Thermodynamics And Kinetics Flashcards
Thermodynamics
Study of energy transfer and change
Can be used to predict how much energy a given process requires
Thermodynamic functions are based on probabilities and are valid only for systems composed of large number of molecules
Cannot usually be applied to specific microscopic phenomena such as a single collision between two molecules
Kinetics
Study of reaction rates and mechanisms
Can explain how essential chemical reactions can happen within milliseconds with the help of enzymes in the cell
Can be used to predict the rate of a chemical reaction
Often provides insight into the mechanism of the reaction at the molecular level
What can average speed of microscopic atoms and molecules contained in a space tell us?
Manifests as macroscopic observable properties such as pressure, temperature, and volume
What are the three categories of thermodynamic systems?
Open, closed, and isolated
System definitions are based on mass and energy exchange within the surroundings
Open: Can exchange both mass and energy with surroundings
Closed: can exchange energy, but not mass
Isolated: Cannot exchange energy or mass
What are two types of properties which can be used to describe the macroscopic state of a system?
Extensive: proportional to size of system (Volume, n moles)
Intensive: independent of size of system (Pressure P, Temperature T)
If two identical systems are combined and a property is the same for both the single and combined systems, then intensive
If property doubles when systems are combined, then extensive
Dividing one extensive property by another gives an intensive property
Temperature
Represents the amount of molecular movement in a substance
Motion of molecules divided into translational, rotational, and vibrational energies, which together describe overall energy of molecular motion
Sum of these energies is the thermal energy
Increase in thermal energy increases temperature
Temp can be thought of as the thermal energy per mole of molecules
- So temp is intensive property
- Combine two systems and thermal energy and moles double, temp same
How does the temperature of a gas or liquid relate to the translational kinetic energy of its molecules?
Directly proportional relationship
Translational motion
One of three energies of molecular motion
Can be divided into three degrees of freedom, or modes: 1. Along the x-axis, 2. Along the y-axis, and 3. Along the z-axis
Equipartition theory states that in a normal system each mode of motion will have the same average energy
- Energy of each mode is equal to 1/2 kT, k is Boltzmann’s constant (1.38 x 10^-23 J/K)
Boltzmann constant
Symbol k 1.38 x 10^-23 J/K Related to ideal gas constant R by Avogadros’ number N_A R = N_A k OR k = R/N_A
What is the average kinetic energy of a single molecule in any fluid? A mole of molecules in a fluid?
KE_molecule = 3/2 kT
KE_mole = 3/2 RT
T is temperature in Kelvin
Absolute Zero
Lowest possible temperature
-273 deg C
Or 0 deg K
Temp at which no molecular movement
At a pressure of 1 atm what temperatures does water freeze and boil at?
Freezes at 0 deg C or 273 K
Boils at 100 deg C or 373 K
What does Standard temperature and pressure refer to? What does standard ambient temperature and pressure refer to?
Stand temperature and pressure (STP): pressure of 1 atm, temperature of 273 K
Standard ambient temperature and pressure (SATP): pressure of 1 atm and temperature of 298 K (25 deg C)
What does the graph of volume vs. temperature look like for any given fixed pressure?
Exactly linear for any given pressure, but different slope
Higher slope for lower pressure, lower slope for higher pressure
Extrapolate line back to x intercept to get absolute zero temperature of 0 K or 273 deg C
What are the different ideal gas constants, R?
R = 0.0821 L atm / mol K R = 8.314 J atm / mol K
Pressure
Proportional to random translational kinetic energy of a group of molecules per volume occupied
At microscopic level, pressure results from molecules pushing against their container as they move randomly, exerting force that causes the container to stretch until equilibrium is reached through an opposing force
How does the rate of a given reaction usually compare to the frequency of collisions?
