Equations sheet and formulas used in class PDF

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Equations sheet and formulas used in class...

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MCAT%Equations% !

Name

Equation

Units

Mechanics & Energy ∆x ∆t ∆d ∆t ∆v ∆t

Average speed Average velocity Acceleration Newton’s Second Law

F!"# = ma

Static Friction

F!,!"# = µ! F!

Kinetic Friction

F! = µ! F!

Force of gravity acting perpendicular to an inclined plane Force of gravity acting parallel to an inclined plane

m s m s m s! m s! m 1 Newton = 1 kg ∙ ! s m 1 Newton = 1 kg ∙ ! s 1 Newton = 1 kg ∙

mgcosθ

1 Newton = 1 kg ∙

m s!

mgsinθ

1 Newton = 1 kg ∙

m s!

Torque

τ = rFsinθ

N∙m

Work

W = Fdcosθ

1 Joule = N ∙ m

Work (pressurevolume curve)

W = P∆V

J

Center of mass Mechanical Advantage Power Power

x=

m! x! + m! x! + m! x! m! + m! + m! F!"# MA = F!" P=

W ∆E = t t

P = Fv

1 watt W = W

J s

Kinetic Energy

1 KE = mv ! 2

J

Work-Kinetic Energy theorem

W!"# = ∆KE = K ! − K !

J

Gravitational Potential Energy

U = mgh

J

1 ! kx 2

J

F = −kx

N

Elastic Potential Energy Hooke’s Law Frequency of a wave Speed of a wave

U=

f=

1 T

v = fλ

1 = Hz s m s

Fluids Density Specific Gravity

ρ=

m V

ρ!"#$%& ρ!"#

%$Buoyant Force

F! = mg = ρ!"#$% Vg

Pascal’s Law

F! F! = A! A !

Hydrostatic Pressure

P = P! + ρgz

Poiseuille’s Law

Q=

πr ! ∆P 8ηL

Continuity Equation

A! v! = A! v!

Bernoulli’s Equation

1 P! + ρv!! + ρgh! = P! … 2

Gases Absolute Temperature Pressure

g cm!

K = ℃ + 273 P=

F A

N

Ideal Gas Law

PV = nRT

Boyle’s Law

P! V! = P! V! V! V! = T! T! n! n! = V! V!

Charles’ Law Avogadro’s Law Average kinetic energy of a gas particle Heat capacity at constant volume for an ideal monatomic gas Heat capacity at constant pressure for an ideal monatomic gas van der Waals equation of state Dalton’s Law of Partial Pressures

3 KE!"# = k ! T 2

J

3 C! = nR 2

J K

5 C! = nR 2

J K

P=

nRT n! a − ! V − nb V

P! = X! P! P = P! + P! + P!

Thermodynamics Heat transferred

q = mc∆T

Standard Heat of Reaction

∆H°!,!"#$%&'( −

° ∆H!,!"#$%#&%'

Standard Heat of Reaction

° ∆H!"#$% !"#$%& −

∆H°!"#$% !"#$%&

Change in Gibbs Free Energy Linear Expansion (Solids) Volumetric Expansions (Solids & Liquids)

∆G = ∆H − T∆S ∆L = αL∆T ∆V = βV∆T

1

cal J = 4.184 g∙K g∙K

kJ mol

Sound I I!

Sound Level

β = 10log

Sound Level

β! = β! + 10log

Intensity Doppler Effect

dB I! I!

P A v ± v! f! = f v ∓ v! I=

λ= Waves in Open Pipes f=

f=

W m! Hz

2L n

v nv = λ 2L

λ= Waves in Closed Pipes

dB

4L n

v nv = λ 4L

Light & Electromagnetic Radiation Speed of Light

c = fλ

Energy of Photon

E = hf

m s

Geometrical Optics Law of Reflection

𝜃! = 𝜃! c v

Index of Refraction

n=

Snell’s Law

n! sinθ! = n! sinθ!

Critical Angle

𝜃! = 𝑠𝑖𝑛!!

n! n!

Focal length of lenses in a series

1 1 1 2 = + = f o i r −i m= o 1 P= f 1 1 1 1 1 = + + + ⋯+ f f! f! f! f!

Power of lenses in a series

P = P! + P! + P! + ⋯ + P!

Magnification for a system of lenses

m = m! × m! × m!

Optics Equation Magnification Lens Power

diopters

diopters

Electrostatics

Voltage (Potential Difference)

kq! q! r! F! kQ! = ! E= r q kQq U= r U kQ V= = r q V d W!" ∆V = V! − V! = q

Power

VI

W

Power

V! R

W

Power

I! R

W

Coulomb’s Law Electric Field Electrical Potential Energy Electrical Potential Intensity of Uniform Electric Field

F! =

N V N or m C J 1V=1

J C

V m Volts

Circuits Current Ohm’s Law

I=

Q t

V = IR

1A=1

C s

Resistors in Series

R ! = R! + R ! + R !

Ohms (Ω)

Resistors in Parallel

1 1 1 1 = + + 𝑅! 𝑅! 𝑅! 𝑅!

Ω

Resistivity Capacitance Energy of a Charged Capacitor Capacitors in Series Capacitors in Parallel

𝜚= 𝑄

𝑅∙𝐴 𝐿

𝐴 𝑑 𝑉 ! Q 1 1 U= = Q∆V = C(∆V)! 2 C 2 1 1 1 1 = + + 𝐶! 𝐶! 𝐶! 𝐶! 𝐶=

= 𝜀!

𝐶! = 𝐶! + 𝐶! + 𝐶!

Ohm-meter (Ω ∙ m) 1F=1

C V

F F

Magnetism Magnetic Force

F! = qvBsinθ

Lorentz Force

F = qE + qvBsinθ

1T=1

N∙s m∙C

Atomic Structure & Stoichiometry Maximum number of electrons in a shell

2n!

Kinetic Energy of a Photoelectron

hf − ϕ

eV

Bonding & Reactions Formal Charge

1 FC = V − NB − B 2

Dipole Moment

p =q∙d

Specific rotation

α =

α!"# c×l

Electrochemistry Electrodeposition Equation

mol M =

It nF

C∙m degrees

Cell potential

cell pot. = red. pot − ox. pot

Kinetics Rate law

rate = k A

Arrhenius Equation Law of Mass Action

!

B

!

!!!

k = Ae !" k !" =

!

C A

!

D B

! !

Molecular Structure & Absorbance Spectra 1 λ

Wavenumber

cm!!

Solutions Autoionization of water

K ! = H! O! OH ! = 10!!"

pH

− log H !

pOH

− log OH !

Base Dissociation Constant

H! O! A! HA B! OH ! k! = BOH

pK !

−logK !

pK !

−logK !

Acid Dissociation Constant

HendersonHasselbalch Point of Inflection

Solubility Product Constant

k! =

pH = pK ! + log

[Conj. base] [acid]

pH = pK ! or 14 − pK ! for A! B! : K !" = A!!

!

B!!

!

Separations & Purifications Retardation factor

R! =

distance spot moved distance solvent front moved

Circulation & Respiration Henry’s Law

A = K ! × P!

Amino Acids & Proteins Electrophoresis (migration velocity of a molecule)

v=

Ez f

Genetics p+q=1 Hardy-Weinberg p! + 2pq + q! = 1

Enzymes Michaelis-Menten

v=

v!"# S K ! + [S]

Plasma Membrane & Nervous System Nernst Equation Osmotic Pressure

E!"## = E°!"## −

RT ln (Q) nF

Π = iMRT ! !...