thermo exam 1

define the extent of reaction (ξ)

• numerical value in mols

• describes the change in moles for products and reactants

• single value for all products and reactants of a reaction at any given time

• ξ = |Δn|/v where n is moles of the reaction species and n is its stoichiometric coefficient

what does it mean when ξ = 0?

• reaction has not begun

• all concentrations are at initial values

is ξ extensive or intense?

• extensive

  • depends on the amount (or size) of the matter

  • if the scale of a reaction was doubled, ξ would be twice as large for any given value of t

• an intensive property of the reaction would be the percent completion, which is independent of the reaction scale

what is the relationship for mols of reactants and products, respectively, at time t, given ξ?

• products: n = n₀ + vξ

• reactants: n = n₀ - vξ

where v is the stoichiometric coefficient for the given reaction species.

as the extent of a reaction increases, the mols of its products __

increase

as the extent of a reaction increases, the mols of its reactants __

decrease

how is the rate of change in moles of products and reactants described with respect to time?

(d/dt)n = ± v (d/dt)ξ

• + for products

• - for reactants

how is concentration measured?

amount/volume

• mol/dm³

• mol/L

what is the conversion from mlc/cm³ to mol/dm³?

(mlc/cm³) × (mol/6.022×10²³ mlc) × (10cm/dm)³

• 1dm³ = 1L = 10cm³

how is the rate of change in concentration of products and reactants described with respect to time?

(1/v) (d/dt)[I] = ± (1/V) (d/dt)ξ

• + for products

• - for reactants

where V is the volume of the reaction species

and v is its stoichiometric coefficient

what equations define the rate of a reaction (v)?

v(t) = (1/V) (d/dt)ξ = - (1/v) (d/dt) [R] = (1/v) (d/dt) [P]

how is the rate of reaction (v) measured?

concentration/time

• mol⋅dm^-³⋅s^-1

starting from the rate law v = k[A]^m[B]ⁿ, solve for the units of the rate constant (k)

what are the units of the rate constant (k) for 0th, 1st, 3/2th, 2nd, and 3rd order reactions?

• 0th: concentration/time = mol⋅dm^-3⋅s^-1

• 1st: /time = s^-1

• 3/2th order: concentration^-1/2/time = mol^-1/2⋅dm^3/2⋅s^-1

• 2nd: concentration^-1time^-1 = mol^-1⋅dm³⋅s^-1

• 3rd: concentration^-2time^-1 = mol^-2⋅dm⁶⋅s^-1

describe the method of isolation

• method to determine the order of each reactant (m and n)

• involves maintaining a large excess of one reactant for the entire duration of the experiment,

  • while the concentration of the other reactant is changed to see how it effects the rate

• for v = k[A]^m[B]ⁿ, k[A]^m becomes roughly constant, and the rate is directly proportional to [B]ⁿ

list the drawbacks of the method of isolation

• excess concentration of one of the reactants may not be possible for solubility reasons

• reaction may be too fast for excess concentration to effect the rate

• 
  

describe the method of initial rates

• involves controlling the reactants’ initial concentrations

• then measure the rate of reactant consumption or product generation very soon after reactants are mixed

  • assume this concentration is the initial concentration at t=0 [ ]₀

• repeat of multiple relative amounts of the reactants

derive the equation used to find the order of a reactant in the method of initial rates

what is the equation used to find the order of a reactant in the method of initial rates?

m = (ln(rate1/rate2))/((ln[A₁])/ln[A₂]))

graph the reactant and product concentration vs time for a zero, first, and second order reaction. how would the first and second order graphs change for a higher or lower k value?

• for a larger k, the reaction happens much faster

  • the reactant curve has a sharper drop and reaches zero in less time,

  • while the product curve rises much faster

• for a smaller k, the reaction happens much slower

  • the reactant curve declines very gradually over a longer period, while

  • the product curve rises slower

product concentrations mirror the reaction concentrations

derive the integrated rate law for a first order reaction

derive the integrated rate law for a second order reaction

how would you make the plots of concentration vs time a straight line in the case of a first or second order reaction? how would you determine the rate constant?

• first order: plot the ln(concentration)

• second order: plot 1/concentration

• in both cases, the rate constant (k) is equal to the slope of the line (Δy/Δx)

derive the half life equation for a first order reaction

*independent of concentration

what is the relationship between the half-life (t_1/2) and the rate constant (k) for a first order reaction?

• inversely proportional (t_1/2 = 0.693/k)

• as reaction gets quicker (big k), half life gets shorter (little t_1/2)

• as reaction gets slower (little k), half life gets longer (big t_1/2)

describe the relationship between the decrease in concentration and half life (t_1/2), as shown on a graph for a first order reaction

• t_1/2 : [A]₀ to (1/2)[A]₀

• t_1/2 : (1/2)[A]₀ to (1/4)[A]₀

• t_1/2 : (1/4)[A]₀ to (1/8)[A]₀

• t_1/2 : (1/8)[A]₀ to (1/16)[A]₀

derive an expression for the time-dependent behavior of the product concentration in a first order reaction

derive the half-life equation for a second order reaction

• 1/[A]₀k = t_1/2

• *does depend on concentration

describe the relationship between the decrease in concentration and half life (t_1/2), as shown on a graph for a second order reaction

