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Chemistry 12HL Reactivity 1-3
Reactivity 1
1.1: Measuring enthalpy changes
Heat transfers
energy is a measure of the ability to do work
to move an object against an opposing force
can be transferred through heat, light, sound, electricity, etc.
heat - form of energy transfer that occurs as a result of a temperature difference
when heat is transferred to a system, the average KE of molecules and the temperature are increased → KE is more dispersed among the particles
System and Surroundings
system → area of interest
open system → energy/matter can be exchanged with surroundings
closed system → energy can be exchanged but matter cannot
isolated system → energy and matter cannot be exchanged with surroundings
surroundings → everything else in the universe
Enthalpy of a system
enthalpy → chemical potential energy of a system
system acts as a reservoir of chemical potential energy/enthalpy
when heat is added to a system from its surroundings, its enthalpy increases (+ΔH)
when heat is given out by a system, its enthalpy decreases (-ΔH)
ΔH = change in enthalpy
endothermic:
exothermic:
Direction of a reaction
there is a natural direction for change
to lower stored/potential energy (exothermic)
chemicals change in a way that reduces their chemical potential energy
products of an exothermic reaction are more stable than the reactants
stability is a relative term
most combustion reactions are exothermic
the energy needed to break the bonds is less than the energy produced as bonds form
activation energy → minimum KE to react
some bonds must be broken before new bonds are formed
Measuring enthalpy changes
standard enthalpy change (ΔHꝊ)
pressure → 100kPA
concentration of 1mol/dm³ for all solutions
all substances in their standard states
usually 298K as temperature
thermochemical equations
ex: CH4(aq) + 2O2(g) → CO2(g) + 2H2O(l) ΔHreaction = -890kJ/mol
1 mole of CH4 reacts with 2 moles of O2 to produce 1 mole of CO2 and 2 moles of H2O and releases 890kJ of heat energy
Calculating enthalpy changes
absolute temperature (K) is a measure of the average KE of the particles
more/less particles with same heat energy added will result in a different temperature
q=mcΔT
q: heat added (J), m: mass (g), c: specific heat capacity (J/gK), ΔT: temperature change (K)
specific heat capacity → heat needed to increase the temperature of a unit mass of a substance by 1K
depends on the number of particles present
Combustion: enthalpy changes
enthalpy change of combustion (ΔHc) can be determined using this apparatus:
heat absorbed by the water can be calculated from the temperature change and mass
heat absorbed by calorimeter can also be calculated using c
temperature of the water increases due to heat released from the combustion reaction
heat released as ethanol and oxygen turn into carbon dioxide and water
there is a decrease in enthalpy in this reaction
Reaction in the solution: enthalpy changes
calculated by carrying out the reaction in an isolated system
heat released/absorbed by reaction can be measured from the temperature change in the water (solvent)
calorimeter made from an insulator to maximize heat transferred to water by reaction
error → all heat produced in the reaction is absorbed by the water
heat is lost from the system as soon as its temperature rises above the temperature of its surroundings
by extrapolating the cooling section to the time when the reaction started, it now creates some allowance for heat loss, so now we can assume:
no heat loss from system
all heat goes from reaction to water
solution is dilute
water has density of 1g/cm³
1.2: Energy Cycles in Reactions
energy changes occur when bonds are broken or new bonds are formed
energy is required to separate particles and energy is released when particles come together
net enthalpy change is the difference between these two energy contributions
law of conservation of energy → energy cannot be created or destroyed, only transferred
Bond enthalpy
bond enthalpy → energy needed to break one mole of bonds in gaseous molecules in standard conditions
ex: Cl2(g) → 2Cl(g) ΔH=+242kJ/mol
breaking bonds is an endothermic process (positive enthalpy change)
bond enthalpies differ, it may be harder to break depending on environment
to compare bond enthalpies which occur in different environments, average bond enthalpies will be used
all bond enthalpies refer to reactions in the gaseous state
any enthalpy changes resulting from the formation/breaking of intermolecular forces are not included
multiple bonds (involves more bonding electrons) generally have higher bond enthalpies and shorter bond lengths
the more polar the bond, the stronger it will be
making bonds is an exothermic process (negative enthalpy change)
the same amount of energy is absorbed when a bond is broken as is released when a bond is formed
Energy changes in reactions
ex: complete combustion of methane
CH4 + 2O2 → CO2 + 2H2O
energy is taken in to break the C-H and O=O bonds in the reactants
energy is given out when the C=O and O-H bonds are formed in the products
reaction is exothermic overall as the bonds formed are stronger than those broken
opposite would be true for endothermic reactions
ΔH = ΣEbonds broken - ΣEbonds formed
some reactants need to be given an initial energy (activation energy) before they will react
some bonds in the reactants must break before new bonds can form
rate of some reactions can be explained by the relative bond enthalpy of the bonds broken
Hess’s Law
the enthalpy change for any chemical reaction is independent of the route, provided the same starting conditions and final conditions, and reactants and the products, are the same
ΔH3=ΔH1+ΔH2
due to the conservation of energy
can be used to find enthalpy change of reactions that cannot be measured directly
Calculating enthalpy changes
