CHEM 1120 EXAM 2

Chapters 14 & 15

Reaction rate

The speed of a chemical reaction (how fast the reaction makes products or uses reactants)

• Fast rate = large fraction of molecules reacting in a given period of time

• Slow rate = small fraction of molecules reacting in a given period of time

Reactant concentrations affect on reaction rate

The greater the concentration of reactant molecules, the faster the reaction (increased frequency of reactant molecule contact)

Concentration of gases depends on the partial pressure of the gas (higher pressure = higher concentration)

Concentration depends on molarity (M) = moles solute / L solution

Temperatures affect on reaction rate

Increasing temperature increases the reaction rate

In general, for every 10 C rise in temp, the speed of the reaction doubles

Breaking bonds requires energy (endo) while forming bonds gives off energy (exo)

Higher temp = higher kinetic energy of gas molecules (many collisons occur with enough energy to break bonds in reactants, faster rate of reaction)

Activation energy

The energy required to get the reaction started (comes from forming bonds and from temperature (kinetic energy))

Nature of the reactants affect on reaction rate

Refers to what kind of reactant molecules there are and their physical condition

• Smaller molecules tend to react faster than large molecules (quicker collisons bc faster molecules)

• Powdered solids are more reactive than blocks (more surface area)

• Certain types of chemicals are more reactive than others

• Ions react faster than molecules

Structure and orientations affect on reaction rate

Rate depends on the structure and relative orientation of colliding reactant particles

The orientation of the collisions between reactant molecules

Rate equation

To be consistent, the change in concentration of each substance is multiplied by 1/coefficient

Average rate

The change in measured concentrations in any particluar time period

• Linear approximation of a curve

• The larger the time interval, the more the average rate deviated from the instantaneous rate since reaction slows with time

The instantaneous rate

The change in concentration at any one particular time (ex: rate at 20 seconds)

• Slope at one point of a curve

• Determined by taking the slope of a line tangent to the curve at that point

Rate law

The rate law shows how the rate of a reaction depends on the concentration of one or more of the reactants

Rate law must be determined experimentally

The rate of a reaction is directly proportional to the concentration of each reactant raised to a power

Rate = k [A]ⁿ [B]^m

• n & m are the orders with respect to each reactant

• k is the rate constant

• the reaction is (m+n)^th order overall

Reaction order

The power tells you how much that reactant is contributing to the overall rate

Zero order

Rate = k [A]⁰ = k

The rate of the reaction does not depend on initial concentration

Doubling [A]⁰ will have no effect on reaction rate

Rate = M/s, k = M/s

First order

Rate = k[A]¹

The rate is directly proportional to the reactant concentration

Doubling [A] will double the rate of the reaction

Rate = M/s, k = s^-1

Second Order

Rate = k[A]²

The rate is directly proportional to the square of the reactant concentration

Doubling [A]² will quadruple the rate of the reaction

Rate = M/s, k = 1 / Ms

Integrated rate laws

Integrating the rate law shows the relationship between the concentration of A and the time of the reaction

First order integrated rate law

Rate law: rate = k[A]¹

Integrated rate law: ln[A]_t = -kt +ln[A]₀ (y = mx+b)

A graph of first order: ln[A] vs time is a straight line where slope = -k and the y intercept = ln[A]₀

Half life: t_1/2 = ln2 / k

Second order integrated rate law

Rate law: rate = k[A]²

Integrated rate law: 1 / [A]_t = kt + 1 / [A]₀

A graph of second order: 1 / [A] vs time results in a straight line where slope = k and the y intercept = 1 / [A]₀

Half life: t_1/2 = 1 / (k[A]₀)

Zero order reactions

Rate law: rate = k[A]⁰ = k

Integrated rate law: [A]_t = -kt + [A]₀

A graph of zero order: [A] vs time results in a straight line where slope = -k and the y intercept = [A]₀

Half life: t_1/2 = [A]₀ / 2k

Half life (t_1/2)

The half life of any reaction is the time it takes for the concentration of the reactant to fall to half its initial value

The half life depends on the order of the reaction

The half life of a first order reaction is constant

Relationship between order and half life

1. Zero order: the lower the intial concentration of the reactants, the shorter the half life

t_1/2 = [A]₀ / 2k

2. First order: half life is independent of the concentration

t_1/2 = ln(2) / k

3. Second order: half life is inversely proportional to the initial concentration. Increasing the initial concentration shortens the half-life

t_1/2 = 1 / (k[A]₀)

The effect of temperature on rate

• Changing the temperature changes the rate constant of the rate law

• k = A (-E_a / e^RT )

• T = temp in Kelvin

• R = gas constant in energy units (8.314 J / (K x mol)

• E_a = activation energy

• A = frequency factor constant = the rate the reactant energy approaches the activation energy

Activation energy

The amount of energy needed to convert reactants into the activated complex or transition state.

The difference in energy between the reactants and the activated complex.

Activated complex

A chemical species with partially broken and partially formed bonds (always high in energy because of its partial bonds)

Frequency factor

The number of molecules that begin to form the activated complex in a given period of time (you want a lot for a lot of product)

The arrhenius equation: the exponential factor

• The exponential factor in the Arrhenius equation is a number between 0 and 1, representing the fraction of reactant molecules with sufficient energy so they can make it over the energy barrier.

• The energy comes from converting the kinetic energy of motion to potential energy in the molecules when the molecules collide.

