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AP Chemistry Topics DVHS 2020-2021, Reference Sheets, chem2, phpWMMvPi,…
AP Chemistry Topics DVHS 2020-2021
Thermodynamics
Enthalpy - ΔH
products minus reactants again
\(ΔH°_{rxn} = \Sigma(ΔH°_{products})-\Sigma(ΔH°_{reactants})\)
Gibbs Free Energy - ΔG
Relationship to \(K_{eq}\)
Larger the Keq, the greater extent of reaction, more likely it is to be spontaneous
\(ΔG = ΔG° + RT \ln{Q}\)
when ΔG° is zero
K = 1
When ΔG = 0
At equilibrium
\(ΔG° = -RT\ln{K_{eq}}\)
\(\log({\frac{K_1}{K_2}}) = \frac{-ΔH°}{R} (\frac{1}{T_2}- \frac{1}{T_1})\)
Spontaneity
reaction is spontaneous (will occur) if ΔG is negative, and is nonspontaneous (will not occur) when ΔG is positive.
spontaneous when:
ΔH is negative and ΔS is positive for all temperatures.
Nonspontaneous when:
ΔH is positive and ΔS is negative for all temperatures
\(ΔG°_{rxn} = \Sigma(ΔG°_{products})-\Sigma(ΔG°_{reactants})\)
Entropy - ΔS
increases with temperature, molecular complexity, gas phase
Measure of the disorder of the system
tries to maximize the number of microstates in a macrostate
\(ΔS°_{rxn} = \Sigma(S°_{products})-\Sigma(S°_{reactants})\)
relationship between variables
ΔG = ΔH - TΔS
1st law
Energy not created nor destroyed, simply transferred
2nd law
Entropy of Universe always increasing, chemical reactions must contribute in some way
3rd law
Zero entropy is defined as a crystal lattice structure at a temperature of 0 Kelvin.
Equilibrium
Equilibrium Constant
ratio of the concentrations of products to reactants at equilibrium raised to their stoichiometric coefficients
solids and liquids not included
law of mass action of a reaction
\(K_{eq}\)
\(K_c\)
In terms of concentration
\(K_p\)
In terms of pressures
\(K_{sp}\)
solubility product constant
\(K_p = K_c (RT)^{Δn}\)
where delta(n) is the change in the number of moles of gas in the products minus reactants
Increase in temperature
If an Endothermic forward reaction
shift right
higher value of Keq
If an Exothermic forward reaction
shift left
lower Keq
Decrease in temperature
If an Endothermic forward reaction
shift left
lower Keq
If an Exothermic forward reaction
shift right
higher Keq
Only changes with temperature
Le Chatelier's Principle
Equilibrium will shift to minimize "stressors"
Stressors
Change in...
Pressure
concentration
Temperature
ICE tables
used to calculate equilibrium concentrations
Initial, change, equilibrium
5% rule
If the initial concentrations are at least 1000x larger than Keq
Ignore the change (x) for those
Bonding
Coulomb's Law
\(F = k\frac{q_1q_2}{r^2}\)
Attraction between opposite charges decreased with distance
Greater charge magnitude = greater attractive force
VSEPR
Shapes
Trigonal Pyramidal
AX3E
107.5 degrees
sp3
NH3
Bent (<120)
AX2E
<120 degrees
sp2
SO2
trigonal Planar
AX3
120 degrees
sp2
BeH2
Bent (104.5)
AX2E2
104.5 degrees
H2O
sp3
Linear
AX2
AX2E3
180 degrees
sp
CO2
Octahedral
AX6
90 degrees
SF6
d2sp3
See-Saw
AX4E
SF4
dsp3
90 degrees
Trigonal Bipyramidal
dsp3
AX5
120, 90 degrees
PCl5
Square Pyramidal
90 degrees
AX5E
d2sp3
BrF5
T-Shaped
dsp3
AX3E2
<90 degrees
ClF3
resonance / Formal Charge
Resonance
When more than one valid lewis structure can be drawn