standard enthalpy change of combustion (ΔHcꝊ)
enthalpy change that occurs when one mole of the substance burns completely under standard conditions
can be measured by calculating temperature change of water heated by the combustion
reactants - products
standard enthalpy of formation (ΔHfꝊ)
enthalpy change that occurs when one mole of the substance is formed from its elements in their standard states
standard measurements taken at a specific temperature (usually 298K) and pressure of 1×105 Pa
standard state of an element is its most stable form under these conditions
products - reactants
Lattice enthalpies
first ionization energy (ΔHiꝊ) → energy needed to form the positive ion of a gaseous atom
endothermic process (pulling electron away from electrostatic force)
first electron affinity (ΔHeꝊ) → enthalpy change when one mole of gaseous atoms attracts one mole of electrons
exothermic process (electron is attracted to positively charged nucleus)
lattice enthalpy (ΔHlatꝊ) → formation of gaseous ions from one mole of a solid crystal breaking into gaseous ions
ex: NaCl(s) → Na+(g) + Cl-(g) ΔHlatꝊ=+790kJ/mol
Born-Haber cycles
formation of an ionic compound from its elements is supposed to take place in a number of steps, including the formation of the solid lattice from its constituent gaseous ions
from Hess’s Law, the enthalpy change for the overall formation of the solid must equal the sum of the enthalpy changes accompanying the individual steps
ex: Na(s)+1/2 Cl2(g) → NaCl(s) ΔHf(NaCl)=-411kJ/mol
Na(s)→Na(g) sodium is atomized ΔHatom(Na)=+107kJ/mol
½ Cl2(g)→Cl(g) 1/2E(Cl-Cl)=1/2(+242KJ/mol) E=bond enthalpy
Na(g)→Na+(g)+e- ΔHi(Na)=+496kJ/mol
Cl(g)+e-→Cl-(g) ΔHe(Cl)=-349kJ/mol
Na+(g)+Cl-(g)→NaCl(s) -ΔHlat=+786kJ/mol → sum
1.3: Energy from fuels
Combustion reactions
many substances undergo combustion reactions when heated in oxygen
s-block metals form ionic oxides (basic)
p-block non-metals generally form covalent oxides (acidic)
many hydrocarbons/alcohols are used as fuels as their combustion reactions release energy at a reasonable rate to be useful
high activation energy → do not spontaneously combust, safe transport and storage
kinetically stable
complete combustion of organic compounds break the carbon chain → results in CO2 + H2O and a release in (a lot of) heat energy
complete combustion → products are fully oxidized
when oxygen supply is limited, incomplete combustion occurs
incomplete combustion of organic compounds
if the air supply is limited/compound has high carbon content, incomplete combustion occurs
results in carbon monoxide / carbon (soot)
releases less heat than complete combustion
Fossil fuels
an ideal fuel releases significant amounts of energy at a reasonable rate and produces minimal pollution
fossil fuels are non-renewable → used at a rate faster than they are replaced
liquid fuels have significantly greater energy densities than gases (per unit volume)
fossil fuels were formed by the reduction of biological compounds
oxygen is lost from biological molecules which generally result in hydrocarbons
coal → most abundant, 80-90% carbon (by mass)
crude oil → mixture of straight-chain and branched-chain saturated alkanes, cycloalkanes, and aromatic compounds, used as fuel for transportation and electricity
natural gas → primarily methane, cleanest fossil fuel → low carbon content
coal
advantages
cheap, abundant
longest lifespan (compared to other fossil fuels)
can be converted into synthetic liquid fuels and gases
safer than nuclear power
ash produced can be used to make roads
disadvantages
contributes to global warming (CO2 emissions)
contributes to acid rain (SO2)
produces particulats (electrostatic preceptors can remove most of these)
difficult to transport
waste can lead to visual + chemical pollution
mining is dangerous
petroleum
advantages
easily transported in pipelines/tankers
convenient fuel for use in cars → volatile, burns easily
high enthalpy density
sulfur impurities can be easily removed
disadvantages
limited lifespan and uneven world distribution
contributes to acid rain and global warming
transport can lead to pollution
carbon monoxide is produced through incomplete combustion (pollutant)
photochemical smog is produced
natural gas
advantages
higher specific energy
clean and easily transported
does not contribute to acid rain
disadvantages
limited supplies
contributes to global warming
risk of explosion (leaks)
Combustion of alkanes
increase in %carbon content down the homologous series suggests that incomplete combustion increases with length of the carbon chain
mass of CO2 produced per unit mass of fuel increases with %carbon content
the higher %carbon content (and lower %hydrogen), the lower the specific energy
The greenhouse effect
it is estimated that CO2 contributes to about 50% of global warming
greenhouse gases allow shortwave radiation from the Sun to pass through the atmosphere but absorb the longer wave infrared radiation that was re-radiated from Earth’s surface
CO2 is a GHG as its molecules increase their vibrational energy by absorbing IR radiation
3 of the vibrational modes of CO2 are IR active → dipole changes as it vibrates
molecules then re-radiate the absorbed energy back to Earth’s surface → global warming
greenhouse effect increased as CO2 levels increased, causing (due to change in temperature):
changes in agriculture (crop yields)
changes in biodistribution due to desertification and loss of cold-water fish habitats
rising sea levels caused by thermal expansion and melting of polar ice caps/glaciers
Biofuels
photosynthesis converts light energy into chemical energy
chlorophyll (green pigment) absorbs solar energy which is used in this reaction:
6CO2(g) + 6H2O(l) → C6H12O6(s) + 6O2(g)
carbon dioxide + water → (using solar energy) glucose + oxygen
biofuels → produced from the biological fixation of carbon over a short period of time