Rate of given reaction is usually much lower than frequency of collisions
Most collisions do not result in a reaction
Relative kinetic energies of a colliding compound must be greater than or equal to a threshold energy called activation energy
Atoms of both molecules must align in a specific way for collision to result in a reaction
- When molecules do not properly align, no reaction occurs, even if particles have sufficient kinetic energy to overcome activation energy
Arrhenius equation
k = zpe^{-Ea/RT}
Where z: collision frequency, p: fraction of collisions having effective spatial orientation (steric factor), and e^{-Ea/RT} fraction of collisions having sufficient relative energy
K is rate constant of reaction
Often written as k = A e^{-Ea/RT}
Increase in activation energy reduces value of k
Increase in either z or p (A) increases k
Value of rate constant is affected by pressure (relevant for gases), presence of catalysts, and temperature
How does increasing temperature affect the rate of a reaction?
Increases the number of possible collisions with sufficient activation energy, therefore increases the rate of a reaction
Higher temperature increases rate of forward and reverse reactions
Reaction rate
Describes how quickly the concentration of the reactants or products are changing over the course of the reaction
Rates are most often presented in units of molarity / s (M /s or mol / L s) because represent change in concentration of the reactants and the products over time
Concentration of substances can affect rate of reaction
Elementary reaction
Reaction that occurs in a single step
Stoichiometric coefficients of elementary equation give the molecularity of reaction (number of molecules that need to collide at one time for reaction to occur)
Molecularity of Reaction
Number of molecules that need to collide at one time for a reaction to occur
E.g. given elementary reaction aA + bB -> cC + dD
Molecularity is a + b (if both are 1, then bimolecular)
Most common molecularities are unimolecular, bimolecular, and termolecular
Most reactions represent the sum of multistep reactions
Average reaction rate over time for example: rate = - delta [A] / a t = - delta [B] / b t = delta [C] / c t = delta [D] / d t
Intermediates
Species that are products of one step and reactants of a later step in a multistep reaction
Get used up before end of reaction, so not shown in overall chemical equation
Often present in low concentrations
If sufficiently low, could pretend a reaction is elementary as an approximation for rate law
How do reverse reactions complicate calculation of reaction rates?
In early reaction, when reactants are high and concentration of products is zero, formation of products may have a different rate than later on, when there is a reverse reaction going to form reactants from the products
Rates rely on the concentration of reactants, so complicated
Tend to determine reaction rates based only on concentrations observed by experimenter in initial moments of reaction
Rate Law
Equation for reaction rate which incorporates only the concentration of reactants
Rate_forward kf [A]^{alpha} [B]^{beta}
Where kf is rate constant for forward reaction, alpha and beta are reaction order of each reactant, and sum of alpha + beta is overall order of reaction
If reaction is elementary then alpha = a and beta = b (stoichiometric coeffs), if not then alpha and beta must be determined experimentally
Remember that rate constant kf is not the rate of the reaction (proportional)
Reaction Order
Indicates how changes in the reactant concentrations influence the reaction rate
Order of each reactant indicates the particular influence of that reactant, while order of overall reaction provides more general information about relationships btwn reactant concentrations and reaction rate
Order of overall reaction is sum of exponents in rate law
Exponent of reactant in the rate law is reaction order for one reactant
What’s an example of a zero-order reaction in biology?
Occurs in enzyme-catalyzed reactions when concentration of substrate far outweighs concentration of enzyme
All enzyme catalytic sites are saturated and addition of additional substrate has no effect on reaction rate
Or multistep reaction where that particular reactant is in fast step of reaction
Rate-determining step
Rate of slowest elementary step determines rate of overall reaction
If second step in reaction, the first step also contributes (formation of reactants for slow step)
Catalyst
Substance that increases the rate of a reaction without being consumed or permanently altered
Increase rate of both the forward and reverse reactions by providing an alternative reaction mechanism that competes with uncatalyzed mechanism
- Can enhance product selectivity and reduce energy consumption
- May lower activation energy
- May increase steric factor
Most work by decreasing activation energy
Does not change equilibrium ratio of products and reactants
Types of catalysts
Heterogeneous or homogeneous
Heterogeneous: different phase than reactants and products (gas or aqueous particle react on a solid)
- particles can stick to or adsorb to surface of solid (IMFs)
- Rate of catalysis depends on strength of attraction btwn reactant and catalyst
- Rates can be enhanced by increasing SA of catalyst (grind solid into powder)
Homogeneous: Same phase as reactants and products (gas or liquid)
- Aqueous acid or base solutions
Auto-catalysis
Product of reaction acts as a catalyst for the reaction
E.g. Acid-catalyzed hydrolysis of ester, where product of carboxylic acid creates more acid to further catalyze reaction
Rate law of catalyst
Reactions with catalysts require separate rate constants
Total rate is given by sum of rates of both reactions (catalyzed and uncatalyzed)
Sometimes rate law includes conc of catalyst if catalyst in small concentration in reaction
E.g. uncatalyzed, rate = k0 [A]
Catalyzed, rate = kH+ [H+] [A]
Total rate law, rate = k0[A] + kH+ [H+][A]
Biological example of a catalyst
Enzyme: protein catalyst that speeds up almost every chemical reaction in human body
Enzymes mostly far more effective than catalysts found in lab due to specificity
Turnover rate: Number of reactions occurring at a single active site on one enzyme ~1000 / second
- Can be tens of thousands of times faster
How does a solvent effect the rate of a reaction?