Actual structures are an average of the resonance structures
Create "resonance bonds" that are equivalent to one another
The most likely resonance structure is based on stability in Formal charge
Formal Charge
The valence electrons minus (the nonbonding electrons+ half of the bonding electrons)
v.e.'s minus (dots and sticks)
Stable structures tend to minimize formal charge on each atom
Stable structures tend to have more negative formal charges for more electronegative atoms in the molecule
Hybridization
sp
sp^2
sp^3
"blending of orbitals"
s + p + p + p --> sp + sp + p + p
s + p + p + p --> sp^2 + sp^2 +sp^2 + p
Sigma and Pi bonding
Sigma (\(\sigma\))
Stronger
between bonded nuclei
any combination of orbital over lap
Pi (\(\pi\))
Weaker
Above and below bonded nuclei
Unhybridized "p" orbital overlap
Types of Bonds
Covalent
Electrons shared
Small difference in EN
Ionic
Electrons Transferred
Large difference in EN
Metallic
Electrons delocalized
Occurs between the same metal
Lattice Energy
A change in energy
Enthalpy of Reaction
Energy to form Ionic compound from gaseous ions
Na+ (g) + I- (g) --> NaI (s)
Takes Energy to Break Bonds
Endothermic
Positive deltaH
energy released when bonds formed
Exothermic
Negative DeltaH
ΔH = sum(n)[bond energies broken] - sum(n)[bond energies formed]
"reactants minus products"
Can use average bond energies
Will lead to a deviation, because they are average bond energies
Higher for smaller ionic compounds
They are smaller, so their ionic charge exhibits a greater attractive force to each other
more stable / harder to break
higher melting temperatures
higher (more negative) lattice energy
Example: LiF
Higher for compounds with large charges
higher melting points
Higher attractive force for one another
Example: GaP
Bond order
Double
In the middle of Triple and Single
1 sigma, 1 pi
4 electrons shared
Triple
Strongest
Shortest
1 sigma, 2pi
6 electrons shared
Single
Weakest
Longest
1 sigma
2 electrons shared
Thermochemistry
Q = mcΔT
equation used to calculate energy transfer occurring for a sample with a given mass (g), specific heat (J/g'C), and change in temperature (C).
state functions
A function where the path taken between two points does not matter - a "change" or delta
Energy is a state function, in this case it doesn't matter what happens to it between the beginning and the end, as long as the change in energy is the same.
delta H - Enthalpy
Enthalpy - ΔH
The change in the energy of the products minus the reactants.
Heat of Formation
Energy to form a molecule from their constituent elements in their standard states (298K and 1 atm)
Heat of formation of any element in its standard state is zero
Hess' Law
when manipulating reactions, follow these guidelines for changing ΔH
If reactions added
add their ΔH's
If reaction reversed
Flip the sign of ΔH
If reaction multiplied by a coefficient
multiply ΔH by that coefficient
heating curve
Used to calculate energy added or removed when states are changed.
Kinetics
relationship of k to Keq
For a reaction \(A \leftrightarrow B\)
\(rate (forward) = k_f[A]\)
\(K_{eq} = \frac{[B]}{[A]}\)
\(rate (reverse) = k_r[B]\)
At equilibrium, rate (forward) = rate (reverse)...