ethanol is a liquid biofuel → used in internal combustion engines
made from biomass by fermenting plants high in starches and sugars
C6H12O6 → 2C2H3OH + 2CO2
process done at around 37C in absence of oxygen by yeast (provides enzyme)
advantages (when used in gasohol: 10% ethanol, 90% unleaded gasoline)
renewable, lower emissions of CO and nitrogen oxides, decreases dependance on oil)
disadvantages
ethanol absorbs water (it can form hydrogen bonds) so it seperates from the hydrocarbons
can cause corrosion
methane → made form bacterial breakdown of plant mateiral in absence of oxygen
C6H12O6 → 3CO2 + 3CH4
advantages of biofuels
cheap + readily available
renewable (if crops/trees are replanted)
less polluting than fossil fuels
disadvantages of biofuels
uses land → can be used for other purposes (ex: growing food)
high cost of harvesting and transportation
takes nutrients from soil / uses large amounts of fertilizers
lower specific energy than fossil fuels
Fuel cells
hydrogen fuel cell
H2(g) + ½ O2(g) → H2O(l)
this is a redox reaction (transfer of electrons from hydrogen to oxygen)
can produce an electric current if reactants are physically seperated
hydrogen fuel cell operates with either an acidic or alkaline electrolyte
in fuel cells, reactants are continuously supplied to different electrodes
hydrogen-oxygen fuel cell → alkaline electrolyte (most commonly used)
fuel cell will function as long as H2 and O2 are supplied
electrodes are often made of porous carbon with added transition metals (ex: nickel)
KOH (potassium hydroxide) provides the OH- ions that are transferred across the cell
problem: hydrogen gas must be extracted from other sources so might not be renewable
methanol fuel cell; DMFC → Direct Methanol Fuel Cell
methanol → stable liquid at normal environmental conditions, high energy density, easy to transport
DMFC → fuel is oxidized under acidic conditions on a catalytic surface to form CO2
H+ ions formed are transported across a proton exchange membrane from anode to cathode where they react with oxygen to form water
electrons are transported through an external circuit from anode to cathode
water is consumed at the anode and produced at the cathode
difference between fuel cells and primary voltaic cells:
fuel cells do not run out
fuel is supplied continuously to the cell as it is oxidized
1.4: Entropy and spontaneity
second law of thermodynamics: matter and energy tend to disperse and become more dispersed
entropy (S) → degree of dispersal of matter and energy of a system
spontaneous change → dispersion occurs naturally without work
Entropy
the natural tendency to change can be reversed if work is done
entropy → measure of dispersal/distribution of matter/energy in a system
ordered states with small energy distribution → low entropy
ex: gas particles concentrated in a small volume
disordered states with high energy distribution → high entropy
ex: gas particles dispersed throughout
as time moves forward, matter and energy become more dispersed → increases total entropy of universe
Predicting entropy changes
doubling number of particles also increases opportunity for matter/energy to be dispersed
doubling amount of a substance → entropy doubles
solid state → most ordered state with least dispersal → low entropy
increasing entropy: solid→liquid, solid→gas, liquid→gas
decreasing entropy: liquid→solid, gas→solid, gas→liquid
change due to number of particles (in gaseous state) is usually greater than any possible factor
Absolute entropy
entropy of a substance under standard conditions → section 13
all entropy values are positive
a perfectly ordered solid at absolute zero has an entropy of zero
Calculating entropy changes
calculated using differences between total entropy of the products and total entropy of the reactants
ΔS = ΔSproducts - ΔSreactants
calculations similar to enthalpy changes
entropy values are absolute values → always positive
Entropy changes of surroundings
to consider the total entropy change of a reaction, the entropy change in surroundings must also be considered
in an exothermic reaction, heat is transferred to the surroundings → general dispersal of energy
entropy of the surroundings increases as heat given out by reaction increases diispersal of surroundings
change in entropy of surroundings = enthalp ychange in the system x -absolute temperature
ΔSsurroundings = -ΔHsystem/T
exothermic reaction (-ΔH) increases entropy of surroundings
Calculating total entropy changes
second law of thermodynamics says that for a spontanous change:
ΔStotal = ΔSsystem + ΔSsurroundings > 0
ΔStotal = ΔSsystem - ΔHsystem/T > 0
endothermic reactions occur if change in entropy of system can compensate for negative entropy change of surroundings produced as the heat is transferred from surroundings to the system
strongly endothermic reactions are possible because there is a very large increase in dispersal of matter and entropy of the system
order may increase in local areas but only at the expense of greater disorder elsewhere
for chemical reactions, neither ΔHsystem or ΔSsystem can reliably be used to predict the feasability of a reaction
Gibbs energy
criterion or feasability of a reaction is given by:
ΔStotal = ΔSsystem - ΔHsystem/T > 0
ΔGsystem = ΔHsystem - TΔSsystem = -TΔStotal < 0
ΔGsystem → Gibbs energy
must be negative for a spontaenous process
for spontaneity, reaction must have ΔGsystem < 0
measure of quality of energy available
measure of energy free to do work rather than leave as heat
spontaneous reactions have negative Gibbs energy because they can do useful work
it is not essential for all heat to be transferred to surroundings to produce the necessary increase in the total entropy
enough energy must be transferred to surroundings to compensate for entropy decrease in the system, but the remaining energy is available to do work