Liquid molecules have 100 x more collisions / s than gas, but most collisions w/ solvent, so do not lead to reaction
Rate constant in liquid is function of both solvent characteristics and temperature
Solvent characteristics:
- dielectric: electrical insulation of reactants, making more stable
- solvation: reactants spread out and surrounded by solvent, decreasing collisions
- viscosity: reactants get trapped in solvent cages (cage effect), making rate of collisions of reactants equal to rate of collision of reactants in gas
Stirring or shaking liquids increases number of collisions
State
Physical condition of system as described by a specific set of thermodynamic properties
Macroscopic state of any one-component fluid system in equilibrium can be described completely by just three properties and all other properties can be derived
- at least one property must be extensive
State functions
Properties that describe the current state of a system Thermodynamic state functions are macroscopic properties of a system Internal energy (U), Temperature (T), Pressure (P), Volume (V), Enthalpy (H), Entropy (S), Gibbs energy (G)
Path Functions
Properties that do not describe the state of a system, but rather depend on the pathway used to achieve that state
E.g. Work and heat
How do we relate thermodynamic functions to a system on a molecular scale?
Using statistics
Statistically-based thermodynamic functions are highly useful for predictions on a macroscopic scale
- Usefulness of predictions increases with number of samples (i.e. molecules)
Internal energy
Collective energy of molecules measured on a microscopic scale
Energy includes vibrational, rotational, translational, electronic, intermolecular potential, and rest mass energy
Does not include macroscopic mechanical energies such as kinetic energy of entire system or potential energy of entire system raised off the ground or does not include bond enthalpy: energy associated with formation of intramolecular chemical bonds
Internal energy is state function
For ideal gas, any state function can be expressed as function of temperature and volume only, but internal energy depends only on temperature
Vibrational energy
Energy created by back-and-forth motion of atoms within a molecule
Makes insignificant contributions to internal energy for light diatomic molecules at T < few hundred K
Atoms in monatomic gas have no vibrational energy
Rotational energy
Energy created by rotation of a molecule around its center of mass
Spatial orientation of body changes, but center of mass remains fixed and each point within molecule remains fixed relative to other points
Atoms in monatomic gas have no rotational energy
Translational energy
Energy created by movement of center of mass of molecule
For monatomic gases, translational energy is sole contributor to kinetic energy
Electronic energy
Potential electrical energy created by the attractions between electrons and their nuclei
In chemical rxn, changing electronic energy accounts for greatest change in internal energy
With no chemical rxn, electronic energy remains nearly constant
Intermolecular potential energy
Energy created by intermolecular forces between molecular dipoles
For gas at room temp, very small contribution to internal energy
At high pressures, contribution becomes significant
Makes up substantial portion of internal energy in liquids and solids
Rest mass energy
Energy described in Einstein’s equation E = mc^2
What component of internal energy can change for an ideal gas?
Translational energy is only component of internal energy that can change for ideal gas
As a result, any change in internal energy of ideal gas causes corresponding temperature change
Not true for real gases, liquids, or solids bc internal energies can change through changes in other components that do not affect temperature
What are the two ways to transfer energy between systems?