\(k_r[B] = k_f[A]\)
\(k_f/k_r = \frac{[B]}{[A]}\)
\(\frac{k_f}{k_r} = K_{eq}\)
The rate constant (k)
Units
Zero order
\(\frac{M}{s}\)
Second order
\({M^{-1}}{s^{-1}}\)
First order
\(\frac{1}{s}\)
nth order
\(M^{1-n} s^{-1}\)
Relationships that alter k
Flip a reaction
do 1/k for the reverse constant
Multiplying a reaction by a number
k is raised to that power
Add reactions with separate k values
multiply their k values
A proportionality constant used in the differential rate law
For a reaction, Keq only changes with temperature
Method of Initial rates
Find the change in concentration and compare to the change in rate
If concentration multiplier is proportional to rate multiplier -->
First order
If concentration multiplier does not change rate
Zero order
If the rate multiplier is the square of the concentration multiplier
Second order
used with a data set of concentration and initial rate
reaction Mechanisms
Catalyst
Substance that speeds up the reaction without getting consumed -- used as a reactant in the beginning, then produced as a product at the end of the mechanism
Heterogenous
Different state as reactants
Homogenous
Same state as reactants
Order from a mechanism
look at the slowest step
this is called the rate determining step
the rate law will match the concentrations of the substances in that step with their stoichiometric coefficients as exponents
Intermediate
Substance that is produced as a product in one step, then used as a reactant in the next step
Most reactions can happen in multiple elementary "steps"
Steps add up to the overall reaction
Types of reactions
Bimolecular
Two molecules colliding to react
2A --> B
A + C --> D
Termolecular
More than two molecules colliding to react
3B --> E
A+B+C --> D
Single step termolecular reactions unlikely
Unimolecular
One reactant decomposing
A --> B
Reaction Order
Second
Rate is proportional to the square of reactant concentration
\(Rate = k[A]^2\)
Zero
Rate is independent of reactant concentration
Rate = k
First
Rate is proportional to reactant concentration
Rate = k[A]
Pseudo 1st and 2nd orders
When the concentrations of one reactant is much larger than the others
It can be ignored since it hardly changes
This new rate is called a pseudo order
Uses pseudo rate constant, k'
Integrated Rate laws
Zero order
\([A]_t = [A]_o - kt\)
First order
\(\ln[A]_t = \ln[A]_o - kt\)
Second order
\(\frac{1}{[A]_t} - \frac{1}{[A]_o} = kt\)
With half life
Second order
\(t_{1/2} = \frac{1}{k[A]_o}\)
Zero order
\(\frac{[A]_o}{2k}\)
First order
\(t_{1/2} = \frac{\ln2}{k}\)
order from a Graph
First order
ln[A] vs t is linear
slope = -k
Second order
1/[A] vs t is linear
slope = k
Zero order
[A] vs t is linear
slope = -k
Arrheinius equations
two point form, (T1, k1); (T2, k2):
\(\ln(\frac{k_1}{k_2}) = \frac{E_a}{R}(\frac{1}{T_1}-\frac{1}{T_2})\)
\(k = A e^{(\frac{-E_a}{RT})}\)
\(\ln(k) = (\frac{-Ea}{R})(\frac{1}{T}) + \ln(A)\)
Where -Ea/R is the slope of the graph of ln(K) vs 1/T, and A is the y-intercept
Atomic Structure
c=λv
E=hv
\(E=\frac{hc}{λ}\)
\(c = 2.998×10^8 ms^{-1}\)
\(h = 6.626×10^{-34} J\cdot s\)
Periodicity
Trends
Electron Affinity
Change in energy when an electron is added
Can be positive (endothermic), or negative (exothermic)
Increases (becomes more negative) across a period
Higher Zeff --> more attraction for electrons --> high affinity for electrons
Decreases down a group (actually closer to 0 - becomes less negative)
Larger radius --> less attractive force for electrons --> no affinity for electrons
Atomic Radius
Increases Down a Group
Larger principal energy levels of orbitals--> larger distance away
Half the distance between two identically bonded nuclei
Decreases Across (L-> R) a row
Increased Zeff --> increased attraction for electrons --> electrons pulled closer in
\(Z_{eff}\)
Effective nuclear charge
Protons minus shielding electrons
Stays constant down a group (IDEALLY)
Valence electrons in a group is the same
Increases across a period
Adding a proton is a bigger change than adding an electron
Electronegativity
Tendency for an atom to attract bonding electrons
Increases across a row/period
Higher Zeff --> larger attraction for electrons
Decreases down a group
Larger radius, electrons further away from source of attraction (nucleus) --> less likely to gain/attract electrons toward the atom
Ionization Energy
Energy to remove an electron from an atom in the gaseous state
Increases Across a row
Higher Zeff --> higher attraction for electrons --> more energy needed to remove them
