SCH4U - Unit 2

Energy

  • Energy - The capacity to do work

    • Measured in Joules(J), where 1 J = 1 kgxm2/s2

    • 1 kJ = 1000J

    • Calorie - The energy needed to raise the temperature of 1g of water by 1 K

    • 1000 cal = 1Kcal, or 1 food calorie

  • Thermal Energy - The energy associated with the random motion of atoms and molecules

  • Chemical Energy - Energy stored within the bonds of chemical substances

  • Kinetic Energy - Energy due to motion

    • EK = mv2/2

  • Potential Energy - Energy due to position, that gives it the ability to do work

    • Eg = mgh

  • First Law of Thermodynamics - The total energy of the universe is constant and can neither be created nor destroyed, only transformed

  • Internal Energy - The sum of all kinetic and potential energies of all the atoms and molecules in a substance

    • Et = EK + EP

    • For instance, an object thrown upwards will slow as it moves upwards, but then speed up as it falls due to gravity, yet always have constant internal energy

      • Upwards, kinetic energy decreases while potential energy increases

      • Downwards, kinetic energy increases while potential energy decreases

Work

  • The change in internal energy is equivalent to the heat transferred and the work done

    • ΔEt = q + W

      • If q is positive, heat is absorbed by the system

      • If q is negative, heat is released by the system

      • If W is positive, work is done on the system

      • If W is negative, work is done by the system

    • Expansion Work - The work done when a system changes size

      • If work is 0, the internal energy is equal to the heat transferred

      • W = F(d), or W = -P(ΔV)

  • q = mCΔt

  • System - The area being studied

    • Open System - A system which allows energy and matter to be transferred

    • Closed System - A system which allows energy to be transferred, but not matter

    • Isolated System - A system which allows neither energy nor matter to be transferred

  • Surroundings - Everything outside of a system

Enthalpy

  • Enthalpy - The value, represented by H, used to quantify the heat flow in or out of a system at a constant pressure

    • Heat - The transfer of thermal energy

    • Temperature - The average kinetic energy of the molecules of a substance

    • Specific Heat - The amount of heat required to raise the temperature of one gram of a substance by one degree Celsius/Kelvin, represented by C

    • H = Et + PΔV

    • When no work is done, ΔH = q

    • ΔH = Hproducts - Hreactants

      • ΔH - The heat released or absorbed during a reaction at a constant pressure

      • If ΔH is negative, heat is released

      • If ΔH is positive, heat is absorbed

  • Exothermic - A reaction which releases heat into the surroundings

  • Endothermic - A reaction which absorbs heat from the surroundings

  • Calculating ΔH:

    • Calorimetry

      • Uses a calorimeter, which contains the reaction within water

      • If heat is absorbed by the water, then the reaction released an equivalent amount of heat

      • If heat is released by the water, then the reaction absorbed an equivalent amount of heat

      • Use q=mCΔT to find q, then used ΔH=q/n to find molar enthalpy

    • Hess’s Law - The energy transferred in a reaction is the same in a multi-step reaction if the reactants and the products are the same

      • Rearrange given equations so the necessary substances are correctly on the reactant or product side

        • If a reaction is reversed, the ΔH will become its opposite

      • Multiply each reaction by coefficients to match the coefficients in the desired equation

      • Write all of the equations as one large equation with all the reactants on one side, and all of the products on the other

      • Combine like substances and cancel any product that appears in equal amounts on both sides

      • Add together all of the ΔH values to find the ΔHrxn

    • Heats of Formation - The heat change for a substance being formed at a standard state, represented by ΔHfo, that is a measurement of the stability of the substance

      • The heats of formation of an element is 0

      • Find the necessary heats of formation in their correct state

      • Multiply by any coefficients, as necessary, to represent the energy in the reaction

      • Add together all of the energy of the reactants and products separately

      • ΔHrxn = ΔHfo(total products) - ΔHfo(total reactants)

Change of Phase

  • For a substance that remains at the same phase as it changes heat energy, all of the energy causes the molecules to change in temperature, so q=mCΔT can be used to calculate heat energy absorbed or released

  • When substances change phases, the change in heat is used to break apart or form bonds and altering the shape/potential energy, rather than increase or decrease temperature

    • Heat of Fusion - The amount of energy required to change 1 gram of pure substance from solid to liquid at its melting point

      • The energy absorbed or released when a substance changes between a solid and liquid

      • Qsolid = mHF

    • Heat of Vaporization - The amount of energy required to convert 1 gram of pure substance from liquid to gas at its boiling point

