4.S: Kinetics (Study Guide)
4.1: Prelude to Kinetics
chemical kinetics – area of chemistry dealing with speeds/rates of reactions
4.2: Reaction Rates
- reaction rate – speed of a chemical reaction
[latex]\displaystyle \textit{average rate} = \frac{\textit{change #moles B}}{\textit{change in time}}= \frac{\Delta\textit{moles B}}{\Delta t}\textit{ if }A \to B \nonumber[/latex]
[latex]\Delta\textit{moles B} = \textit{moles B at final time}- \textit{moles B at initial time} \nonumber[/latex]
[latex]\displaystyle \textit{average rate} = -\frac{\Delta\textit{moles A}}{\Delta t}\textit{ if }A \to B \nonumber[/latex]
- rate calculated in units of M/s
- brackets around a substance indicate the concentration
- instantaneous rate – rate at a particular time
- instantaneous rate obtained from the straight line tangent that touches the curve at a specific point
- slopes give instantaneous rates
- instantaneous rate also referred to as the rate
- for the irreversible reaction [latex]aA+bB\to cC+dD[/latex]
[latex]\displaystyle\textit{rate} = -\frac{1}{a}\frac{\Delta [A]}{\Delta t} = -\frac{1}{b}\frac{\Delta [B]}{\Delta t} = \frac{1}{c}\frac{\Delta [C]}{\Delta t} = \frac{1}{d}\frac{\Delta [D]}{\Delta t} \nonumber[/latex]
4.3: Factors that Affect Reaction Rates
- rates of reactions affected by four factors
- concentrations of reactants
- temperature at which reaction occurs
- presence of a catalyst
- surface area of solid or liquid reactants and/or catalysts
4.4: Rate Laws
- Rate law – expression that shows that rate depends on concentrations of reactants
- k = rate constant
- Rate = k[reactant 1]m[reactant 2]n
- m, n are called reaction orders
- m+n, overall reaction order
- reaction orders do not have to correspond with coefficients in balanced equation
- values of reaction order determined experimentally
- reaction order can be fractional or negative
4.4.1 Reaction Order and Rate Constant Units
- units of rate constant depend on overall reaction order of rate law
- for reaction of second order overall
- units of rate = (units of rate constant)(units of concentration)2
- units of rate constant = M-1s-1
- zero order – no change in rate when concentration changed
- first order – change in concentration gives proportional changes in rate
- second order – change in concentration changes rate by the square of the concentration change, such as 22 or 32, etc…
- rate constant does not depend on concentration
4.5: Integrated Rate Laws
- rate laws can be converted into equations that give concentrations of reactants or products
4.5.1 First-Order Reactions
[latex]\textit{rate} = -\frac{\Delta [A]}{\Delta t} = k[A] \nonumber[/latex]
and in integral form:
[latex]\ln[A]_t - \ln[A]_0 =-kt \nonumber[/latex]
or
[latex]\ln\frac{[A]_t}{[A]_0} = -kt \nonumber[/latex]
[latex]\ln[A]_t = - kt + \ln[A]_0 \nonumber[/latex]
- corresponds to a straight line with [latex]y = mx + b[/latex]
- equations used to determine:
- concentration of reactant remaining at any time
- time required for given fraction of sample to react
- time required for reactant concentration to reach a certain level
4.5.2 Second-Order Reactions
- rate depends on reactant concentration raised to second power or concentrations of two different reactants each raised to first power
[latex]\text{Rate} = k[A]^2 \nonumber[/latex]
[latex]\displaystyle\frac{1}{[A]_t} = kt + \frac{1}{[A]_0} \nonumber[/latex]
[latex]\displaystyle\textit{half life} = t_{\frac{1}{2}} = \frac{1}{k[A]_0} \nonumber[/latex]
- half life dependent on initial concentration of reactant
4.5.2 Zero-Order Reactions
- A zero-order reaction thus exhibits a constant reaction rate, regardless of the concentration of its reactants.
