General Chemistry B Chapter 11

General Chemistry B

Liquid and Intermolecular Forces

Chapter 11

Intermolecular forces, the forces that exist between molecules.

1

Dr. Said M. El-Kurdi

11.1 A MOLECULAR COMPARISON OF GASES, LIQUIDS, AND SOLIDS

Gas Liquid Solid

Assumes both volume and shape of its container

Assumes shape of portion of container it occupies

Retains own shape and volume

Expands to fill its container

Does not expand to fill its container

Does not expand to fill its container

Is compressible Is virtually incompressible

Is virtually incompressible

Flows readily Flows readily Does not flow

Diffusion within a gas occurs rapidly

Diffusion within a liquid occurs slowly

Diffusion within a solid occurs extremely slowly

2 Dr. Said M. El-Kurdi

Gases, liquids, and solids. Chlorine, bromine, and iodine are all made up of diatomic molecules as a result of covalent bonding.

Differences in the strength of the intermolecular forces

Cl2 gaseous Br2 liquid I2 solid

11.2 INTERMOLECULAR FORCES


In contrast, the energy required to break the covalent bond in HCl is 431 kJ/mol .

Only 16 kJ/mol is required to overcome the intermolecular attractions in liquid HCl in order to vaporize it.

Many properties of liquids, including boiling points, reflect the strength of the intermolecular forces.

Similarly, the melting points of solids increase as the strengths of the intermolecular forces increase.

The stronger the attractive forces, the higher the temperature at which the liquid boils.


The melting and boiling points of substances in which the particles are held together by chemical bonds tend to be much higher than those of substances in which the particles are held together by intermolecular forces.


Another kind of attractive force, the ion–dipole force, is important in solutions.

Three types of intermolecular attractions exist between electrically neutral molecules:

3. hydrogen bonding

1. Dispersion forces

2. Dipole–dipole attractions van der Waals forces

All intermolecular interactions are electrostatic, involving attractions between positive and negative species


In this equation Q1 and Q2 are the charges on the particles, d is the distance between their centers, and is a constant, 8.99 109 J-m/C2

Why then are intermolecular forces so much weaker than ionic bonds?

Dipole moments are usually reported in debyes (D), a unit that equals 3.34 10−30 coulomb-meters (C-m).


Dispersion Forces

Nonpolar gases like helium, argon, and nitrogen can be liquefied.

The motion of electrons in an atom or molecule can create an instantaneous, or momentary, dipole moment.

Fritz London


This attractive interaction is called the dispersion force (or the London dispersion force in some texts).

It is significant only when molecules are very close together.

The strength of the dispersion force depends on

Polarizability is the ease with which an electron distribution can be deformed.

The larger the molecule (the greater the number of electrons) the more polarizable it is.

More polarizable molecules have larger dispersion forces.


Dispersion forces increase as molecular weight increases.


The greater the surface area available for contact, the greater the dispersion forces.

Dispersion forces depend on the shape of the molecule


The presence of a permanent dipole moment in polar molecules gives rise to dipole–dipole forces.

Dipole–Dipole Forces

Acetonitrile (CH3CN, MW 41 amu, bp 355 K), polar molecule, dipole moment of 3.9 D, so dipole–dipole forces are present.

Propane (CH3CH2CH3, MW 44 amu, bp 231 K). Essentially nonpolar, dipole–dipole forces are absent.

These forces originate from electrostatic attractions between the partially positive end of one molecule and partially negative end of a neighboring molecule.


For molecules of approximately equal mass and size, the strength of intermolecular attractions increases with increasing polarity


Hydrogen Bonding

The boiling points of the compounds containing group 4A elements (CH4 through SnH4, all nonpolar) increase systematically moving down the group.

This is the expected trend because polarizability and, hence, dispersion forces generally increase as molecular weight increases.


Hydrogen Bonding

The three heavier members of groups 5A, 6A, and 7A follow the same trend, but NH3,H2O, and HF have boiling points that are much higher than expected


Hydrogen bonding is a special type of intermolecular attraction between the hydrogen atom in a polar bond (particularly H-F, H-O, and H-N) and nonbonding electron pair on a nearby small electronegative ion or atom usually F, O, or N (in another molecule).