      • The energy absorbed or released when a substance changes between a liquid and a gas

      • Qliquid = mHV

      • This value is generally lower than the heat of fusion

        • When going from a solid to a liquid, only some bonds need to be broken, whereas when going from a liquid to a gas, all bonds must be broken

  • When finding the heat energy of a substance that spans multiple phases, q=mCΔT and the heat of fusion/heat of vaporization must be calculated

    • Consider that some substances may have different heat capacities at different phases

    • Once all pertinent q values are solved for, they can be added

Entropy

  • Second Law of Thermodynamics - The state of entropy of the entire universe will always increase over time, and the entropy can never be negative

    • All things in the universe tend towards chaos

  • Entropy - The disorder or randomness of a system, represented by S

    • The less attraction between molecules, the more disordered it becomes

    • ΔSuniverse = ΔHsystem/T + ΔSsystem = ΔSsurroundings + ΔSsystem

    • For example, when a system warms up, it becomes more disordered, and the surroundings become ordered

    • When something dissolves, the system becomes more disordered

    • If ΔS is positive, the system becomes disordered

    • If ΔS is negative, the system becomes ordered

Gibbs Free Energy

  • Gibbs Free Energy - The amount of energy absorbed or released by the equation which indicates spontaneity

    • ΔGrxno = ΔHrxno - TΔSrxno

    • ΔGrxno = ΔGfo(total products) - ΔGfo(reactants)

    • If ΔG is positive, the reaction is non-spontaneous

      • Favours reactants

    • If ΔG is negative, the reaction is spontaneous

      • Favours products

    • If ΔG is zero, the reaction is at equilibrium

      • Products and reactants are equally favoured

ΔH

T

ΔS

ΔG

(-)

any

(+)

(-) spontaneous

(+)

any

(-)

(+) non-spontaneous

(-)

High

(-)

(+) non-spontaneous

(-)

Low

(-)

(-) spontaneous, enthalpy driven

(+)

High

(+)

(-) spontaneous, entropy driven

(+)

Low

(+)

(+) non-spontaneous

  • To find the point at which ΔG goes from positive to negative, set ΔG to 0, and isolate for T

    • T = ΔHrxn/ΔSrxn

  • When a solid is dissolved in a solvent, although it requires heat to break bonds, it becomes very disordered, and thus makes the overall reaction spontaneous

K Constant and Equilibrium

  • Equilibrium Constant - The ratio between the concentrations of the products and reactants at equilibrium, represented by K

    • ΔGrxno = -RT(lnK)

      • R = 8.314J/K

      • If K>1, the reaction is spontaneous

      • If K<1, the reaction is non-spontaneous

    • ΔGrxn new = ΔGrxno + RT(lnQT)

      • Use when the reaction does not happen at a standard state

      • QT represents the reaction quotient

        • Q = (product of reactants)/(product of products)

        • Each reactant and product should be raised to its order

      • If more reactants are added, Q becomes smaller, and the whole reaction will become more spontaneous

Coupled Reactions

  • When one desired reaction is thermodynamically unfavourable, it can be coupled with a thermodynamically favourable reaction that produces a product that makes the initial reaction more favourable

  • These reactions share at least one common intermediate

  • The overall ΔG will be less than zero to make this multi-step reaction product-favoured

Reaction Rates

  • Factors that cause the reaction rate to increase

    • An increase in the concentration of reactants

    • Higher temperatures

    • Adding catalysts which help the molecules interact/collide

    • Increasing pressure

    • Existing in a state with less/weaker intermolecular forces

      • Rategas > Rateliquid > Ratesolid

    • Mixing the reactants

  • Average reaction rate of disappearance for reaction A→B

    • RateAvg = -Δ[A]/Δt = Δ[B]/Δt

    • For reaction A→2B

      • RateAvg = -Δ[A]/Δt = Δ[B]/2Δt

    • The average rate decreases as the reaction proceeds because there are fewer collisions between the reactant molecules

  • Instant reaction rate

    • Solve for using rate laws

    • Rate = k[reactant]m

      • k is the rate constant

        • If k is large, there will be a rapid reaction

        • If k is small, it will be a small reaction

      • m is the rate order

      • If there are multiple reactants, multiply each with their individual order

        • Rate = k[reactant1]x[reactant2]y…

Orders of Reactions

  • To determine the order of a reactant:

    • Find two reactions where the concentration of only one reactant (the one being observed) changes