Decreases down a group
Larger radius --> electrons further away from atom --> they experience less attractive force --> less energy to remove them
Electron Rules
Pauli Exclusion
No two electrons can have the same set of quantum numbers
Hund's Rule
Electrons will occupy other orbitals before pairing up
Afbau's principle
Electrons will occupy the lowest energy levels first
PES
y-axis: number of electrons (strictly integers)
x-axis: binding energies (MJ/mol)
Peaks represents areas of electron presence
Orbitals
p
d
s
f
\(E_n = \frac{-2.18×10^{-18}}{n^2}\)
\(\frac{1}{\lambda} = R_m(\frac{1}{n^2_1} - \frac{1}{n^2_1})\)
\(R_m = 1.0968×10^7 m^{-1}\)
Electron charge \(e = -1.602×10^{-19}\) coulomb
Gas Laws
Charles' Law
\(\frac{V_1}{T_1} = \frac{V_2}{T_2}\)
Relates volume and temperature
As the temperature increases, so does the volume
Direct relationship
linear
Boyles' Law
As the volume decreases, the pressure increases
Indirect Relationship
\(P_1V_1 = P_2V_2\)
relates volume and pressure
non-linear
Units
atmospheres
1 atm = ambient pressure at sea level
R = 0.08206
kPa
1 kPa = 1000 Newtons / m^2
101.3 kPa = 1 atm
R = 8.314
torr / mmHg
760 mmHg = 1 atm
mmHg used as millimeters of a column of Mercury supported by the pressure
R = 62.3
pounds per square inch
14.7 psi = 1 atm
Density
g/L=
kg/m^3
g/mL
kg/mL
Volume
L
=1000 mL
mL
cm^3
=1 mL
1x10^6 cm^3 = 1m^3
1000 dm^3 = 1m^3
1000 L = 1m^3
Gay-Lussac's Law
Relates Temperature and Pressure
Direct Relationship
\(\frac{P_1}{T_1} = \frac{P_2}{T_2}\)
As the temperature increases, so does the pressure
linear
Combined Gas Law
\(\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}\)
Relates all variables ideally
Ideal Gas Law
PV = nRT
n is number of moles (mol)
P is pressure
mmHg / torr
atm
kPa
T is temperature
Kelvin
V is volume
Litres
R is the gas constant
62.3 (L
mmHg)/(mol
K)
8.314 (L
kPa)/(mol
K)
0.08206 (L
atm)/(mol
K)
PVM=mRT
PM=DRT
D is density in g/L
m is mass, in g
M is molar mass, in g/mol
Kinetic Molecular Theory
A set of properties of ideal gases
Collisions between gas particles are elastic
Average kinetic energy of the gas depends upon temperature
Gases in constant, random motion
Pressure in the container caused by gas collisions against the sides of the container
Volume of individual gas particles is near zero (negligible)
Composed of hard, spherical particles with infinitely small volume
Manometer Equation
P = ρgh
ρ is the fluid density (kg/m^3)
g is gravitational acceleration (9.8 m/s^2)
h is the height of the column (m)
P is the pressure of the base of fluid (Pascals / Newtons per square meter)
Used for the pressure of a column of a liquid being opposed by gas
In a manometer
Velocity and Kinetic energy
Kinetic energy
Average kinetic energies of gases are the same at the same temperatures
\(KE=\frac{1}{2}mv^2\)
\(KE_{avg}=\frac{3}{2}RT\)
Velocities of different gases are different at different temperatures
"root mean squared" velocity based on molar mass
\(v_{rms}=\sqrt{\frac{3RT}{M}}\)
R= 8.314 J/mol-K
M is in kg/mol
The lighter the gas particles, the higher the root mean squared velocity
Effusion
A gas escaping a pinhole- compares rates for different gases with different molar masses
\(\frac{r_a}{r_b}=\frac{\sqrt{M_b}}{\sqrt{M_a}}\)
r is the rate
M is the molar mass, in g/mol
Graham's Law
Diffusion
\(\frac{d_a}{d_b}=\frac{\sqrt{M_b}}{\sqrt{M_a}}\)
"d" is distance traveled (m)
"M" is molar mass in g/mol
Two gases going down a long path. Like a "race"
Non-Ideal Gases. ("Real Gases")
Have molecules that take up space
Take up more space than ideal gases
Have elastic collisions due to intermolecular forces
Have lower pressure than ideal gases
Van Der Waal's Equation
\((P+\frac{n^2a}{V^2})(V-nb)=nRT\)
where "a" and "b" are constants
Conditions for the
least
ideal gases
Molecules with strong IMFs (very polar)
Large molecules
Low temperatures
Low volumes
High pressures
High number of gas particles
PV is not constant
Conditions for the
most
ideal gases
High temperatures
High volumes
Low number of gas particles
Molecules that are nonpolar
Small molecules (radii)
Low pressures
PV is constant
Intermolecular Forces
Ion-Dipole Forces
Occurs when ions are attracted to water molecules after ionic compounds dissolve
Is Very strong (1st)
Only if ionic compound is soluble
London Dispersion Forces (Van Der Waals)
Dipoles that occur due to the instantaneous uneven distribution of electrons in a molecule
Temporary
Weakest (4th)
Are increased by....