this is the amount of energy that can be converted to electrical energy in a fuel cell
necessary energy transferred to surroundings = -TΔSsystem
energy available to do work = -ΔHsystem + TΔSsystem = -ΔGsystem
ΔG = ΔH - TΔS
ΔG is related to total energy change and this is just a reformulation of the 2nd law of thermodynamics
ΔG takes into account direct entropy change from transformation of chemicals in the system and indirect entropy change of surroundings resulting from the transfer of heat energy
ΔHsystem < TΔSsystem (T is always positive)
at low temperatures (TΔSsystem=0), this condition is met (exothermic) as ΔHsystem<0
endothermic reactions (positive ΔSsystem) can be spontaneous at higher temperatures
TΔSsystem > ΔHsystem
temperature Tspontaneous at which an endothermic reaction becomes spontaneous can be determined from:
Tspontaneous * ΔSsystem = ΔHsystem
Tspontaneous = ΔHsystem/ΔSsystem
The effect of ΔH, ΔS, and T on spontaneity of the reaction
ΔGsystem = ΔHsystem - TΔSsystem
if ΔG<0, reaction is spontaneous so:
if ΔHsystem > TΔSsystem, reaction is spontaneous
so if T is high, most likely not spontaneous makes ΔHsystem is high
GIbbs energy and equilibrium
only reactions where all reactants are formed into products have been considered
equilibrium mixture when ΔG=0
spontaneous reactions only occur when ΔG<0, so when ΔG=0
a mixture of reactant and product has higher entropy than pure samples
total entropy reaches a maximum when reactant = product
reaction quotient (Q) → ratio of products to reactants
ex: Q=[products]/[reactants] so at beginning, Q=0 and at the end, Q=infinity
equilibrium mixture when ΔG<0 (negative)
at beginning of reaction, total Gibbs energy of reactants > products so reaction proceeds in forward direction and Q increases (products increase, reactants decrease)
as reaction proceeds, Gibbs energy (system) decreases until equilibrium is reached (Q=K)
once equilibrium is reached, all possible changes are not likely to happen (ΔG increases)
position of equilibrium corresponds to a mixture with more products than reactants
minimum Gibbs energy → equilibrium state, net reaction stops
relative amounts of reactants and products are at equilibrium
composition of equilibrium mixture is determined by the difference in Gibbs energy between reactants and products
K=[productseqm]/[reactantseqm] > 1 when ΔG<0
The equilibrium constant K
relationship between K (equilibrium constant) and ΔG (change in Gibbs energy)
so ΔG=-RT * lnK
useful when K is difficult to measure directly
ex: reaction is too slow to reach equilibrium/amounts of components are too small to measure
relationship between ΔG and extent of reaction:
2.1: How much? The amount of chemical change
Using chemical equations to find volumes of gaseous reactants and products
Avogadro’s Law → equal amounts of all gases measured under the same conditions of temperature and pressure contain equal numbers of molecules
equal number of particles of all gases occupy equal volumes
V has a direct relationship with n
volume occupied by one mole of any gas (molar volume, Vm) must be the same for all gases when measured under the same temperature and pressure
at STP, one mole of gas has a volume of 22.7dm³/mol
STP → OC (273K) and 100kPa
increase in temperature = increase in molar volume
increase in pressure = decrease in molar volume
number of moles of gas (n) = volume/molar volume
Titration
uses volumetric analysis to find unknown volumes or concentrations
pipette used to measure known volume into a conical flask
other solution put into a burette
point at which the two solutions have reacted completely → equivalence point
known when indicator changes color at the end point
titre → volume needed to reach equivalence point
Back titration
done in reverse by returning to the end point after it has passed
used when end point is hard to identify or when one of the reactants is impure
known excess of one reactant is added to reaction mixture, and unreacted excess is then determined by titration against a standard solution
reacting amount is determined by subtracting the amount of unreacted reactant from its original amount used
Limiting reactant and theoretical yield
limiting reactant → reactant that determines the quantity of product
always the one fully used up, other reactants are added in excess
theoretical yield → maximum amount of product obtainable (assuming 100% of limiting reactants is used)
usually expressed in grams or moles
Percentage yield
theoretical yield assumes that chemical reactions have no loss, waste, or impurities
experimental yield → actual yield with factors taken into account
factors that may cause experimental yield to be lower than the theoretical yield:
side reactions occuring
decomposition of reactants and/or products
loss of product during purification
reversible chemical reactions preventing process completion
factors that may cause experimental yield to be higher than the theoretical yield:
impurities in a product
when a product has not been fully dried
factors that impact experimental yield in both directions (depending on type of reaction):
an incomplete reaction
percentage yield = experimental yield/theoretical yield * 100
Atom economy
Green Chemistry → sustainable design of chemical products and chemical processes
aims to minimize use of chemical substances that are hazardous to human health / the environment
percentage yield does not give a quantity of waste produced
atom economy is maximized by turning as much reactant atoms into products
% atom economy = molar mass of desired product / molar mass of all reactants * 100
efficient processes have high atom economies → uses fewer resources and generates less waste
2.2: How fast? The rate of chemical change
Rate of reaction
rate of reaction → rate of change in concentration