The strong intermolecular attractions in HF, H2O, and NH3 result from hydrogen bonding.


Bond energies of hydrogen bonds vary from about 4 kJ/mol to 25 kJ/mol.

Hydrogen bonds can be considered a type of dipole–dipole attraction.

Hydrogen bonds are typically much weaker than covalent bonds, which have bond enthalpies of 150 –1100 kJ/mol

Hydrogen bonds are generally stronger than dipole–dipole or dispersion forces



Hydrogen bonds play important roles in many chemical systems, including those of biological significance.

For example, hydrogen bonds help stabilize the structures of proteins and are also responsible for the way that DNA is able to carry genetic information.

In most substances the molecules in the solid are more densely packed than in the liquid, making the solid phase denser than the liquid phase.

By contrast, the density of ice at 0°C (0.917 g/mL) is less than that of liquid water at 0°C (1.00 g/mL), so ice floats on liquid water.


The empty channels in the structure of ice make water less dense as a solid than as a liquid.

Hydrogen bonding in ice


Ion–Dipole Forces

An ion–dipole force exists between an ion and a polar molecule


The magnitude of the attraction increases as either the ionic charge or the magnitude of the dipole moment increases.

Ion–dipole forces are especially important for solutions of ionic substances in polar liquids, such as a solution of NaCl in water.

Dispersion forces are found in all substances

With polar molecules dipole–dipole forces are also operative

For example, in liquid HCl dispersion forces are estimated to account for more than 80% of the total attraction between molecules, while dipole–dipole attractions account for the rest.

Hydrogen bonds, when present, make an important contribution to the total intermolecular interaction.

Their strength depends on molecular shapes and molecular weights.


In general, the energies associated with dispersion and dipole–dipole forces are 2–10 kJ/mol

All these interactions are considerably weaker than covalent and ionic bonds, which have energies that are hundreds of kilojoules per mole.

Ion–dipole attractions have energies of approximately 15 kJ/mol

The energies of hydrogen bonds are 5–25 kJ/mol



Dr. Said M. El-Kurdi 25

11.3 SELECT PROPERTIES OF LIQUIDS

Viscosity: The resistance of a liquid to flow,

The greater a liquid’s viscosity, the more slowly it flows.

The stronger the intermolecular forces, the higher the viscosity.

Viscosity depends on:

A liquid flows by sliding molecules over one another.

Viscosity usually decreases with an increase in temperature.

Viscosity increases as molecules become entangled with one another.

SI units for viscosity are kg/m-s.

Octane, for example, has a viscosity of 7.06 10-4 kg/m-s at 0 °C and 4.33 10-4 kg/m-s at 40 oC.


For a series of related compounds, viscosity increases with molecular weight


Surface Tension

Surface tension is the energy required to increase the surface area of a liquid by a unit amount.

This causes the liquid to behave as if it had a “skin”.

Bulk molecules (those in the liquid) are equally attracted to their neighbors.

Surface molecules are only attracted inward towards the bulk molecules.

Therefore, surface molecules are packed more closely than bulk molecules.


Water has a high surface tension (H-bonding)

Hg(l) has an even higher surface tension (there are very strong metallic bonds between Hg atoms).

Water placed in a glass tube adheres to the glass because the adhesive forces between the water and glass are greater than the cohesive forces between water molecules.

Cohesive forces are intermolecular forces that bind molecules to one another.

Adhesive forces are intermolecular forces that bind molecules to a surface.

The curved surface, or meniscus, of the water is therefore U-shaped



capillary action: The rise of liquids up very narrow tubes

The liquid climbs until the force of gravity on the liquid balances the adhesive and cohesive forces.

Capillary action helps water and dissolved nutrients move upward through plants.


11.4 Phase Changes

Melting or fusion: solid liquid.

Phase changes are changes of state.

Matter in one state is converted into another state.

Sublimation: solid gas.