Heat (q) and work (w)
Heat is spontaneous transfer of energy from a warmer body to a cooler body
Any energy transfer that is not heat is work
Heat Transfer
Occurs through random collisions between molecules of two systems
In each collision, energy is transferred from higher energy molecule to lower energy molecule
Higher energy molecule could even be in cooler system (remember averages)
Overall, majority of energy transfers from warmer to cooler system
Warmer body becomes cooler and cooler body becomes warmer until equilibrium
How can mitochondria help with thermoregulation?
When temperature of body begins to fall, mitochondria insert channels in inner membrane that dissipate the proton gradient
Energy “lost” as heat warms the body
Zeroth law of thermodynamics
Two systems in thermal equilibrium with a third system are in equilibrium with each other
Two bodies in thermal equilibrium share a thermodynamic property- temperature, a state function
Remember, that when two bodies at different temperatures are placed in thermal contact, on macroscopic level the temperatures of the two become equal
What are the three ways that energy transfer through heat can occur?
Conduction, convection, and radiation
Conduction: thermal energy transfer via molecular collisions
Convection: thermal energy transfer via fluid movements
Radiation: thermal energy transfer via electromagnetic waves
Conduction
Thermal energy transfer via molecular collisions
Requires direct physical contact
Higher energy molecules of one system transfer some of their energy to lower energy molecules of other system via molecular collisions
Also can be conducted through single object
Thermal conductivity (k): object’s ability to conduct heat
- depends on composition and temperature
Convection
Thermal energy transfer via fluid (liquid or gas) movements
Differences in pressure or density drive warm fluid in direction of cooler fluid
Radiation
Thermal energy transfer via electromagnetic waves
Heated metal glows red, orange-yellow, white, and finally blue-white as hot metal radiates visible EM waves
Before it begins to glow, radiates EM waves at frequency too low to be visible to human eye
All objects with T > 0K radiate heat
Does not require a medium to pass through (can propagate through vacuum)
Newton’s law of cooling
Body’s rate of cooling is proportional to temperature difference between body and environment
Emissivity
When radiation strikes an opaque surface, only a fraction is absorbed and the rest is reflected
- Fraction absorbed indicated by emissivity of surface (depends on surface composition, between 0 and 1)
Blackbody radiator: emissivity of 1, absorb 100% of incident radiation, so appear totally black
What are two types of work a chemical system at rest can do?
PV work and non-PV work
- Most important non-PV work for MCAT is electrical work
Work defined as energy transfer due to a force
Done whenever a force is applied over a distance (changes object’s kinetic and / or potential energy)
What is an example of PV work?
Gas that expands in a balloon
Gas must exert forces to both stretch the balloon and to expand into opposing pressure of atmosphere
- energy dissipated in process
- Outside stress will initiate PV work (exposure of gas in balloon to heat source)
At constant pressure, what is the magnitude of PV work?
P x delta V
When system does work on surroundings, work is assigned negative value, because transferring energy out of the system (could be opposite sign on MCAT, look for how it is defined)
How can you determine the amount of PV work done from a pressure vs. volume graph?
Area under the curve of a PV diagram
Work is a path function, so the path that was taken determines how much energy was transferred out the system
What is the defining feature that distinguishes work from heat on a molecular scale?