as the reaction proceeds, reactants are converted into products
concentration of reactants decrease and concentration of products increase
rate of reaction (moldm³/s)= increase in product concentration / time taken = decrease in reactant concentration / time taken
if the line is a curve, use the gradient of the tangent
rate of reaction is not constant, but is greatest at the start and decreases over time
Measuring rate of reaction
change in volume of gas produced
used if one of the products is a gas
collecting the gas and measuring change in volume at regular time intervals
using a gas syringe or displacement of water in an inverted burette
displacement method can only be used if gas collected has low solubility in water
change in mass
if one of the products is a gas, this can be done by setting the reaction on a scale
does not work if the gas is hydrogen → too light
change in transmission of light: colorimetry/spectrophotometry
used if one of the reactants/products is colored (so gives characteristic absorption in the visible region)
sometimes indicator is added to make it a colored compound
colorimeter/spectrophotometer measures the intensity of light transmitted by reaction components
rate of product formation → change in absorbance
change in concentration → titration
quenching → a substance is introduced that effectively stops the reaction, obtaining a “freeze frame” shot
done to avoid chemically changing the reaction mixture
samples are taken from the reaction mixture at regular time intervals and analyzed by titration
titration takes time, during which the reaction would proceed → quench
change in concentration using conductivity
total electrical conductivity of a solution depends on the total concentration of its ions and charges
measured using a conductivity meter
non-continuous methods of detecting change during a reaction: ‘clock reactions’
measure time it takes for the reaction to reach a certain chose point
uses time as the dependent variable
limitation: only gives average rate of reaction
Collision theory
particles in a substance move randomly as a result of their kinetic energy
not all particles will have the same kinetic energy, but instead a range
therefore the measurement is an average
increasing temperature = increasing average kinetic energy of particles
kinetic theory of matter (S1.1)
Maxwell-Boltzman energy distribution curve
DIAGRAM HERE
the number of particles having a specific value of kinetic energy (or probability of that value occuring) against values of kinetic energy
area under the curve → total number of particles in sample
nature of collisions between particles
when reactants are placed together, their kinetic energy cause them to collide
energy from collisions may cause bonds to break and new bonds to form
as a result, products ‘form’ and the reaction stops
rate of reaction depends on the number of successful collisions which form products
successful collisions depend on:
energy of collision
geometry of collision
energy of a collision
particles must have the required activation energy (Ea) necessary for overcoming repulsion between molecules, and often breaking bonds in reactants
when Ea is supplied, reactants achieve the transition state from which products can form
activation energy is thus an energy barrier for the reaction → different for all reactions
Ea → threshold value
if you pass, you may react
DIAGRAM HERE → activation energy
particles with Ek>=Ea will collide successfully
particles with Ek<Ea may still collide, but unsuccessfully
therefore, rate of reaction depends on proportion of particles that has Ek>Ea
DIAGRAM HERE → Maxwell curve activation energy
generally, reactions with high activation energy will proceed more slowly as fewer particles will have the required energy for a successful collision
geometry of a collision
DIAGRAM HERE → different collisions
because collisions between particles are random, there are many likely orientations → only some are successful
therefore, rate of reaction is determined by:
values of kinetic energy greater than activation energy
appropriate collision geometry
Factors that influence the rate of reaction
temperature
increasing temperature increases average kinetic energy of particles
DIAGRAM HERE → Maxwell curve
area under both curves is the same → same number of particles
at higher temperature, more particles have higher kinetic energies so the peak of the curve shifts rightwards
as temperature increases, collision frequency increases due to higher kinetic energy → more collisions involving particles with necessary activation energy
therefore, more successful collisions (every +10K, reaction rate doubles)
concentration
increasing concentration increases frequency of collisions between reactants → more successful collisions
as reactants are used up, the concentration decreases and the rate of reaction decreases
pressure
increasing pressure “compresses” the gas, effectively increasing concentration
surface area
increasing surface area allows for more contact and a higher probability of collisions
instead of one big chunk, divide it into smaller sections to increase total surface area
stirring can increase total surface area by ensuring individual particles are spread
catalyst → a substance that increases rate of reaction without itself undergoing chemical change
most catalysts work by providing an alternative route for the reaction that has lower activation energy
DIAGRAM HERE → uncatalyzed reaction, catalyzed reaction
without increasing temperature, more particles will have Ek>Ea, so will be able to undergo successful collisions
catalysts equally reduce Ea for both forward and reverse reactions, so does not shift equilibrium or yield
DIAGRAM HERE → Maxwell curve
catalysts increase efficiency, and there are “best” catalysts for certain reactions → otherwise reactions move too slowly or are conducted at too high temperatures