Freezing: liquid solid.

Vaporization: liquid gas.

Deposition: gas solid.

Condensation: gas liquid.


Energy Changes Accompanying Phase Changes

Melting or fusion: ΔHfus > 0 (endothermic). The enthalpy of fusion is known as the heat of fusion. Vaporization: ΔHvap > 0 (endothermic). The enthalpy of vaporization is known as the heat of vaporization. Sublimation: ΔHsub > 0 (endothermc). The enthalpy of sublimation is called the heat of sublimation. Deposition: ΔHdep < 0 (exothermic). Condensation: ΔHcon < 0 (exothermic). Freezing: ΔHfre < 0 (exothermic).


Generally the heat of fusion (enthalpy of fusion) is less than heat of vaporization.

It takes more energy to completely separate molecules, than to partially separate them.


Heating Curves: Plot of temperature change versus heat added.

When we heat an ice cube initially at -25 °C and 1 atm pressure



Supercooling: When a liquid is cooled below its freezing point and it still remains a liquid.


Critical Temperature and Pressure

A gas normally liquefies at some point when pressure is applied.

For water vapor at 100 °C . If we increase the pressure on the water vapor, liquid water will form when the pressure is 760 torr.

If the temperature is 110 °C, the liquid phase does not form until thepressure is 1075 torr.

At 374 °C the liquid phase forms only at (217.7 atm).

Critical temperature is the highest temperature at which a substance can exist as a liquid. Critical pressure is the pressure required for liquefaction at this critical temperature.



The greater the intermolecular forces, the easier it is to liquefy a substance. Thus, the higher the critical temperature.

supercritical fluid: A substance at temperatures and pressures higher than its critical temperature and pressure is in a state.


11.5 Vapor Pressure

Molecules can escape from the surface of a liquid into the gas phase by evaporation.

These molecules move into the gas phase

As the number of molecules in the gas phase increases, some of the gas phase molecules strike the surface and return to the liquid.

After some time, the pressure of the gas will be constant.

Suppose we place a quantity of ethanol (CH3CH2OH) in an evacuated, closed container,

A dynamic equilibrium has been established.


Dynamic equilibrium is a condition in which two opposing processes occur simultaneously at equal rates.

Vapor pressure of a liquid is the pressure exerted by its vapor when the liquid and vapor are in dynamic equilibrium.

The pressure of the vapor at this point is called the equilibrium vapor pressure.

Volatility, Vapor Pressure, and Temperature

If equilibrium is never established, the vapor continues to form. Eventually, the liquid evaporates to dryness. Liquids that evaporate easily are said to be volatile. The higher the temperature, the higher the average kinetic energy, the faster

the liquid evaporates.


The temperature of the boiling point increases as the external pressure increases.

Vapor Pressure and Boiling Point

Liquids boil when the external pressure at the liquid surface equals the vapor pressure.

The normal boiling point is the boiling point at 760 mm Hg (1 atm).


11.6 PHASE DIAGRAMS

A phase diagram is a graphic way to summarize the conditions under which equilibria exist between the different states of matter.


The Phase Diagram of H2O


The Phase Diagram of CO2


11.7 LIQUID CRYSTALS

Solids are characterized by their order.

Liquids are characterized by almost random ordering of molecules.

There is an intermediate phase where liquids show a limited amount of ordering.

Liquid crystals are substances that exhibit one or more ordered phases at a temperature above the melting point.


Example: cholesteryl benzoate. It melts at 145 °C.

The liquid flows (liquid properties) but has some order (crystal properties).

It has some properties of liquids and some of solids.


Types of Liquid Crystals


Selected Problems: 15, 17- 23, 26, 28, 35, 39, 43, 45, 46, 51, 52, 61, 66, 69, 73, 75, 77, 78.


General Chemistry B

PROPERTIES OF SOLUTIONS

Chapter 13


13.1 THE SOLUTION PROCESS

A solution is formed when one substance disperses uniformly throughout another.

A solution is a homogeneous mixture of solute and solvent.