• Increasing temperature will increase the number of molecules with sufficient energy to overcome the energy barrier and the reaction rate.

Arrhenius Plots

• The equation is in the form y = mx + b

• y = ln (k)

• x = ( 1 / T )

• y - intercept = ln A (A has the same units as k)

• A graph of ln(k) vs. (1 / T) is a straight line

Arrhenius Equation: Two-point form

Can be used if you only have two data points (T, k)

Reaction Mechanism & Elementary step

The series of individual chemical steps or reactions that occur to produce the overall observed reaction.

Each step in a mechanism is an elementary step, which cannot be broken down into simpler steps

Intermediates

Materials that are products in an early mechanism step and reactants in a later step

Molecularity

The number of reactant particles in an elementary step

1. Unimolecular- 1 particle

2. Bimolecular- 2 particles (could be the same or different)

3. Termolecular- 3 particles (very rare)

Rate laws for elementary steps

The rate law of an ELEMENTARY step can be deduced from the molecularity of the step

Rate-determining step

The slow step of the reaction mechanism. Product production cannot occur any faster than the slowest step, the step determines the rate of the overall reaction.

The slowest step has the largest activation energy.

The rate law of the rate-determining step determines the rate law of the overall reaction.

Criteria to validate a mechanism

1. The elementary steps must sum to the overall balanced reaction

2. The rate law predicted by the rate-determining step of the mechanism must be consistent with the experiementally observed rate law.

Catalysts

Catalysts are consumed in an early mechanism step and then made in a later step.

They affect the rate of a reaction without being consumed

They work by providing an alternative mechanism for the reation with a lower activation energy

Speed up = positive catalysts

Slow down = negative catalysts

Heterogeneous catalysts

Species present in different phases

Heterogeneous catalysts hold one reactant molecule in proper orientation for reaction to occur when the collision takes place

Sometimes they also help to start breaking bonds

Ex: solid catalytic converter in a cars exhast system

Homogeneous catalyst

All species present in the same phase

Homogeneous catalysts react with one of the reactant molecules to from a more stable activated complex with a lower activation energy

Ex: Cl (g) in the destruction of O₃ (g)

4 steps of a heterogeneous catalysts reaction

1. Adsorption: the reactants are absorbed onto metal surfaces

2. Diffusion: the reactants diffuse on the surface until they approach each other

3. Reaction: the reactants react to from the products

4. Desorption: the products desorb from the surface into the gas phase

Enzymes: Biological catalysts

Enzymes are protein molecules that catalyze biological reactions

They are required for many biological reactions to proceed at a reasonable rate as the molecules are large and complex

Enzymes absorb the substrate reactant onto an active site that orients the substrate for reaction

Hemoglobin

Hemoglobin (Hb) is a protein found in red blood cells that reacts with O₂

It enhances the amount of O₂ that can be carried through the bloodstream

Hb + O₂ ⇋ HbO₂

Dynamic equilibrium

When the rates of the forward and reverse reactions are equal

The concentrations of reactants and products are constant (NOT EQUAL)

Denoted by ⇋

There is always a tendency to restore equilibrium

Equilibrium Constant (K)

The relationship between the chemical equation and the concentrations of reactants and products is called the law of mass action

aA + bB ⇋ cC + dD

• the lowercase letters represent the coefficients of the balanced chemical equations

• always products over reactants

• K has no units

Reversible processes

Processes that proceed in both the forward and reverse directions

O₂ Transport

Hb + O₂ ⇋ HbO₂

In the lungs:

• Concentration of O₂ is high, the equilibrium shifts to the right, Hb and O₂ combine to make more HbO₂

In the muscles:

• Concentration of O₂ is low, the equlibrium shifts to the left, HbO₂ breaks down increasing the amount of free O₂.

Significance of K

• K « 1, reverse reaction is favored, forward reaction doesnt proceed very far

• K » 1, forward reaction is favored, reverse reaction does not proceed very far

• K = 1 neither direction is favored, forward reaction proceeds about halfway

Relationship between K and chemical equations

K_forward = 1/K_reverse

K₂ = K₁ⁿ

K₃ = K₁ x K₂

Equilibrium constants for reactions involving gases

The concentration of a gas in a mixture is proportional to its partial pressure.

Partial pressures always in atm

K_c & K_p Connection

K_c = K_p when △n = 0

△n is the difference between the number of moles of gaseous reactants and the number of moles of gaseous products

Heterogeneous Equilibria

The concentrations of pure solids and pure liquids do not change during the course of a reaction, so they are NOT included in the equilibrium constant expression. You include (aq) and (g).

The Reaction Quotient (Q)

• The concentration ratio of the products (rasied to the power of their coefficients) to the reactants (rasied to the power of their coefficients) is called the reaction quotient, Q.

• Used when a reaction mixture with both reactants and products is not at equilibrium.

• You compare the current concentration ratios to the equilibrium constant.

Predicting the direction of change with Q

• Q > K, the reaction proceeds faster in the reverse direction (reactants will increase)

• Q < K, the reaction proceeds faster in the forward direction (products will increase)

• Q = K, the reaction is at equilibrium (products and reactions will not change)

If a reaction mixture contains just reactants, then Q =0 and the reaction proceeds in the forward direction

If a reaction mixture contains just products, then Q = ∞, and the reaction proceeds in the reverse direction