Catalysts
every biological reaction is controlled by a catalyst → enzyme
there is a specific enzyme for every particular biochemical reaction
biotechnology → field that searches for possible applications of certain enzymes
catalysts can replace stoichometric reagants → greatly enhances selectivity of processes
therefore, important aspect of Green Chemistry
catalysts are effective in small quantities and can frequently be reused
therefore do not contribute to chemical waste → increases atom economy
Reaction mechanisms
most reactions that occur at a measurable rate occur as a series of simple steps, each involving a small number of particles
this sequence of steps is known as the reaction mechanism
the individual steps (elementary steps) usually cannot be observed directly
therefore this is only a theory → cannot be proved (but there are clues)
often the products of a single step in the mechanism are used in a subsequent step
exists only as reaction intermediates, not as final products
ex: NO2(g) + CO(g) → NO(g) + CO2(g)
mechanism follows these elementary steps:
NO2(g) + NO2(g) → NO(g) + NO3(g)
NO3(g) + CO(g) → NO2(g) + CO2(g)
overall reaction: NO2(g) + CO(g) → NO(g) + CO2(g)
reactants and products cancel out → reaction intermediates
NO2 in reactants in step 1 and products in step 2 cancel out
NO3 in products in step 1 and reactants in step 2 cancel out
molecularity → used in reference to an elementary step to indicate number of reactant species involved
unimolecular → elementary step that involves a single reactant particle
bimolecular → elementary step with two reactant particles
trimolecular reactions are rare → extremely low probability of >2 particles colliding at same time with sufficient energy and correct orientation
Rate-determining step
the rate-determining step is the slowest step in the reaction mechanism
products of the reaction can only appear as fast as the products of this slowest elementary step
rate-determining step therefore determines overall rate of reaction
DIAGRAM HERE → reaction coordinate, potential energy
two maxima represent the transition states
minimum represents the intermediate species
in this example, first maxima (first step) is higher, so more activation energy required → thus slowest step, so rate-determining
catalysts usually find an alternative for the slowest step to speed up the reaction (rate-determining step made faster or changes)
Rate equations
rate equations are determined experimentally and depend on the mechanism of a reaction
consider the reaction: C60O3 → C60O + O2
we can follow the reaction by recording the change in absorbance of light of a certain wavelength
absorbance is directly proportional to concentration of C60O3
rate of reaction is equal to the rate of change in concentration of C60O3
rate=- [C60O3]/t (negative because concentration is decreasing)
rate can be calculated by finding gradient of line’s tangent at a specific point
rate slows down as concentration of C60O3 decreases
similarities in concentration VS time and rate VS time graphs suggests that the rate must be related ot concentration at each time
straight-line graph between absorbance and rate confirms that the rate of reaction is directly proportional to concentration of C60O3
reaction rate is directly proportional, so reaction rate = k[C60O3]
k is the rate constant
this equation is a rate equation → first order rate equation because the concentration of the only reactant is raised to the first power
rate of all reactions can similarly be shown to depend on concentration of one or more of the reactants, and the particular relationship depends on the reaction
generally, rate is proportional to products of concentrations of reactants, each raised to a power
A+B → products so rate=k[A]m[B]n
m and n are known as the orders of the reaction with respect to A and B
overall reaction order is sum of individual orders (m+n)
orders can only be determined by experiment (empirically)
no connection between reaction equation (coefficients, moles) and rate equation
Rate equation and reaction mechanism
as the rate of reaction depends on the rate-determining step, the rate equation for the overall reaction must depend on the rate equation for the rate-determining step
because the rate-determining step is an elementary step, its rate equation comes directly from its molecularity:
A → products: unimolecular, so rate=k[A]
2A → products: bimolecular, so rate=k[A]²
A+B → products: bimolecular, so rate=k[A][B]
rate equation for rate-determining step, predictable from its reaction equation, leads to the rate equation for the overall reaction
when rate-determining step is not the first step, the intermediate cannot be used in the rate equation → instead, substitute
order of reaction with respect to each reactant is not linked to coefficients in overall equation, but is instead determined by their coefficients in the equation for the rate-determining step
Order of a reaction
reaction that is zero-order with respect to a particular reactant → the reactant is required for reaction but does not affect rate as it is not present in the rate-determining step
if a reactant is present in the rate-equation, it partakes in the rate-determining step
reaction order can be fractional or negative in more complex reactions
concentration-time graphs do not give a clear distinction between first and second order
rate-concentration graphs clearly reveal the difference
zero-order: rate=k[A]0=k
DIAGRAM HERE
concentration-time → straight line, constant rate
gradient of line = k
rate-concentration → horizontal line
first-order: rate=k[A]
DIAGRAM HERE
concentration-time → rate decreases with concentration
rate-concentration → straight line passing through origin with gradient k
second-order: rate=k[A]²
DIAGRAM HERE