Solutions may be gases, liquids, or solids

The solvent is the component present in the largest amount.

The other components are the solutes.


The mixing of gases is a spontaneous process, meaning it occurs of its own accord without any input of energy from outside the system.

The Natural Tendency Toward Mixing

It is the increase in disorder of the system that favors the solubility of any substance, even if the solution process is endothermic.

The solution process is accompanied by an increase in disorder or randomness.

Consider the formation of a gaseous solution of O2(g) and Ar(g).

The extent of spreading of the molecules and their associated kinetic energies is related to a thermodynamic quantity called entropy


Thus, the formation of solutions is favored by the increase in entropy that accompanies mixing.

When the solvent or solute is a solid or liquid, intermolecular forces become important in determining whether or not a solution forms.

The Effect of Intermolecular Forces on Solution Formation


Three kinds of intermolecular interactions are involved in solution formation:

3. Solvent–solute interactions between solvent and solute particles occur as the particles mix.

1. Solute–solute interactions between solute particles must be overcome in order to disperse the solute particles through the solvent.

2. Solvent–solvent interactions between solvent particles must be overcome to make room for the solute particles in the solvent.

Solutions form when the magnitudes of the solvent–solute interactions are either comparable to or greater than the solute–solute and solvent–solvent

interactions.




Energetics of Solution Formation

Solution processes are typically accompanied by changes in enthalpy.

When NaCl dissolves in water, the process is slightly endothermic Hsoln = 3.9 kJ/mol

We define the enthalpy change in the solution process as:

Separation of solute molecules (ΔHsolute)

Separation of solvent molecules (ΔHsolvent)

Formation of solute-solvent interactions (ΔHmix)

ΔHsoln = ΔHsolute + ΔHsolvent + ΔHmix


ΔHsoln can either be positive or negative, depending on the intermolecular forces.

Forming attractive intermolecular forces is always exothermic.

Breaking attractive intermolecular forces is always endothermic.

ΔHsolute and ΔHsolvent are both positive.

ΔHmix is always negative.

Δ ΔHmix > (ΔHsolute + ΔHsolvent) or Hmix < (ΔHsolute + ΔHsolvent)

MgSO4 added to water has ΔHsoln = –91.2 kJ/mol. NH4NO3 added to water has ΔHsoln = + 26.4 kJ/mol.


Nonpolar solvents dissolve nonpolar solutes

How can we predict if a solution will form?

In general, solutions form if the ΔHsoln is negative.

If ΔHsoln is too endothermic, a solution will not form.

Polar solvents dissolve polar solutes

NaCl doesn't dissolve to any great extent in gasoline.

Water and octane do not mix.


Solution Formation and Chemical Reactions

Some solutions form by physical processes and some by chemical processes.

NaCl(s) + H2O (l) Na+(aq) + Cl–(aq)

chemical process

physical process

Ni(s) + 2HCl (aq) NiCl2(aq) + H2(g)


13.2 SATURATED SOLUTIONS AND SOLUBILITY

If crystallization and dissolution are in equilibrium with undissolved solute, the solution is saturated.

There will be no further increase in the amount of dissolved solute.

Solubility is the amount of solute required to form a saturated solution.

The solubility of a given solute in a given solvent is the maximum amount of the solute that can dissolve in a given amount of the solvent at a specified temperature, given that excess solute is present.


A solution is said to be supersaturated if more solute is dissolved than in a saturated solution.

A solution with a concentration of dissolved solute that is less than the solubility is said to be unsaturated.

The solubility of NaCl in water at 0 oC is 35.7 g per 100 mL of water.

the nature of the solute. the nature of the solvent. the temperature. the pressure (for gases).

13.3 Factors Affecting Solubility

The tendency of a substance to dissolve in another depends on:


Solute-Solvent Interactions

Intermolecular forces are an important factor in determining solubility of a solute in a solvent.

The stronger the attraction between solute and solvent molecules, the greater the solubility.

Pairs of liquids that mix in any proportions are said to be miscible. Ethanol and water are miscible liquids.