Surface Area
Size
Occur in all molecules
Hydrogen Bonding
Occurs between Hydrogen and some highly electronegative atom (N, O or F)
Is responsible for much of water's properties
Is quite strong (2nd)
Permanent
Heating Curve/phase diagram
Can be exothermic or endothermic
Critical Temperature
The temperature above which the vapor cannot be liquefied
Temperature Constant During Phase Changes
Critical Pressure
Pressure needed to liquefy the substance at critical temperature
Triple point
The point where the pressure is low enough so that phases are indistinguishable
Critical Point
The point where the critical temperature and pressure occurs
Slope of liquid/solid line
Positive
solid state denser than liquid state
mercury
negative
liquid state denser than solid state
water
Dipole-Dipole Forces
Dipoles that occur on a molecule due to geometry (Polar molecules)
Permanent
Decently strong (3rd)
Occurs only in polar molecules
When difference in electronegativities between ends of each dipole is greater...
DP-DP attraction increases
Related Properties
Vapor Pressure
The Weaker the IMFs...
The higher the Vapor Pressure
Boiling / Melting Points
The stronger the IMFs...
The higher the MP/BP
Solubility
The greater the IMFs...
The more soluble in polar solvents
The Weaker the IMFs...
The more soluble in nonpolar solvents
Solutions
Heats of Solution
ΔH solution = ΔH solvent + ΔH solute + ΔH mix
ΔHsolvent: the energy required to break solvent interactions in the solution.
the amount of energy that is absorbed or released in total after a solute dissolves in a solvent.
exothermic which means it is a negative value
NaOH
This can be endothermic which implies it is a positive value
NH4NO3
ΔHmix: the energy released as solvent forms attractions to the dissolved in the solution
ΔHsolute: the energy required to break apart a solute in the solution.
A solution will form if it is a spontaneous reaction
-ΔH , any +ΔS
solution
+ΔH , large +ΔS
solution
+ΔH , -ΔS
No solution
-ΔH , small -ΔS
solution
-ΔH , large -ΔS
No solution
Raoult's Law
Deviations from Raoult's Law
Positive
when weak solute solvent interactions allow more solvent to escape into the vapor which increases the vapor pressure
Negative
when strong solute solvent interactions and a negative heat of solution value lower the amount of solvent escaping as a vapor which lowers the overall vapor pressure.
Pressure of the gas above the solution of volatile liquids equals the mole fraction of the solvent times the vapor pressure of the solvent.
\(P_{solution} = 𝝌_{solvent} * P°_{solvent}\)
Volatile
significant amount of the liquid vaporizes into gaseous state
High equilibrium vapor pressures
\(P_{total} = 𝝌_aP°_a + 𝝌_bP°_b...\)
a solvent that achieves dynamic equilibrium between the gas and liquid phase in a solution.
Nonvolatile
liquid largely remains in its liquid state
Low equilibrium vapor pressures
a solvent that does not transition to the vapor phase for a given temperature in a solution.