    • Find the factor by which the concentration changes

    • Find the factor by which the initial rate changes

    • If the factor of concentration is a value other than one, and the factor of the initial rate is one (not changing), that reactant is zero order

      • e.g., If the reactant doubles, the initial rate does not change

    • If the factor of concentration and the factor of the initial rate are equal, that reactant is first order

      • e.g., If the concentration doubles, the initial rate doubles

    • If the factor of concentration is the square root of the factor of the initial rate, that reactant is second order

      • e.g. If the concentration doubles, the initial rate quadruples

    • Repeat for all reactants individually

  • To determine the order of a reaction:

    • Add together the orders of each individual reactant

    • Zero order reaction - Rate = k[A]0

    • First order reaction - Rate = k[A]1

    • Second order reaction - Rate = k[A]2

Integrated Rate Laws

  • When considering time in relation to reaction rates, integrated rate laws must be used

    • Zero order reaction - [A]t = -kt + [A]i

    • First order reaction - ln[A]t = -kt + ln[A]i

    • Second order reaction - 1/[A]t = +kt + 1/[A]i

  • When graphing concentration as a function of time, the relation of t to [A] can indicate what order the reaction is

    • Zero order - [A]

    • First order - ln[A]

    • Second order - 1/[A]

  • To find half-life, use the following equations

    • Zero order - t1/2 = [A]i/2k

    • First order - t1/2 = 0.693/k

    • Second order - t1/2 = 1/k[A]i

Collision Theory

  • As temperature increases, the rate constant k increases because it is temperature dependent

  • Collision Theory Model - Molecules can only react if they collide in the right orientation with enough energy to cause bond breakage

    • Activation Energy - The amount of energy required to break bonds, represented by Ea

      • It is the minimum amount of energy required to start the reactant

    • As temperature increases, the fraction of molecules that can overcome the activation energy increases

      • f = e-Ea/RT

        • An increase in temperature by 10 degrees causes the fraction of colliding molecules doubles, and thus the rate constant doubles

  • Arrhenius’s Math

    • k = Ae-Ea/RT

      • Frequency Factor - The number that represents the likelihood that collisions would occur with the proper orientation for a reaction, represented by A

        • The greater the frequency factor is, the probability and speed of the reaction will increase

        • It is temperature dependent

      • A = (fraction of collisions with proper orientation)(collision frequency)

      • A changes slightly with temperature

    • ln(k) = -Ea/RT + ln(A)

      • To solve for Ea, k must be determined

      • ln(k) plotted against 1/T should create a straight slope

      • The slope is -Ea/R, or -Ea/8.314

      • The y-intercept is A

    • ln(k2/k1) = Ea/R x (1/T1 - 1/T2)

      • Uses two different temperatures and rate constants

      • The rate constant is proportional to the rate

Reaction Mechanisms

  • Reaction Mechanism - The sequence or steps of smaller reactions that describes the actual process by which reactants become products

    • Reactions can be made of multiple elementary reactions

  • One step of a multi-step reaction will always be slower, and thus determine the rate of the overall equation

    • Observing this rate can determine the overall rate law

  • Intermediate - A highly reactive and unstable substance produced during a middle step of a chemical reaction

    • It will be produced and then consumed

    • They are not in the initial step or final product, and thus, not used in rate laws

  • Catalyst - A compound that increases the rate of a chemical reaction, but is not consumed

    • It will exist as both a reactant and a product

    • They change the mechanism of the reaction and decrease the activation energy

    • Heterogeneous Catalyst - A catalyst which is not the same state as the reaction materials

    • Homogenous Catalyst - A catalyst which is the same state as the reaction materials

    • Enzyme - A biological catalyst

  • Steady State Approximation - The assumption that the rates of forward and reverse reactions are equal in reactions with a fast first step

    • Rateforward = Ratereverse

    • k1[A] = k-1[A]

    • This value can be substituted in the rate law to determine the slower rate

      • Rate = (k2k1)[A]/k-1

      • (k2k1)/k-1 = K

        • K is the overall rate constant

  • The overall sum of all elementary reactions, once simplified, should result in the overall balanced reaction, and it must equal the determined rate law

  • Transition State - The point of a reaction where the activated complex has partially formed product bonds and partially broken reactant bonds, and potential energy is at the highest

    • The energy difference required to get from the reactants to the activated complex is the activation energy

    • The greater the activation energy required, the slower the reaction rate becomes

      • It becomes harder to collide and overcome this energy barrier

      • RT ln(kcat/kuncat) = Ea uncatalyzed - Ea catalyzed