Immiscible liquids do not mix significantly.

Gasoline and water are immiscible.



like dissolves like

Substances with similar intermolecular attractive forces tend to be soluble in one another.



The solubility of a gas in any solvent is increased as the partial pressure of the gas above the solvent increases

Pressure Effects

The solubilities of solids and liquids are not appreciably affected by pressure

The relationship between pressure and gas solubility is expressed by Henry’s law

Where Sg is the solubility of gas, Pg the partial pressure, k = Henry’s law constant.



Temperature Effects

The solubility of most solid solutes in water increases as the solution temperature increases


the solubility of gases in water decreases with increasing temperature

Thermal pollution: if lakes get too warm, O2 become less soluble and are not available for plants or animals.


13.4 EXPRESSING SOLUTION CONCENTRATION

The concentration of a solution can be expressed either qualitatively or quantitatively.

The terms dilute and concentrated are used to describe a solution qualitatively.

Mass percentage Mole fraction Molarity Molality

various ways to express concentration quantitatively


Mass Percentage, ppm, and ppb

mass percentage of a component in a solution, given by

36 % HCl by mass contains 36 g of HCl for each 100 g of solution.


For dilute solutions

parts per million (ppm)

parts per billion (ppb)

1 ppm contains 1 g of solute for each million grams of solution or, equivalently, 1 mg of solute per kilogram of solution.

Thus, 1 ppm also corresponds to 1 mg of solute per liter of aqueous solution.

Because the density of water is 1 g/mL , 1 kg of a dilute aqueous solution has a volume very close to 1 L.



Mole Fraction, Molarity, and Molality

the mole fraction (X) of a component of a solution is given by

the molarity (M) of a solute in a solution is defined as


The molality of a solution, denoted m, is a concentration unit that is also based on moles of solute.

Molality equals the number of moles of solute per kilogram of solvent:



Converting Concentration Units


To interconvert molality and molarity, we need to know the density of the solution.



13.5 COLLIGATIVE PROPERTIES

Some physical properties of solutions differ in important ways from those of the pure solvent.

“depending on the collection”

Colligative properties: physical properties of solutions that depend on the quantity (concentration) but not the kind or identity of the solute particles

freezing-point lowering boiling-point raising vapor-pressure lowering osmotic pressure


Vapor-Pressure Lowering

Nonvolatile solutes (with no measurable vapor pressure) reduce the ability of the surface solvent molecules to escape the liquid.

Therefore, vapor pressure is lowered.


The amount of vapor pressure lowering depends on the amount of solute.

Raoult’s law

The partial pressure exerted by solvent vapor above the solution, Psolution, equals the product of the mole fraction of the solvent, Xsolvent, times the vapor pressure of the pure solvent, P°solvent.

For example, the vapor pressure of pure water at 20 °C is P°H2O = 17.5 the temperature constant while adding glucose (C6H12O6) to the water so that the mole fractions in the resulting solution are XH2O = 0.800 and XC6H12O6 = 0.200


The presence of the nonvolatile solute lowers the vapor pressure of the volatile solvent By

The vapor-pressure lowering, ΔP, is directly proportional to the mole fraction of the solute, Xsolute

17.5 torr - 14.0 torr = 3.5 torr


Adding 1 mol of NaCl to 1 kg of water lowers the vapor pressure of water more than adding 1 mol of C6H12O6. Explain.


An ideal solution is defined as one that obeys Raoult’s law.

Real solutions show approximately ideal behavior when: the solute concentration is low. the solute and solvent have similarly sized molecules. the solute and solvent have similar types of intermolecular attractions.

ideality for a solution implies total uniformity of interaction.

Raoult’s law breaks down when the solvent-solvent and solute-solute intermolecular forces are much greater or weaker than solute-solvent intermolecular forces.


Boiling-Point Elevation

Because the solution has a lower vapor pressure than the pure solvent, a higher temperature is required for the solution to achieve a vapor pressure of 1 atm. As a result, the boiling point of the solution is higher than that of the pure solvent.