concentration-time → curve, steeper at start than first-order graph but leveling off more quickly
rate-concentration → parabola (square function), gradient proportional to concentration and initially zero
order of reaction can only be determined experimentally, thus these graphs are required to distinguish them
Determination of the overall order of a reaction
methods for determining order of reaction depends on the reactants
two methods, but only initial rate method is covered
initial rates method
carrying out a number of separate experiments with different starting concentrations of reactant A, and measuring the initial rate of each reaction
concentration of other reactants are held constant to see effect of A on reaction rate
changing concentration of A but no effect on rate → zero order with respect to A
changing concentration of A produces directly proportional changes in rate of reaction → first order with respect to A (doubling concentration of A doubles reaction rate)
changing concentration of A leads to the square of that change in the rate → second order with respect to A (doubling concentration of A leads to a four-fold increase in reaction rate)
use of the integrated form of the rate equation
calculus is used to analyze the integral of rate equation
direct graphical analysis of functions of concentration against time
The rate constant, k
units of k vary with order of reaction
zero order: rate=k, k=moldm³/s
first order: rate=k[A], k=rate/concentration=s-1
second order: rate=k[A]², k=dm³/mols
third order: rate=k[A]³, k=dm6/mol²s
k is temperature dependent → general measure of rate of a reaction at a particular temperature
temperature dependence of k depends on value of activation energy
high Ea → temperature rise causes significant increase in particles that can react
low Ea → same temperature rise will have proportionally smaller effect on reaction rate
temperature dependence of k is expressed in the Arrhenius equation
The Arrhenius equation
Suante Arrhenius showed that the function of molecules with energy greater than the activation energy at temperature T is proportional to e-Ea/RT (R is gas constant)
reaction rate and therefore rate constant are also proportional to this value
k=Ae-Ea/RT
A → Arrhenius factor (frequency factor, pre-exponential factor)
A takes into account the frequency of successful collisions based on collision geometry
A is a constant for a reaction and has same units as k (so varies with order)
Arrhenius plot → lnk=-Ea/RT + lnA
rule of thumb → 10K increase doubles reaction rate
2.3: How far? The extent of chemical change
Dynamic equilibrium
reaction takes place at same rate as its reverse reaction, so no net change is observed
physical systems (ex: bromine in a sealed container at room temperature)
bromine is a volatile liquid (boiling point close to room temperature)
significant amount of Br2 molecules will have enough energy to leave the liquid state (evaporate)
container is sealed so bromine vapour cannot escape → concentration increases
some vapour molecules will collide with surface of liquid, lose energy, and become liquid
Br2(l) ⇌ Br2(g)
rate of condensation increases with concentration of vapour (more vapour particles)
eventually, rate of condensation will equal rate of evaporation
no net change → equilibrium (only occurs in a closed system)
DIAGRAM HERE → rate of condensation = rate of evaporation
chemical systems (ex: dissociation between hydrogen iodide (HI) and its elements (H2, I2)
2HI(g) ⇌ H2(g) + I2(g)
colourless gas ⇌ colourless gas + purple gas
there will be an increase in purple hue when the reaction starts (production of I2)
at some point, the increase in colour will stop
rate of dissociation of HI is fastest at the start as the concentration of HI is the greatest, then falls as the reaction proceeds
reverse reaction had initially zero rate (no H2 or I2 present) then starts slowly and increases in rate as concentrations of H2 and I2 increase
eventually, the rate of the forward and reverse reactions will equal, so concentrations remain constant
equilibrium → dynamic because both reactions are still occuring
if the contents of the flask were analyzed at this point, HI, I2, and H2 would all be present with constant concentrations → equilibrium mixture
DIAGRAM HERE → equilibrium
if the experiment were reversed (starts with H2 and I2), eventually an equilibrium mixture will again be reached
reactants ⇌ products
→ forward, ← backward
constant concentrations of products and reactants does not mean equal amounts
equilibrium position → proportion of reactant and product in equilibrium
predominantly products → lie to the right
predominantly reactants → lie to the left
Equilibrium Law
consider the reaction: H2(g) + I2(g) ⇌ 2HI(g)
if we were to carry out a series of experiments on this reaction with different starting concentrations of H2, I2, and HI, we could wait until each reaction reached equilibrium and then measure the composition of each equilibrium mixture
there is a predictable relationship among the different compositions of these equilibrium mixtures
[HI]²/[H2][I2] → concentration at equilibrium ([HI] is squared because that is its coefficient in the equation)
K → constant value, equilibrium constant (fixed value at specified temperature)
every reaction has its particular value of K
equilibrium constant expression for reaction: aA + bB ⇌ cC + dD
K = [C]eqmc[D]eqmd / [A]eqma[B]eqmb
[A] → concentration, a → coefficient in reaction equation, products → numerator, reactants → denominator
high value of K → at equilibrium, proportionally more products than reactants
lies to the right, reaction almost to completion
K values tells differing extents of reactions
higher value = reaction has taken place more fully
K » 1: reaction almost goes to completion (right)
K « 1: reaction hardly proceeds (left)
Le Chatelier’s principle
