reactions can occur.

A December 1977 explosion in Westwood, LA, blew away the top 100 feet of head house atop this grain elevator facility. The blast killed 36 people and injured nine, making it the worst such disaster in U.S. history.

For a dust explosion to occur, several factors must come together, according to Dust Explosions in Process Industries by Rolf K. Eckhoff. First, there must be fuel, or grain dust. The critical parameter for grain particle size is 0.1 mm or smaller. As the size of the particle decreases, the risk of a deflagration or explosion increases.

The nature of the reactants: If a reaction involves the breaking and reforming of bonds (complex) compared to just the forming of bonds (simple) then it generally takes longer. The reactants position in the reactivity series also affects reaction rate.

Equilibrium

Not all reactions proceed to completion. Many establish a dynamic equilibrium between products and reactants, where the rates of the forward and reverse reactions are equal. LeChatelier's Principle states that if a stress is placed on a system in equilibrium, the system will respond by altering the equilibrium in such a way as to minimize the stress.

Equilibrium Chemical Reactions

On the other hand, there are many chemical reactions that stop far short of completion. An example is the dimerization of nitrogen dioxide:

NO2(g) + NO2(g)    N2O4(g)

The reactant, NO2, is a dark brown gas, and the product, N2O4, is a colorless gas. When NO2 is placed in an evacuated, sealed glass vessel at 25°C, the initial dark brown color decreases in intensity as it is converted to colorless N2O4. However, even over a long period of time, the contents of the reaction vessel do not become colorless. Instead, the intensity of the brown color eventually becomes constant, which means that the concentration of NO2 is no longer changing.  Making the container colder makes equilibrium to shift to left and warming shift the equilibrium to right.

Other examples:

3H2(g) + N2(g)  2NH3(g)

Any chemical reaction could be considered as a forward and backward reactions occurring at the same time() as described previously. If the rates of backward and forward reactions chemical reactions are comparable both reactants and products can coexist leading to a condition called chemical equilibrium reaction.

Dynamic Equilibrium

The equilibrium process is dynamic; products and reactants continuously interconvert at the same rate.

Physical Equilibrium

• Phases and phase transitions

liquid -> gas : Vaporization

gas -> liquid : Condensation

solid -> liquid : Fusion (Melting)

liquid -> solid : Freezing

solid -> gas : Sublimation

gas -> solid : Deposition

Example: H2O(l)  H2O(g)

• Solubility

Supersaturated solution

Chemical Equilibrium

When a chemical reaction takes place in a container which prevents the entry or escape of any of the substances involved in the reaction, the quantities of these components change as some are consumed and others are formed. Eventually this change will come to an end, after which the composition will remain unchanged as long as the system remains undisturbed. The system is then said to be in its equilibrium state, or more simply, "at equilibrium".

The Chemical Equilibrium Constant

Equilibrium constant comes from a law that applies to chemical equilibrium called Law of Mass action.

The Generalized Equilibrium-Constant Expression for a Chemical Reaction

Law of Mass Action:

Law of mass action describes an equilibrium process by quantifying the equilibrium concentration of reactants and products. It uses the ratio of backward and forward reactions and express it terms of an equilibrium constant (K).  For example consider a hypothetical equation:

j A + k B  l C + m D

[C]l[D]m                    [A]… are equilibrium concentration of A, B, C, D etc.

K = -----------------                      j, k, l, m are stoichiometric coefficients

[A]j[B]k                           K = equilibrium constant

Equilibrium Expression:

Equilibrium expression is the Law of mass action equation with the equilibrium concentration of reactants and products and the equilibrium constant (K).

Example: Equilibrium expression for the formation of NH3 gas:

N2(g) + 3H2(g)   2NH3(g)

[NH3]2

K = ------------ = 6.02 x 10-2 L2/mol2 at 127oC

[N2][H2]3

Equilibrium Constant (K): The constant in the equilibrium expression is called equilibrium constant (K).

2 H2(g) + O2(g)   2H2O(g)

[H2O]2

K = -------------

[H2] 2[O2]

MgCO3(s)  MgO(s) + CO2(g)

K = [CO2]

Equilibrium position

An increase in the rate of the forward reaction favors products. This increases the numerator of the rate constant expression, hence, the magnitude of the equilibrium constant. The equilibrium favors reactants. A very low value for the equilibrium constant indicates that the ratio of products to reactants is very low. Therefore reactant concentration is larger than product concentration.

Write the equilibrium constant for he following reaction:

2HI(g)   2H2(g) + I2(g)

A reaction chamber contains following mixture at equilibrium:

2H2(g) + S2(g)    2 H2S(g)

[H2] = 0.22 M

[S2]  = 1.0 x 10-6 M

[H2S] = 0.80 M

Calculate the equilibrium constant.

Rate and Reversibility of Reactions

Once a system has reached equilibrium, any factor which causes a change in the rate of either the forward or reverse reaction will disturb or shift the equilibrium. The system will readjust itself so that a new equilibrium is reached and the rates will again become equal. Reestablishing the equilibrium is summarized by Le Châtelier.

Le Châtelier's Principle

When a stress is applied to a system at Equilibrium, the system readjusts so as to relieve or offset the stress. Stress is any imposed factor which upsets the balance in rates between the forward and reverse reactions. Stress factors may be changes in concentrations [], total pressure with gases only, volume changes (which cause the pressure changes), and temperature.

For the hypothetical equilibrium reaction

A(g) + B(g)  C(g) + D (g)

Predict weather the amount of A in a 5.0-L container would, or remain the same for each of the following changes.

a. Removal of some B.

b. Removal of some C.

d. Removal of a catalyst.

a.   A would increase; C and D would react to produce more B, to compensate for its removal, and more A as well.  the equilibrium shifts to the left.

b.   A would decrease; A and B would react to produce more C, to compensate for its removal.  The equilibrium shifts to the right.

c.   A would increase; excess D would react with C to produce more A and B.  The equilibrium shifts to the left.

d.      A would remain the same; removal of the catalyst would delay the attainment of equilibrium, but not affect the equilibrium position.