• 1t_1/2 : [A]₀ to (1/2)[A]₀

• 2t_1/2 : (1/2)[A]₀ to (1/4)[A]₀

• 4t_1/2 : (1/4)[A]₀ to (1/8)[A]₀

• 8t_1/2 : (1/8)[A]₀ to (1/16)[A]₀

how is the equilibrium constant defined for a first order reaction?

k_c = [P]_eq/[R]_eq = k₁ / k_-1

plot the graph of initial to equilibrium concentrations of products and reactants vs time for a first order reaction

• can divide [A]/[A]₀ quantity at equilibrium by [B]/[A]₀ quantity at equilibrium to solve for the equilibrium constant (k_c)

when is the relaxation method preferred to the isolation or initial rate method?

for reactions where the half-life is much shorter than the time to mix the reagents

describe the relaxation method, including how to determine if a reaction is first order, endothermic, or exothermic

• a reaction is allowed to reach equilibrium

• the temperature is quickly (almost instantaneously increased a few degrees)

• this changes the equilibrium constant, therefore changing the concentrations of products and reactants as the system reaches its new equilibrium (relaxes)

• spectrometry is used to measure the new concentrations

• the time it takes to reach the new equilibrium is called relaxation time

  • if changing the concentrations has no effect on concentration time, it is indicated to be a first order reaction

• Using L’Chatlier’s Principle,

  • if the concentration of products increases, it is indicated to be an endothermic reaction (heat is a reactant —> drives =ium to products)

  • if the concentration of reactants increases, it is indicated to be an exothermic reaction (heat is a product —> drives =ium to reactants)

derive the Arrhenius equation from d(lnk)/dT = E_a/RT²

define the terms E_a and A in the Arrhenius equation

• E_a refers to the activation energy

  • the minimum amount of chemical energy colliding reactant molecules must possess for a chemical reaction to occur

  • like an energy “hump” or barrier

  • units: kJ/mol

• A is the pre-exponential factor

  • it represents the total frequency of collisions that must occur between reactant molecules that have the correct spacial alignment to react

  • based on how often the molecules bump together, and

  • a steric factor (how likely the specific molecules are to be well-aligned)

  • same units as the rate constant (k)

draw two reaction coordinate diagrams, each illustrating the meaning of activation energy and enthalpy (∆H). draw one endothermic and one exothermic diagram.

use the equation sheet to write an equation for E_a in terms of two values of k, their respective temperatures, and constants.

E_a = ln(k2/k1)*R*(T1T2/T2 - T1)

use the equation sheet to write an equation for T₂ in terms of two values of k, T₁, Ea, and constants.

rewrite the Arrhenius equation so it may be graphed as a straight line. graph the equation and note the slope and y-intercept.

• ln(k) = ln(A) - E_a/(RT)

• plot ln(k) vs 1/T

• slope is -E_a/R

• y-intercept is ln(A)

describe the difference between elementary and complex reactions

• elementary reactions: occur in a single-step, no intermediates

  • rate law can be derived from the reaction coefficients

• complex reactions: multiple steps long, intermediates

  • rate law cannot be derived from the reaction coefficients

what is meant by the "molecularity" of an elementary reaction?

• unimolecular = 1 reactant

• bimolecular = 2 reactants

• termolecular = 3 reactants

draw forward and reverse arrows to identify complex and elementary reactions

describe the principle of detailed balance

• for every elementary step in a reaction, kc = k₁/k_-1

• not necessarily true for the reaction as a whole

• write the [P][P]/[R][R] out for each elementary step and multiply them

  • result with canceled intermediates and exponent repeats is = to the overall rate constant

• for a complex reaction, can draw it out stepwise and sum the reactants

describe the "steady state approximation"

• assumes rate of formation is equal to the rate of consumption of an intermediate, such that d[I]/dt = 0

draw graphs of the concentrations of reactant, product, and intermediate for different relative magnitudes of k₁ and k₂ , and identify in which case it is appropriate to apply the steady state approximation

• if k₁ is much larger than k₂, then the intermediate will build up and slowly be consumed

  • SSA does not apply

• if k₂ is much larger than k₁, then the concentration of the intermediate will be roughly constant

  • SSA does apply

How to write the rate law for a 2-step reaction in which the first step is rate-determining (as in

HW question 4).

use the stoich from the reactants in the first step, as if ti were the entire reaction

How to write the rate law for a 2-step reaction in which the first step reaches a rapid equilibrium and the second step is rate-determining (as in HW question 10).

unanswered

if a proposed mechanism agrees with the observed rate law for a reaction, does that necessarily mean that the mechanism is correct?

• no

• different pathways may yield the same overall rate law

if a proposed mechanism does not agree with the observed rate law for a reaction, does that necessarily mean that the mechanism is incorrect?

yes

describe the Lindemann mechanism for unimolecular reactions, such as isomerization and dissociation

unanswered

apply the steady state approximation the case of the Lindemann mechanism

unanswered

What is the reason that these processes (Lindemann mechanism) appear bimolecular at low enough pressure?

unanswered

under what concentration conditions are first order or second order behavior observed for the Lindemann mechanism?

unanswered

draw (or interpret) a graph of the rate constant (k) as a function of concentration, covering both the unimolecular and the bimolecular regions

unanswered

given a series of steps in a chain reaction, identify the various steps (initiation, propagation, inhibition, termination)

unanswered

what is meant by the "chain length"

unanswered