4.5.4 Half-Life
- half-life of first order reaction
[latex]\displaystyle t_{\frac{1}{2}} = -\frac{\ln\frac{1}{2}}{k} = \frac{0.693}{k} \nonumber[/latex]
- half-life – time required for concentration of reactant to drop to one-half of initial value
- [latex]t_{1/2}[/latex] of first order independent of initial concentrations
- half-life same at any given time of reaction
- in first order reaction – concentrations of reactant decreases by ½ in each series of regularly spaced time intervals
4.6: Collision Theory
- collision model – molecules must collide to react
- greater frequency of collisions the greater the reaction rate
- for most reactions only a small fraction of collisions leads to a reaction
- rate constant must increase with increasing temperature, thus increasing the rate of reaction
4.6.1 Activation Energy
- Svante August Arrhenius
- Molecules must have a minimum amount of energy to react
- Energy comes from kinetic energy of collisions
- Kinetic energy used to break bonds
- Activation energy, Ea – minimum energy required to initiate a chemical reaction
- Activated complex or transition state – atoms at the top of the energy barrier
- Rate depends on temperature and Ea
- Lower Ea means faster reaction
- Reactions occur when collisions between molecules occur with enough energy and proper orientation
4.6.1 The Arrhenius Equation
- reaction rate data:
- theArrhenius Equation:
[latex]\displaystyle k = A e^{\frac{-E_a}{RT}} \nonumber[/latex]
- [latex]k[/latex] = rate constant, [latex]E_a[/latex] = activation energy, [latex]R[/latex] = gas constant (8.314 J/(mol K)), [latex]T[/latex] = absolute temperature, [latex]A[/latex] = frequency factor
- [latex]A[/latex] relates to frequency of collisions, favorable orientations
[latex]\displaystyle \ln k = -\frac{E_a}{RT} + \ln A \nonumber[/latex]
- the [latex]\ln k[/latex] vs. [latex]1/t[/latex] graph (also known as an Arrhenius plot) has a slope [latex]–E_a/R[/latex] and the y-intercept [latex]\ln A[/latex]
- for two temperatures:
[latex]\displaystyle \ln \frac{k_1}{k_2} = \frac{E_a}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right) \nonumber[/latex]
- used to calculate rate constant, [latex]k_1[/latex] and [latex]T_1[/latex]
4.7: Reaction Mechanisms
- reaction mechanism – process by which a reaction occurs
- elementary steps – each step in a reaction
- molecularity – if only one molecule involved in step
- unimolecular – if only one molecule involved in step
- bimolecular – elementary step involving collision of two reactant molecules
- termolecular – elementary step involving simultaneous collision of three molecules
- elementary steps in multi-step mechanism must always add to give chemical equation of overall process
- intermediate – product formed in one step and consumed in a later step
- if reaction is known to be an elementary step then the rate law is known
- rate of unimolecular step is first order (Rate = k[A])
- rate of bimolecular steps is second order (Rate = k[A][B])
- first order in [A] and [B]
- if double [A] than number of collisions of A and B will double
- rate-determining step – slowest elementary step
- determines rate law of overall reaction
- intermediates are usually unstable, in low concentration, and difficult to isolate
- when a fast step precedes a slow one, solve for concentration of intermediate by assuming that equilibrium is established in fast step
4.8: Catalysis
- catalyst – substance that changes speed of chemical reaction without undergoing a permanent chemical change
- homogeneous catalyst – catalyst that is present in same phase as reacting molecule
- catalysts alter Ea or A
- generally catalysts lowers overall Ea for chemical reaction
- catalysts provides a different mechanism for reaction
- Heterogeneous catalyst exists in different phase from reactants
- initial step in heterogeneous catalyst is adsorption
- adsorption – binding of molecules to surface
- adsorption occurs because ions/atoms at surface of solid extremely reactive
- Enzymes are biological catalysts
- large protein molecules with molecular weights 10,000 – 1 million amu
- catalase – enzyme in blood and liver that decomposes hydrogen peroxide into water and oxygen
- substrates – substances that undergo reaction at the active site
- lock-and-key model – substrate molecules bind specifically to the active site
- enzyme-substrate complex – combination of enzyme and substrate
- binding between enzyme and substrate involves intermolecular forces (dipole-dipole, hydrogen bonding, and London dispersion forces)
- product from reaction leaves enzyme allowing for another substrate to enter enzyme
- enzyme inhibitors – molecules that bind strongly to enzymes
- turnover number – number of catalyzed reactions occurring at a particular active site
- large turnover numbers = low activation energies