The increase in boiling point relative to that of the pure solvent, Tb

The magnitude of Kb, which is called the molal boiling-point-elevation constant, depends only on the solvent.


Freezing-Point Depression


the freezing point of the solution is lower than that of the pure liquid.

Kf , the molal freezing-point-depression constant




Osmosis

Semipermeable membranes permit passage of some components of a solution. Often they permit passage of water but not larger molecules or ions. Examples of semipermeable membranes are cell membranes

Osmosis, the net movement of solvent is always toward the solution with the higher solute concentration



Osmotic pressure ( ): the pressure required to prevent osmosis by pure solvent

Two solutions are said to be isotonic if they have the same osmotic pressure. Hypotonic solutions have a lower , relative to a more concentrated solution. Hypertonic solutions have a higher , relative to a more dilute solution.



Determination of Molar Mass

The colligative properties of solutions provide a useful means of determining molar mass.



13.6 COLLOIDS

Colloids or colloidal dispersions are suspensions in which the suspended particles are larger than molecules but too small to separate out of the suspension due to gravity.

Particle size: 5 to 1000 nm


The Tyndall effect is the ability of colloidal particles to scatter light.


Hydrophilic and Hydrophobic Colloids


Adsorption: when something sticks to a surface, we say that it is adsorbed.


Stabilization of an emulsion of oil in water by stearate ions


Removal of Colloidal Particles

Biological application

The gallbladder excretes a fluid called bile.

Bile contains substances (bile salts) that form an emulsion with fats in our small intestine.

Emulsifying agents help form an emulsion.

Emulsification of dietary fats and fat-soluble vitamins is important in their absorption and digestion by the body.

colloid particles often may be coagulated (enlarged) until they can be removed by filtration.


Colloid particles move more rapidly when the colloidal dispersion is heated, increasing the number of collisions. The particles stick to each other when they collide.

Adding an electrolyte neutralizes the surface charges on the colloid

particles.

Selected Problems: 15, 17, 23, 27, 29, 33, 39,41, 43, 45, 47, 51, 53, 55, 59, 63, 65, 67, 68, 69, 71, 73, 75, 77, 81, 83.


CHEMICAL KINETICS

General Chemistry B

Chapter 14


14.1 Factors that Affect Reaction Rates

Reaction rate : The speed at which a chemical reaction occurs

physical state of the reactants. concentration of the reactants. temperature of the reaction. presence or absence of a catalyst.

Chemical kinetics: is the study of how fast chemical reactions occur

There are several important factors that affect rates of reactions:


14.2 REACTION RATES

The speed of a chemical reaction—its reaction rate—is the change in the concentration of reactants or products per unit of time.

Let’s consider the hypothetical reaction

The units for reaction rate are usually molarity per second (M/s)


Progress of a hypothetical reaction AB.

The average rate of appearance of B over the 20-s interval from the beginning of the reaction



Change of Rate with Time


It is typical for rates to decrease as a reaction proceeds because the concentration of reactants decreases.


Instantaneous Rate

instantaneous rate of a reaction, which is the rate at a particular instant during the reaction.

The instantaneous rate at t=0 is called the initial rate of the reaction.


Reaction Rates and Stoichiometry


In general, for the reaction

the rate is given by



14.3 CONCENTRATION AND RATE LAWS

One way of studying the effect of concentration on reaction rate is to determine the way in which the initial rate of a reaction depends on the initial concentrations.


If we double [NH4 +] while holding [NO2-] constant, the rate doubles

(compare experiments 1 and 2)

If we increase [NH4+] by a factor of 4 but leave [NO2

-] unchanged (experiments 1 and 3), the rate changes by a factor of 4

These results indicate that the initial reaction rate is proportional to [NH4+]

We express the way in which the rate depends on the reactant concentrations by the equation

which shows how the rate depends on reactant concentrations, is called a rate law.


the rate law generally has the form

For the general reaction

The exponents m and n are typically small whole numbers.

The constant k is called the rate constant. The magnitude of k changes with temperature and therefore determines how temperature affects rate


Once we know the rate law for a reaction and the reaction rate for a set of reactant concentrations, we can calculate the value of k.