a system at equilibrium when subjected to a change will respond in such a way as to minimize the effect of the change
whatever done to a system at equilibrium, it will respond in the opposite way
after a while, a new equilibrium will be established with different composition
changes in concentration
equilibrium mixture disrupted by increase in concentration of a reactant:
rate of forward reaction increases: forward =/ backward anymore
equilibrium will have shifted in favour of products (rightward)
value of K remains unchanged
same happens with decrease in concentration of product
rate of backward reaction decreases → new equilibrium position will be achieved (rightward)
often in industrial processes, product will be removed as it forms
ensures equilibrium is continuously pulled rightward → increasing yield of product
changes in pressure
equilibria involving gases will be affected if there is a change in the number of molecules
there is a direct relationship between pressure exerted by gas and the number of gas particles
increase in pressure → system response: decrease pressure by favouring the side with less molecules
new equilibrium position, K remains unchanged (if temperature does not change)
ex: CO(g) + 2H2(g) ⇌ CH3OH(g)
increase in pressure shifts equilibrium rightward → in favour of smaller number of molecules
increase in pressure → increases yield of CH3OH
if number of molecules are the same for both sides, pressure will not change equilibrium
changes in temperature
K is temperature dependent → changing temperature affects K
ex: 2NO2(g) ⇌ N2O4(g) ΔH=-57kJ/mol (forward reaction exothermic)
decrease in temperature → system produces heat → favours forward exothermic reaction
new equilibrium mixture (rightward) → K increases (higher yield at lower temperature)
increasing yield takes too long→ decreasing temperature lowers rates of reactions
addition of a catalyst
catalyst speeds up rate of reaction by providing alternative reaction pathway with a transition state with a lower activation energy
increases number of particles that have sufficient energy to react (without increasing temperature)
because both forward and backward reactions pass through the same transition state, both rates will increase → no change in equilibrium position and K
will not increase equilibrium yield of a product
speeds up attainment of equilibrium state → products form more quickly
has no effect in equilibrium concentrations → not chemically changed
The reaction quotient, Q
K is calculated using concentrations at equilibrium
Q → calculated using concentrations when not at equilibrium
as time passes and reaction proceeds, concentrations will change and eventually reach equilibrium
Q changes in direction of K → used to predict direction of reaction
if Q=K, reaction at equilibrium, no net reaction occurs
if Q<K, reaction proceeds rightward in favour of products
if Q>K, reaction proceeds leftward in favour of reactants
Quantifying the composition at equilibrium
done by calculating equilibrium constant (K) or concentration of reactants/products
only homogeneous equilibria → all reactants/products in the same phase (gas or solution)
equilibrium law can be used to solve for K and initial/final concentrations
Measuring the position of equilibrium
Gibbs energy change can be used to measure the position of equilibrium
ΔG → measure of work available from a system calculated for a particular composition of reactants and products (ΔG=Gproducts-Greactants)
ΔG=negative → reaction proceeds in forward direction
ΔG=positive → reaction proceeds in backward direction
ΔG=0 → reaction is at equilibrium (Gproducts=Greactants)
at the start of a reaction, total Gibbs energy of reactants is greater than products (lot of work is available) → ΔG=negative, reaction proceeds in forward direction
as reaction proceeds, total GIbbs energy of reactants decreases but of products increase
ΔG less negative, less work is available
system reaches equilibrium when total Gibbs energy of reactants and products are equal
no work can be extracted from system (ex: dead battery)
total Gibbs energy decreases as reaction progresses as work is done by the system
occurs both when reaction starts with reactants and products
equilibrium state → net reaction stops → minimum value of Gibbs energy
DIAGRAM HERE → equilibrium
DIAGRAM HERE → equilibrium
decrease in total Gibbs energy appears as work done or increase in entropy
system has highest possible value of entropy when Gibbs energy at minimum (at equilibrium)
reaction with large and negative ΔG value → spontaneous, equilibrium with high products
reaction with large and positive ΔG value → non-spontaneous, predominantly reactants
ΔG=-RT*lnk
ΔG negative, lnK positive, K>1: equilibrium mainly products
ΔG positive, lnK negative, K<1: equilibrium mainly reactants
ΔG=0, lnK=0, K=1: appreciable amounts of both reactants and products
Rate of reaction and equilibrium
ex: reaction that occurs in a single step
A + B ⇌ C + D
rate of forward reaction: k[A][B]
rate of backward reaction: k’[C][D]
K=[C][D]/[A][B] (equilibrium constant)
at equilibrium, rate of forward reaction = rate of backward reaction
k[A][B]=k’[C][D]
rearranging gives: K=k/k’
if k»k’, K is large → reaction proceeds to completion
if k«k’. K is small → reaction barely takes place
increasing concentration of reactants speeds up forward reaction (vice versa)
shifts equilibrium rightward
equilibrium constant stays the same regardless
adding a catalyst increases k and k’ by same factor → K stays the same
k=Ae-Ea/RT → activation energies of forward and backward reactions are different
differently affected by temperature
for endothermic reactions (Ea(forward) > Ea(backward)), increasing temperature will have greater effect increasing k than k’, so K increases
3.1: Proton transfer reactions
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