CHEM 1001 – Fall 2019
This is not an exhaustive list of equations we will use this term, but it may be used as a tool to familiarize yourself with the most
commonly used equations. You will NOT be provided with equations on the midterm nor final exam.
Name of equation
mass/molar mass
Equation
n = m/M
Description of parts
n – number of moles
m – mass (usually in grams)
M – molar mass (usually in g/mol)
N – number of units (molecules/atoms)
n – number of moles
NAv – Avogadro’s number (6.022x1023 mol-1)
ρ = density (lower case Greek letter Rho,
usually g/L)
m = mass (usually in g)
V = volume (usually in L)
c = concentration (mol/L)
n = number of moles
V = volume (L)
b = molality (mol/kg)
n = moles of solute (mol)
m = mass of solvent (kg)
number of units
N = n*NAv
Density
ρ = m/V
Molarity
c = n/V
Molality
b = n/m
Mole Fraction
XA = nA/ntotal
XA = mole fraction of species ‘A’
nA = number of moles of species ‘A’
ntotal = total number of moles in mixture
Mass percent
%msolute =
(msolute/msolution)
*100%
%msolute = mass percent of solute (%)
msolute = mass of solute (g or kg)
msolution = total mass of solute and solvent in
solution (g or kg)
Use/Comments
To convert between mass, molar
mass and number of moles of a
molecule or compound.
To convert between number of
units and number of moles of a
molecule or compound.
To determine the density of a
liquid or gas.
To determine concentration from
number of moles of solute in total
volume of liquid.
To determine the molality
(concentration) from number of
moles of solute within mass of
solvent.
In a mixture of one or more
species, the mole fraction of each
species can be expressed as a
ratio to the total number of moles.
The sum of the mole fractions of
all the species in a mixture always
= 1.
To determine the percent mass of
solute in a solution.
Dilution
c1V1 = c2V2
Dilution Factor
DF = Vfinal / Vinitial
Stoichiometric Ratio
(S.C. X)/(S.C. Y) =
(nX)/(nY)
c1 = initial concentration (mol/L)
V1 = initial volume (L)
c2 = final concentration (mol/L)
V2 = final volume (L)
DF = dilution factor
Vfinal = final volume of solution (mL, L)
Vinitial = initial volume of solution (mL/L)
S.C. X = stoichiometric coefficient of
compound/molecule in reaction
S.C. Y = stoichiometric coefficient of
different compound/molecule in reaction
nX = number of moles of X produced or
reacted in reaction
Percent Yield
Percent yield =
(actual amount /
theoretical amount)
*100
Light: Frequency
relation to
wavelength
λν=c
Energy of a photon
Ephoton = hνphoton
nY = number of moles of Y produced or
reacted in reaction
Actual amount = mass or moles of product
actually produced
Theoretical amount = potential mass or moles
of product from stoichiometric analysis
*100 (because we express it as a percentage)
λ = (lamda) = wavelength of light/photon (m)
ν = (nu) = frequency of light/photon (s-1 = Hz)
c = speed of light (constant: 3.00x108 m/s)
h = Planck’s constant (6.626x10-34 J s)
νphoton = frequency of photon (s-1)
Ephoton = energy of photon (J)
Measuring change of
concentration by dilution (amount
of solute does not change, only
volume to change concentration).
Use the stoichiometric
coefficients from a balanced
chemical equation to determine
the stoichiometric ratio (and thus
molar ratio) of the components of
the reaction described by the
balanced chemical equation.
To determine the percent yield of
a product after a reaction (always
some lost during stages of
process)
Product of frequency and
wavelength of any given photon
is the speed of light.
Energy of a photon determined
from its frequency.