Ordered or directional collisions mean work and random collisions from high energy molecules to low energy molecules mean heat
Defined in terms of the effect on the surroundings
Capacity to do work arises from the constraint of molecules
- Unconstrained system such as ideal gas with infinite volume can do no work
First law of thermodynamics
Total energy of the system and surroundings is always conserved
Any energy change to a system must equal the sum of heat flow into the system and work done on the system
Delta E = q + w
In a closed system at rest with no electric or magnetic fields, only energy change is internal energy
Delta U = q + w
Difference in sign of w for physicists vs chemists
For MCAT usually: delta E negative when energy transferred out of system during expansion
Enthalpy
Defined as an equation: H = U + PV
Where U is internal energy
Measured in units of energy (joules), but enthalpy is not conserved
Enthalpy of the universe does not remain constant
Since U, P, and V is a state function, enthalpy is also a state function
Enthalpy depends only on T for an ideal gas
Extensive property
Change in Enthalpy
Delta H = delta U + P delta V (at constant pressure)
If a system does work at a constant pressure and in reversible process:
Delta H = [w_nonPV - P delta V + q] + p delta V = w_nonPV + q(constant pressure, closed system at rest, PV work only)
Then if only PV work is done:
Delta H = q (constant pressure, closed system at rest)
At constant volume and constant pressure, Change in U equals about change in H
Standard State
Not standard temperature and pressure
Complicated, varies with phase and other factors and has different values depending on convention chosen
For pure solid or liquid, standard state is reference form of a substance at any chosen temperature and pressure of 1 bar (~750 torr, or 10^5 pascals)
Reference form usually form that is most stable at T and P, for pure gas must behave like ideal gas
Enthalpy is assigned at standard state at 25 deg C to be 0 kJ/mol
Standard enthalpy of formation
Delta Hf^{deg} Enthalpy values assigned to compounds based on change in enthalpy when formed from raw elements in standard states at 25 deg C
Change in enthalpy for reaction that creates one mol of compound from raw elements in standard state (determined experimentally)
Heat of reaction
Since enthalpy approximates heat in many reactions in the lab (constant pressure, constant volume), change in enthalpy from reactants to products is heat of reaction:
Delta H deg _ reaction = delta H^{deg}{fproducts} - delta H^{deg}{freactants}
Remember to include coefficients of each reactant and product when calculating
Negative enthalpy change indicates exothermic reaction, usually produces heat flow to surroundings (at constant pressure)
Positive enthalpy change indicates endothermic reaction
What are five possible ways to know change in enthalpy for a reaction on the MCAT?
- Passage defines delta H outright
- Heat measured with calorimeter and so heat is -delta H
- Sign can be intuited from rxn (melting is endergonic, + delta H)
- Compute from a table of bond energies by number of bonds broken and formed (breaking bonds requires energy)
- Calculate using standard enthalpies of formation (delta H^{deg}_{f})
Entropy
Universe’s tendency towards disorder
Nature’s tendency to create the most probable arrangement that can occur within a system (more ways for that arrangement to occur)
State function and extensive property
Nature’s effort to spread energy evenly between systems
Driving force that dictates whether or not a reaction will proceed (must increase the entropy of the universe, but not necessarily the system in order to proceed)
Second Law of thermodynamics
Entropy of an isolated system will never decrease
Universe is an isolated system, therefore sum of entropy changes of any system and its surroundings equals the entropy change of the universe, which must be equal to or greater than zero
Delta S_system + delta S_surroundings = delta S_universe >= 0
Relationship of entropy to other variables
All other factors being equal, entropy increases with number, size, volume, and temperature
If reaction increases the number of gaseous molecules, reaction has a positive entropy for the reaction system
Third Law of thermodynamics
Assigns a zero entropy value to any pure element or compound in its solid form at absolute zero and in internal equilibrium
At absolute zero, atoms have very little motion, can be realized only in theory
Entropy change
Delta S = q_rev / T
Infinitesimal change in heat (q_rev) per Kelvin in a reversible process
Units in J / K
Cannot be used to calculate change in S for irreversible process because heat is pathway dependent
Delta S for irreversible process can be found by imaging a reversible process between same two states and finding heat transfer for reversible process
Reversibility (in thermodynamics)
Reaction that can take place in both the forward and reverse directions must have an entropy change of zero in both directions
For reversible reaction in an isolated system, entropy change must be zero
Real reversible reactions do not happen
- hypothetical reversible reaction would be quasi-static process, with system in equilibrium with surroundings at all times
- pressure differences must be infinitesimal, heat transfer occurs at same T, infinite amount of time
Alternative definitions of reversibility
Entropy undefined on the microscopic level of molecular reactions
All reactions at microscopic level must be considered reversible
Collision between individual molecules is exact opposite of reverse process, no law in classical physics that favors one direction over another
Equilibrium achieved when rate of forward reaction equals rate of reverse reaction (point of greatest universal entropy)
Change in entropy of a molecular reaction
Delta S^{deg}{reaction} = delta S^{deg}{products} - delta S^{deg}_{reactants}
Gibbs free energy
Incorporates the entropy change in both the system and the surroundings into a single equation that only relies on information about the system
Delta G = delta H - T delta S
H, T, S are all state functions
Delta G < 0 required for spontaneous process, and delta G = 0 required for equilibrium
Extensive property and a state function, not conserved
Represents the maximum non-PV work available from , or “free” for a reaction
Endergonic (positive delta G), exergonic (negative delta G)
What does the negative of the Gibbs free energy refer to?