ΔP = P° solvent - P solution
Raoult’s law Ideal solution
a liquid liquid solution where the energy used to break solute interaction equals the energy released by forming solute solvent interactions
ΔH° solution = 0
Solubility
IMFs and solubility
Factors that affect solubility
P
Temperature
“like dissolves like” rule says that polar solutes will dissolve best in nonpolar solvents and nonpolar solutes will also dissolve in nonpolar solvents.,
Concentration Types
Molality
\(\frac{moles_{solute}}{kilogram_{solvent}}\)
m
Molarity
\(\frac{{moles}_{solute}}{{Liter}_{solution}}\)
M
Mass percent
\(\frac{mass_{solute}}{mass_{solution}}*100\)
%
Parts per million
\(\frac{mass_{solute}}{mass_{solution}}*1*10^6\)
ppm
Mole fraction
\(\frac{moles_{solute}}{moles_{solution}}\)
Parts per billion
\(\frac{mass_{solute}}{mass_{solution}}*1*10^9\)
ppb
Colligative Properties
Osmotic Pressure
\(\Pi = iMRT\)
R = Gas Constant = 0.08206 L×atm/mol×K
M = Molarity of the solution
\(\Pi\) = Osmotic pressure
i = van't hoff factor
T = absolute temperature
Vapor Pressure
Clausius-Clapeyron Equation
\(\ln(\frac{P_1}{P_2}) = \frac{-ΔH_{vap}}{R}(\frac{1}{T_1}-\frac{1}{T_2})\)
Vapor pressures (P) of a substance at different temperatures (T) given the ΔH of vaporization
Van't Hoff Factor, \(i\)
Number of ions a molecule dissociates into in solution
Only achieved in very dilute solutions
\(NaCl \longrightarrow Na^+ + Cl^-\)
i = 2
\(Ca(OH)_2 \longrightarrow 2OH^- + Ca^{2+}\)
i = 3
Properties that only depends on the concentration of solute
Freezing Point Depression
\(ΔT = i * K_f * m_{solute}\)
Kf is 1.86 C/kg*mol
Each mole of solute particles lowers the freezing point of 1 kilogram of water by 1.86 degrees Celsius in water.
differs for different solutes
m is concentration, molal
Boiling point elevation
Henry's Law
\(S_{gas} = k_HP_{gas}\)
kH is called the Henry's Law constant
Differs for gas, solvent, and temperature
Solubility proportional to Partial pressure of a gas in solution
Tyndall Effect
Colloids in solvent scatter light, making a beam visible.
Solutions do not
Acid Base
Salts
Can be acidic or basic
To determine:
To determine the acidity / alkalinity of a hydrolyzable anion, compare the Ka and Kb values for the ion; if Ka > Kb, the ion is acidic; if Kb > Ka, the ion is basic.
Acid salts contain a hydrolyzable proton in the cation, anion, or both
HI
NH4Cl
acidic
Neutral if both ions come from strong acid or base
NaCl
Cl- from HCl (strong)
Na+ from NaOH (strong)
Neutral
Ionic assembly of positive and negative ions
Buffer Solutions
A system consisting of either...
Weak acid and its conjugate base
Weak base and its conjugate acid
Henderson Hasselbach Equation
\(pH=pK_a+\log(\frac{[A^-]}{[HA]})\)
[HA] is concentration of the acid
Used for buffer solutions
[A-] is the concentration of the conjugate base
\(pK_a=-\log(K_a)\)
When a strong acid or base is added, the pH is relatively stable
Weak Acids and Bases
Weak acids do not dissociate completely
Instead, they reach an equilibrium
Use ICE table
pH and pOH
\(pOH=-\log{[OH^-]}\)
\(pH=-\log{[H^+]}\)
\(pH+pOH=14\)
\([H^+][OH^-]=1*10^{-14}\)
Logarithmic scale of acidity
From 0-14
Lower pH --> more acidic
Higher pH --> more basic
Lower pOH --> more basic
Higher pOH --> more acidic
Titrations
Titration curve
graph of pH versus volume of titrant added
Equivalence point
Where moles of acid = moles of base
At halfway to the equivalence point...