Energy of a photon
Kinetic energy (by
difference)
Number of photons
Moles of photons
Energy change of an
atom (by
incoming/outgoing
photon)
Energy change of a
photon
DeBroglie’s equation
Ephoton = hc/λ
KEelectron = Ephoton –
EBE
(also seen as:
Ekinetic(electron) = hν –
hνo )
Nphotons = Etotal /
Ephoton
h = Planck’s constant (6.626x10-34 J s)
Ephoton = energy of photon (J)
c = speed of light (constant: 3.00x108 m/s)
λ = (lamda) = wavelength of light/photon (m)
KEelectron = Kinetic energy of an electron
ejected from an atom (J)
Ephoton = energy of an incoming photon (J)
EBE = binding energy of an electron to an
atom (J)
Nphotons = number of photons (counted; round
to nearest integer)
Etotal = total energy of system (detected) (J)
Ephoton = energy of single photon (J)
nphotons = Nphotons / NAv nphotons = number of moles of photons (mol)
Nphotons = number of photons (counted)
NAv = Avogadro’s number (constant:
6.022x1023 mol-1 )
ΔEatom = ± hνphoton
ΔEatom = change of energy of an atom
ΔEatom = ± Ephoton
(Δ = final – initial)
h = Planck’s constant (6.626x10-34 J s)
νphoton = frequency of photon (s-1)
Ephoton = hν
ΔEphoton = |Efinal –
ΔEphoton = energy change of a photon Efinal =
Einitial|
energy at ending energy level
Einitial = energy at beginning energy level
λ = h/mv
λ = wavelength of electron (m)
h = Planck’s constant (6.626x10-34 J s)
m = mass of particle (kg)
v = speed of particle (m/s)
(Recall: J = (kg m2)/s2 )
Combining the previous two
equations gives relation of energy
of a photon to its wavelength.
Energy difference between
incident photon energy and
existing binding energy of an
electron to an atom leaves
remainder to be kinetic energy of
an electron.
The number of photons detected
can be determined form the total
energy and the energy of an
individual photon being detected
(relates to wavelength or
frequency, as shown above).
A single photon won’t affect
much, but working with moles of
photons will, so convert to
number of moles of photons.
Energy change of an atom can be
positive (absorbing
incoming/incident photon) or
negative (emitting/releasing
photon).
Change of energy of a photon as
induced by the movement
between energy levels.
A particle, such as an electron,
has a relation between its
wavelength, its mass and its
speed.
Balmer-Rydberg
Equation
1
1
1
= 𝑅 [ 2 − 2]
𝜆
𝑚
𝑛
λ = wavelength (nm)
R = Rydberg constant = 0.01097 nm-1
m = lower level (final for emission; initial for
absorption)
n = upper level (initial for emission; final for
absorption)
Alternative BalmerRydberg Equation
En = (-2.18x10-18 J)/n2 En = energy at level “n” (J)
n = energy level being considered
Electrical energy
Eelectrical = 𝑘
Kinetic energy of a
particle (by mass and
speed)
Kinetic energy
(average) of a gas
Ekinetic = KE =
(1/2)(mv2)
2𝑁𝐴
1
v̅ =
Ideal Gas Equation
pV=nRT
𝑟
3𝑅𝑇
𝐸̅𝑘𝑖𝑛𝑒𝑡𝑖𝑐 =
Root Mean Square
Speed
𝑞1 𝑞2
3𝑅𝑇 2
(𝑀)
k = constant (2.31x1016 J pm)
r = distance between charges (pm)
q = charge (1 ESU = 1.602x10-19 Coulombs
(C) )
KE = kinetic energy (J)
m = mass of particle (kg)
v = speed of particle (m/s)
𝐸̅𝑘𝑖𝑛𝑒𝑡𝑖𝑐 = average kinetic energy (J mol-1)
R = gas constant (8.314 J K-1 mol-1)
T = temperature (K)
NA = Avogadro’s number (6.022x1023)
v̅ = average speed (m s-1)
R = gas constant (8.314 J K mol-1)
T = temperature (K)
M = molecular mass (g mol-1)
p = pressure (units vary)
V = volume (usually L)
n = amount (moles)
R = gas constant (varies with units of
pressure)
T = temperature (usually K)
Determining the photon absorbed
(or emitted) by a hydrogen
electron excited by incoming light
(or relaxing after re-emitting the
excitation energy as light).
Only applies to Hydrogen atoms
(H)
Energy of discrete excitation
levels of a hydrogen atom (1, 2, 3,
4, 5) can be calculated.
Only applies to Hydrogen atoms
(H)
Determining the electrical
potential energy between charged
particles.
Kinetic energy of a particle can
be calculated directly from its
mass and speed.
Calculating average kinetic
energy of a gas
Average speed of a gas particle.
Note: exponent of ½ is the same
mathematical function as a square
root
Use the Ideal Gas Equation to
solve a system with a pressure
less than 5atm (use Real Gas
Equation for system with >5atm
pressure).