Once we have both the rate law and the k value for a reaction, we can calculate the reaction rate for any set of concentrations.


Reaction Orders: The Exponents in the Rate Law

The rate law for most reactions has the form

The exponents m and n are called reaction orders. For example, consider again the rate law for the reaction

Because the exponent of [NH4+] is 1, the rate is first order in [NH4

+]. The rate is also first order in NO2

−.

The overall reaction order is the sum of the orders with respect to each reactant represented in the rate law


The overall reaction order is the sum of the orders with respect to each reactant represented in the rate law.

Thus, for the NH4+ – NO2

− reaction, the rate law has an overall reaction order of 1 + 1 = 2, and the reaction is second order overall.

The exponents in a rate law indicate how the rate is affected by each reactant concentration.

If a rate law is second order with respect to a reactant [A]2 then doubling the concentration of that substance causes the reaction rate to quadruple because [2]2 = 4 whereas tripling the concentration causes the rate to increase ninefold: [3]2 = 9


For any reaction, the rate law must be determined experimentally.

In most rate laws, reaction orders are 0, 1, or 2.

However, we also occasionally encounter rate laws in which the reaction order is fractional or even negative.

2 NO(g) + 2 H2(g) N2(g) + 2 H2O(g)

rate = k[NO]2[H2]

a. What are the reaction orders in this rate law? b. Does doubling the concentration of NO have the same effect on rate as doubling the concentration of H2?


Magnitudes and Units of Rate Constants

The units of the rate constant depend on the overall reaction order of the rate law

A large value of k (109 or greater): the reaction is fast. A small value of k (10 or lower): the reaction is slow.



14.4 THE CHANGE OF CONCENTRATION WITH TIME

First-Order Reactions

Rate laws can also be converted into equations that show the relationship between concentrations of reactants or products and time.

A first-order reaction is one whose rate depends on the concentration of a single reactant raised to the first power.

For a reaction of the type A products

…………………… differential rate law

Using integration


………………….. integrated rate law

rearranged

Thus, you can use these equations to determine or

(1) the concentration of a reactant remaining at any time after the reaction has started

(2) the time interval required for a given fraction of a sample to react

(3) the time interval required for a reactant concentration to fall to a certain level.



Second-Order Reactions

A second-order reaction is one whose rate depends either on a reactant concentration raised to the second power or on the concentrations of two reactants each raised to the first power.

second order in just one reactant, A:

Integrating, we get the integrated form of the rate law:




Zero-Order Reactions

A zero-order reaction is one in which the rate of disappearance of A is independent of [A].

The rate law for a zero-order reaction is

where is [A]t the concentration of A at time t and [A]0 is the initial concentration.


Comparison of first orderand zero-order reactions for the disappearance of reactant A with time.


Half-Life

The half-life of a reaction, t1/2, is the time required for the concentration of a reactant to reach half its initial value,

A fast reaction has a short half-life.

We can determine the half-life of a first-order reaction by substituting


The half-life for second-order and other reactions depends on reactant concentrations and therefore changes as the reaction progresses.


14.5 TEMPERATURE AND RATE

The rates of most chemical reactions increase as the temperature rises.

A chemiluminescent reaction produces light.


For example, let’s reconsider the first-order reaction


The Collision Model

Reaction rates are affected both by reactant concentrations and by temperature.

The collision model, based on the kinetic-molecular theory accounts for both of these effects at the molecular level.

The greater the number of collisions per second, the greater the reaction rate.

As reactant concentration increases, therefore, the number of collisions increases, leading to an increase in reaction rate.

Increasing the temperature increases molecular speeds. As molecules move faster, they collide more forcefully (with more energy) and more frequently, increasing reaction rates.


Not all collisions lead to products

In fact, only a small fraction of collisions lead to products.

The Orientation Factor


In order for a reaction to occur, the reactant molecules must collide in the correct orientation and with enough energy to form products.

The minimum energy required to initiate a chemical reaction is called the activation energy, Ea, and its value varies from reaction to reaction.