\(pH=pK_a\)
Experimental method to determine concentration of titrand by titrating it with a titrant of known concentration
Definitions of Acids and Bases
Lewis
Bases can donate lone pairs
Acids can accept lone pairs
Bronsted-Lowry
Bases accept protons
Acids donate protons
Arrheinus
Bases release OH- ions
Acids release H+ ions
Acid-Base Equilibrium
Uses equilibrium constant
\(K_a\) for acids
\(K_b\) for bases
Same as normal Equilibrium
Strong Acids/Bases
Strong acids
\(HBr\)
\(HI\)
\(H_2SO_4\)
\(HCl\)
\(HNO_3\)
\(HClO_3\)
\(HClO_4\)
Strong bases
\(Ca(OH)_2\)
\(NaOH\)
\(KOH\)
\(LiOH\)
\(Ba(OH)_2\)
\(Sr(OH)_2\)
\(Mg(OH)_2\)
\(CsOH\)
\(RbOH\)
100% Ionized solution
Electrochemistry
Cell Potential
Standard reduction potential measured in Volts, places reduction of Hydrogen at 0 Volts
Standard Hydrogen Electrode (SHE)
Difference in potential energy between anode and cathode in a voltaic cell
\(E°_{oxidation} = -E°_{reduction}\)
\(E°_{cell} = E°_{oxidation} + E°_{reduction}\)
Standard cell potential
standard emf
\(E°_{cell}\)
25°C, 1 atm, 1M solutions
E°cell, ΔG°, and K
Nernst Equation
\( E_{cell} = E°_{cell} - \frac{RT}{nF}\ln{Q}\)
At 298K
\( E_{cell} = E°_{cell} - \frac{0.0592}{n}\log{Q}\)
Calculate E at any condition given E at standard conditions and reaction quotient (Q) - Non 1M solutions
F (Faraday's constant) = 96,485 Coulombs / mol electrons
When E = 0 --> at equilibrium
When E°cell = 0 --> Keq = 1
E in Volts
n is moles of electrons in balanced redox half reactions
\(ΔG = -nFE°\)
\( E°_{cell} = \frac{0.0592}{n}\log{K}\) at 298K
\(K = e^{(\frac{nFE°}{RT})}\)
Spontaneous Redox reactions
Negative ΔG°
K > 1
Positive E°cell
Redox
Balancing Redox reactions
Balance oxygen's by placing H2O molecules on either side
Write half reactions
One where species is oxidized
One where it is reduced
Balance hydrogens by placing H+ on either side
Balance charge by placing e- on either side
Add together half reactions with cancelled electrons (e-)
Reduction
Gain of electrons
Oxidation
Los of electrons
Assigning Oxidation states
Oxygen usually -2
Fluorine usually -1
Sum of charges in a neutral ionic compound is 0
Sum of charges in complex ion is the charge on that ion
Metals can take a variety of different charges
Hydrogen mostly +1
Cells
Voltaic (galvanic) cells
Reduction at the cathode
gains weight
+
Cu2+ (aq) + 2e- --> Cu(s)
Oxidation at the Anode
loses weight
-
Zn (s) --> Zn2+ (aq) + 2e-
Line notation
anode metal | anode sol'n || cathode sol'n | cathode metal
Zn (s) | Zn2+ (aq) || Cu2+ (aq) | Cu (s)
|| is salt bridge
| is single phase barrier
electrons flow from anode to cathode
batteries
produce current from chemical energy
Voltmeter
electrons -->
Anode (-)
<-- electrons
Cathode (+)
solution
salt bridge
electrolytic cells
Oxidation at the cathode
-
Connected to negative terminal of input
Reduction at the anode
+
connected to positive terminal of input
electroplating
produces chemical energy from supplied current
Voltage input
electrons in to positive terminal on input-->
Anode
<-- electrons out from negative terminal voltage input
Cathode (-)
solution
Current
measured in amperes
1 amp = 1 coulomb per second
charge over time
\(I = \frac{q}{t}\)
Voltage
1 Volt = 1 Joule / 1 coulomb
Reference Sheets
