MCAT Chemistry and Physics equations

moles

grams/ atomic weight

rate law

k[A]ⁿ[B]ⁿ

percent yield

actual yield/theoretical yield × 100

equilibrium constant

K=[C]ⁿ[D]ⁿ/[A]ⁿ[B]ⁿ

arrhenius equation

k=Ae^ -Ea/RT (linearized: lnk=-(Ea/RT) + lnA)

work (pressure-volume)

w=-P∆V

First law of thermodynamics (energy)

∆E=q+w

Reaction Quotient

Q=Products^coefficients/reactants^coefficients

average kinetic energy of a single molecule

KE=(3/2)(boltzmann's constant)T

Second Law of Thermodynamics (entropy)

∆S(system) + ∆S(surroundings)= ∆S(universe) ≥0

Gibb's free energy (equation 1)

∆G=∆H-T∆S

Gibb's free energy equation (equation 2)

∆G=∆G⁰+RTln(Q)

Enthalpy, under constant conditions, no change in pressure

∆H=∆U+p∆V

Ideal gas law

PV=nRT

Partial Pressure

P=(moles gas A /total moles of gas)P(total)

Dalton's Law

P(total)=P₁+P₂+....

Deviations from ideal gas law

Vreal > Videal Preal < Pideal

Specific heat capacity

q=mcΔT

Heat capacity

q=CΔT

Avogadro's Law (volume moles)

V/(moles)=V/(moles)

Boyle's Law (pressure volume)

PV=PV

Charles Law (volume temp)

V/T=V/T

Molality

m=(moles of solute)/kilograms of solvent

Mole fraction

(moles of solute)/(total moles of all solutes and solvent)

Mass %

mass of solute/total mass of solution X 100

Parts per million

mass of solute/total mass of solution x 106

Raoult's Law

Pv= (mole fraction solvent) X (partial pressure pure solvent)

Henry's Law

C=(henry's law constant)Pv

(c=solubility of gas, p=partial pressure)

Gibb's Free energy for a battery

ΔG=-nFEmax

pH

pH=-log[H+]

Henderson-Hasselbalch Equation

pH=pKa+ log [A]/[HA]

Newton's Second Law

F=ma

Gravity

F=Gm1m2/r^2

Force down an Inclined plane

F=mgsinθ

Normal force on inclined plane

F=mgcosθ

velocity

v=d/t

Acceleration

a= Δv/t

Hooke's Law

F=-k Δx

Force when object is accelerating

Fupward=Fdownward ± ma (add to the weaker side)

Torque

τ=Frsinθ (r=from point of pushing to fulcrum, θ=btw force and r)

Kinetic energy

k=(1/2)mv2

Gravitational Potential energy

u=mgh

Spring potential energy

U=(1/2)k Δx^2

mechanical Work

W=Fdcosθ (d=displacement, θ=angle b/w force and displacement

Power

P= ΔE/t (or W/t or F*d/t or F*velocity)

Density

ρ=m/v

Specific gravity

ρsubstance/ρwater

Pressure of fluid

P=ρgd

Pressure

P=F/A

Volume flow rate

Q=Av (v=velocity)

Bernoullis equation

K=P +(1/2)ρv^2+ρgh

Velocity of liquid

v=√2gh

Change in pressure of fluid

ΔP=QR (R=resistance to flow)

Buoyant force

F=ρVg

Coulomb's Law

F=kqq/r^2

Electric field

E=kq/r^2

Force on a charge,q, in electric field

F=kqq/r^2 (or F=qE)

Electric potential energy

U=kqq/r

electric potential

V=kq/r (or Ed)

Ohm's Law

V=IR

Capacitance

C=Q/V (Q=charge on either plate, V=Voltage)

Energy stored in capacitor

U=(1/2)QV

Effective resistance in series

Reff=R+R+R...

Effective resistance in parallel

1/Reff=1/R+1/R...

Effective capacitance in series

1/Ceff=1/C+1/C...

Effective capacitance in parallel

Ceff=C+C+C...

Magnitude of force through magnetic field

F=qvBsinθ (q=charge, v=velocity, B=magnetic field)

Period of wave

T=1/f

Intensity Level (decibals)

β=10 log I/I0 (if intensity has a zero added, then increase by 10 decibals)

Doppler effect approximation for frequency

Δf/fs=v/c

Doppler effect approximation for wavelength

Δλ/λs=v/c

Energy of emitted photon

E=hf (h=plank's constant)

Frequency of photon

f=c/λ

Index of refraction

n=c/v (c=velocity of light in vacuum, v=velocity of light in medium)

Snell's law

n1sinθ=n2sinθ (θ=angle of refraction)

Focal length of mirror

f=R/2 (R=radius of curvature)

Power of lens

P=1/f

Thin lens equation

1/f=1/d0+1/di (d0=object distance, di= image distance)

Magnification

m=-di/do=hi/ho

Law of effusion

Ea/Eb=√mb/√ma

Average kinetic energy of gases

E=3RT/2

half life

N=N0(.5)^x

enthalpy

∆H=∆(internal energy) ±p∆V

Rf value for TLC

Rf=migration distance of sample/ migration distance of solvent

change in Distance

∆d=(vo)(t)+ (1/2)at^2

change in velocity

∆v=at

v^2 equation

v²=v₀²+2ad

kinetic friction

F=µFnormal

velocity of wave

v=λf

beat frequency

|f₁-f₂|

standing wave wavelength (open pipes and strings)

λ=2L/n (n for open= #nodes; n for string=antinodes)

standing wave wavelength (closed pipe)

λ=4L/n (n= # of 1/4 wavelengths)

resistance

R=(resistivity)(L)/ (cross sectional area)

specific rotation

observed rotation/ (concentration * path length)

beer lambert law

A=lec (a=absorbance, l=path through sample, e=extinction coefficient, c=concentration)

diopter

D=1/focal length

electric power

P=IV (I^2*R or V^2/R)

capacitance (Equation2)

C=Aε/d

nernst equation

E=E⁰-(RT/nF)lnQ (f=faraday's constant, E=voltage of electrochemical cell)

Period of wave (eq2)

T=2√(m/K)