Activation Energy


We can think of this minimum energy as an energy barrier.

The molecule having the arrangement of atoms shown at the top of the barrier is called either the activated complex or the transition state.


The rate depends on the magnitude of Ea; generally, the lower the value of Ea is, the faster the reaction.

The Arrhenius Equation

The number of collisions per unit time. The fraction of collisions that occur with the correct orientation. The fraction of the colliding molecules that have an energy equal to or

greater than Ea.

Arrhenius discovered that most reaction-rate data obeyed an equation based on three factors:

These three factors are incorporated into the Arrhenius equation:


In this equation k is the rate constant Ea is the activation energy R is the gas constant T is the absolute temperature. The frequency factor, A, is constant, or nearly so, as temperature is varied.

reaction rates decrease as Ea increases.

Taking the natural log of both sides


We can also evaluate Ea in a nongraphical way if we know the rate constant of a reaction at two or more temperatures.

Subtracting ln k2 from ln k1 gives

Simplifying





14.6 REACTION MECHANISMS

The steps by which a reaction occurs is called the reaction mechanism.

A reaction mechanism describes the order in which bonds are broken and formed and the changes in relative positions of the atoms in the course of the reaction.

Elementary Reactions

Elementary reactions: Reactions occur in a single event or step


Energy profile for conversion of methyl isonitrile (H3CNC) to its isomer acetonitrile (H3CCN).


Multistep Mechanisms

The number of molecules present in an elementary step is the molecularity of that elementary step.

Unimolecular reactions involve one molecule. Bimolecular elementary reactions involve the collision of two molecules. Termolecular elementary reactions involve the simultaneous collision of three molecules.

A multistep mechanism consists of a sequence of elementary steps. The elementary steps must add to give the balanced chemical equation. Some multistep mechanisms will include intermediates.


intermediates are species that appear in an elementary step but are neither a reactant nor product.

Intermediates are formed in one elementary step and consumed in another.

They are not found in the balanced equation for the overall reaction.

Intermediates are NOT the same as transition states.



Rate Laws for Elementary Reactions

If a reaction is elementary, its rate law is based directly on its molecularity.

Unimolecular processes are first order.

Bimolecular processes are second order.

Termolecular processes are third order


The Rate-Determining Step for a Multistep Mechanism

Most reactions occur by mechanisms with more than one elementary step.

Often one step is much slower than the others.

The slow step limits the overall reaction rate.

This is called the rate-determining step (rate-limiting step) of the reaction.

This step governs the overall rate law for the overall reaction.


Mechanisms with a Slow Initial Step

Consider the reaction:

Can we propose a reaction mechanism consistent with this rate law? Consider the two-step mechanism

Step 2 is much faster than step 1; that is, k2 >> k1 , telling us that the intermediate NO3(g) is slowly produced in step 1 and immediately consumed in step 2.


experimentally

Rate = k1[NO2]2 This theoretical rate law is in agreement with the experimental rate law.


14.7 CATALYSIS

A catalyst is a substance that changes the speed of a chemical reaction without undergoing a permanent chemical change itself.

Homogeneous catalyst: A catalyst that is present in the same phase as the reactants in a reaction mixture

In the absence of a catalyst, this reaction occurs extremely slowly

In the presence of bromide ion, the decomposition occurs rapidly in acidic solution:



A catalyst usually provides a completely different mechanism for the reaction.

In general, catalysts operate by lowering the overall activation energy for a chemical reaction.

Heterogeneous Catalysis

A heterogeneous catalyst is one that exists in a phase different from the phase of the reactant molecules, usually as a solid in contact with either gaseous reactants or with reactants in a liquid solution.


Enzymes

Enzymes are biological catalysts.

Most enzymes are large protein molecules.

Lock-and-key model for enzyme action.


Selected Problems: 19, 23, 25, 28, 29, 33, 35, 37, 43, 44, 45, 48, 51, 57, 59, 64, 73, 75, 77, 85.

General Chemistry B Chapter 11

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