Graham’s Law
Gas system
comparison
Real Gas Equation
Partial pressures and
Mole fraction
Total pressure of a
gas mixture
M = molecular weight of gas (g mol-1)
Rate = rate of diffusion (or effusion) of a gas
(unitless to apply to both diffusion and
effusion)
(piVi)/niTi =
pi,or f = pressure of initial or final conditions
(pfVf)/nfTf
(units vary)
Vi,or f = volume of initial or final conditions
(usually L)
ni,or f = amount of initial or final conditions
(moles)
Ti,or f = temperature of initial or final
conditions (usually K)
2
2
(p + an /V )(V - nb) = p = pressure (units vary)
nRT
a = van der Waal’s constant (intermolecular
forces correction; L2 kPa/mol2)
n = amount (moles)
V = volume (usually L)
b = van der Waal’s constant (volume
correction; L/mol)
R = gas constant (varies with units of
pressure)
T = temperature
pA = XAptotal
pA = partial pressure of compound A in
mixture
XA= mole fraction of compound A (=nA/ntotal)
ptotal = total pressure of system
ptotal = p1 + p2 + … + ptotal = total pressure of system
pn
p# = partial pressure of each compound in a
(also seen as ptotal =
mixture
Σpi
𝑟𝑎𝑡𝑒1
𝑀2
=√
𝑟𝑎𝑡𝑒2
𝑀1
Rate of diffusion or effusion of
gases is dependent
Comparing pV=nRT of an initial
and a final system of gases, note
that R is constant, and at least one
of the 4 variables may be held
constant to find the altered
conditions of the same system.
Use the Real Gas Equation to
solve a system with pressure >
5atm. Be careful that all units of
pressure match before entering
calculation (p, a, and R).
Mole fractions and partial
pressures can be used to describe
and solve mixtures of gases.
This applies Dalton’s law of
partial pressures
Heat flow of system
q=nCΔT
Heat of a calorimeter
qcalorimeter = CcalΔT
Work
w = -pΔV
w = work (J = kg m2 s-2)
p = pressure applied (Pa = kg m-1 s-2)
ΔV = change of volume (m3 = 103 L)
Total energy
ΔE = q + w
(ΔEsystem = ΔEsurroundings)
ΔE = total energy change
q = heat (J)
w = work (J)
Molar Enthalpy of a
system
ΔH = qp/n
Enthalpy of a
reaction
ΔHorxn = ΣvpΔHof,p –
ΣvrΔHof,r
ΔH = enthalpy (J/mol, kJ/mol)
qp = heat flow of system at constant pressure
(J or kJ)
n = number of moles in system
vp = stoichiometric coefficient of each product
ΔHof,p = tabulated enthalpy of formation
values for each product
vr = stoichiometric coefficient of each reactant
ΔHof,r = tabulated enthalpy of formation
values for each reactant
q=heat
n=number of moles of substance
C=molar heat capacity of substance (J/mol
o
C)
ΔT = temperature change
qcalorimeter = heat absorbed by calorimeter (J)
Ccal = heat capacity of the calorimeter (J oC-1)
ΔT = temperature change = Tf – Ti (oC)
Thermal energy flowing into or
out of a system can be calculated
using heat.
In a calorimetry experiment, the
calorimeter itself must be
calibrated so the heat absorbed by
the calorimeter can be accounted
for during the trials with an
unknown compound (or a
compound of unknown heat).
Work = Force * Area
(in gases, the work applied to a
system is seen as a volume
change)
The total energy change of a
system to its surroundings
considers both the heat exchange
and the work applied.
Enthalpy of system can be
determined using the heat flow of
the system.
Enthalpy of a reaction can be
found using tabulated
thermodynamic data and a
balanced chemical equation.
Enthalpy of a
reaction (with
changing pressure)
ΔHreaction = ΔEreaction +
RTΔngases
ΔHreaction = enthalpy of the reaction (J)
ΔEreaction = Energy change of the reaction (J)
R = gas constant (8.314 J K-1 mol-1)
T = temperature (K)
Δngases = change of number of moles of gas
(from balanced reaction equation)
Energy of a reaction
(estimated by bond
energies)
ΔEreaction = ΣBEbroken
– ΣBEformed
ΔEreaction = estimate of total energy of a
reaction
ΣBEbroken = sum of bond energies of bonds
broken (reactant consideration)
ΣBEformed = sum of bond energies of bonds
formed (product consideration)
Formal Charge
FC = (Valence
electrons in the free
atom) – (Valence
electrons assigned to
that atom in the
Lewis structure)
FC = formal charge
Bond Order
BO = ½ (number of
electrons in bonding
MOs – number of
electrons in
antibonding MOs)
BO = bond order
When pressure changes (such as a
gas being used or produced in a
reaction), the enthalpy must
account for this energy change
(otherwise it is equal to a
constant-pressure system where
only heat affects enthalpy).