Amount of non-PV work available in a completely reversible process
Actual amount of non-PV work that we will get out of the system is always less than magnitude of - delta G
Change in Gibbs free energy for standard state?
State function, so same equation applies as for S and H
Delta G^{deg}{reaction} = delta G^{o}{f,products} - delta G^{o}_{f,reactants}
What can Gibbs free energy tell us about the coupling of non-spontaneous and spontaneous reactions?
If a reaction is non-spontaneous, can couple with a spontaneous reaction to make it favorable
E.g. biological non-spontaneous reaction coupled with ATP hydrolysis
Hess’s Law of Heat Summation
Sum of enthalpy changes for each step is equal to the total enthalpy change regardless of the path chosen
Forward reaction has exactly opposite change in enthalpy as reverse reaction with opposite sign
Transition state
State in the middle of a reaction where old bonds are breaking and new bonds are forming
Peak of energy hill in reaction
Not the same as intermediate, which exists for a longer duration of time (lower energy than transition state)
Chemical equilibrium
Condition where the rate of forward reaction equals the rate of the reverse reaction
At equilibrium, no net change in concentrations of products or reactants
Point of greatest entropy
Reactions move towards and then stay at equilibrium
Equilibrium constant
For a reaction: aA + bB -> cC + dD
The equilibrium constant determines the relative amounts of each species at equilibrium:
K = [C]^c [D]^d / [A]^a [B]^b = Products^coeffs / Reactants^coeffs
Law of Mass Action: Mathematical relationship between chemical equation and associated equilibrium constant
K is unitless, will not change unless temperature changes
Concentration of pure liquid or solid given a value of 1 for expression
How can a reaction run to completion?
If forward reaction is so much more favorable than reverse reaction, then for all practical purposes, it runs to completion
Also with Le Chatelier’s principle, if remove product continually, reaction can run to completion
Reaction Quotient
Q = Products^coeff / Reactants^coeff
Describes a state perturbed from equilibrium
Q will always move toward equilibrium
If Q = K, reaction at equilibrium
If Q > K, reaction will shift to increase reactants and decrease products (reverse)
If Q < K, reaction will shift to increase products and decrease reactants (forward)
Le Chatelier’s Principle
When a system at equilibrium is stressed, the system will shift in a direction that will reduce stress
Stress that obeys Le Chatelier’s:
1. Addition or removal of product or reactant
2. Changing pressure or volume of system
3. heating or cooling the system
Haber Process
Exothermic all gas reaction (creates heat), assume it occurs in rigid container at equilibrium:
N2(g) + 3H2(g) -> 2NH3(g) + Heat
Adding N2 gas shifts equation to the right, producing more heat
Adding heat, reaction is pushed to the left
Decreasing size of container shifts reaction to right (less separate molecules)
Effect of Concentration, Pressure, and Temperature on Rxn at Equilibrium
Concentration: reaction proceeds in direction of less concentrated side
Pressure: Reaction shifts in direction with less moles of gas as pressure increases
Temperature: If heat added, reaction shifts away from the side that produces heat
Exceptions to Le Chatelier’s
Solvation reactions: solubility of salt generally increases with increasing temp, even when reaction is exothermic (significant entropy increase w/ dissolution)
Increased pressure due to addition of a nonreactive gas does not cause any shift in forward or reverse reaction rates
How do we relate Gibbs free energy for a particular set of conditions from the standard state Gibbs free energy?
delta G = delta G^{o} + RTln(Q)
Q is reaction quotient
Standard state free energy occurs at 1 bar with all species starting at one molar concentrations and usually at 25 o C
Base 10:
Delta G = delta G^{o} + 2.3 RT log(Q)
K and delta G^{o} vary with temperature, so necessary to look up for specific temperature
At equilibrium, no available free energy to do work, delta G = 0:
Delta G^{o} = -RT ln(K), so K > 1 then delta G^{o} < 0