Estimating energy from bond
energy changes in a reaction can
give an energy change typically
within an order of magnitude of
the accepted value, and at least
hints at energy released versus
absorbed by the system.
Used to determine if there is a
deficiency or excess of electrons
in a proposed Lewis structure
(changes to be made by changing
number of bonds).
Total formal charge of a molecule
should match total charge of a
molecule.
Most likely Lewis Structure has
lowest formal charges.
Represents the net amount of
bonding between two atoms. Can
be used to compare stability of
bonds.
Uses Molecular Orbital Theory
(and diagrams) to note bonding vs
antibonding orbitals and
electrons.
4
Volume of a Sphere
Vsphere = 3 𝜋𝑟 3
V = volume (cm3)
π = pi (constant)
r = radius of sphere (atom/molecule) (cm)
Henry’s Law
[gas(aq)]eq = KH(pgas)eq
[gas(aq)]eq = aqueous concentration of
dissolved gas at equilibrium
KH = Henry’s Law Constant
(pgas)eq = pressure of gas above liquid solution
Vapour Pressure
Reduction
(non-volatile solute)
pvap,soln = XApvap,A
pvap,soln = vapour pressure of the solution
XA = mole fraction of the solvent
pvap,A = vapour pressure of the pure solvent
Vapour Pressure
Reduction
(volatile solute)
pvap,soln = XApvap,A +
XBpvap,B
pvap,soln = vapour pressure of the solution
XA = mole fraction of the solvent
pvap,A = vapour pressure of the pure solvent
XB = mole fraction of the liquid solute
pvap,B = vapour pressure of the pure liquid
solute
Volume of a sphere is used to
represent volume of atoms or
molecules. Useful in determining
packing efficiency (% space used)
of cubic packing structures.
The solubility of a gas depends on
the partial pressure of the gas.
The Henry’s Law Constant is a
different value for each
combination of gas and solvent
(also varies with temperature).
Vapour pressure is a colligative
property, and its reduction based
on the addition of a solute to a
pure solvent is found using the
mole fraction of the solvent in the
solution.
Use this format if the solute is a
solid (non-volatile).
Vapour pressure is a colligative
property, and its reduction based
on the addition of a solute to a
pure solvent is found using the
mole fraction of the solvent in the
solution.
Use this format if the solute is a
liquid (volatile).
Boiling Point
Elevation
ΔTb = iKbb
ΔTb = change of boiling point of a solution
i = van’t Hoff Factor = (particles in products)
/ (particles in reactants)
Kb = ebuilliosocopic constant (boiling point
elevation constant; units typically oC kg/mol)
b = molality of solute (mol/kg)
Freezing Point
Depression
ΔTf = iKfb
Osmotic Pressure
Π = cRT
ΔTf = change of boiling point of a solution
i = van’t Hoff Factor = (particles in products)
/ (particles in reactants)
Kf = cryoscopic constant (freezing point
depression constant; units typically oC
kg/mol)
b = molality of solute (mol/kg)
Π = osmotic pressure (units dependent on
units of R)
c = molarity (mol/L)
R = gas constant (chose value with
appropriate units)
T = temperature (K)
Boiling point is a colligative
property, and its elevation, based
on the addition of a solute to a
pure solvent, is found using the
molality of the solute.
Apply this change to the Tb,solvent:
Tb.soln = Tb,solvent + ΔTb
Freezing point is a colligative
property, and its dpression, based
on the addition of a solute to a
pure solvent, is found using the
molality of the solute.
Apply this change to the Tb,solvent:
Tb.soln = Tb,solvent – ΔTf
Osmotic pressure is a colligative
property. This is the amount of
applied pressure required to
prevent solvent flow through a
semipermeable membrane
(prevent solvent from diluting
solution).