MCAT Equations
permittivity of free space (Ԑ_0)
8.85 x 10^-12 F/m
Gravitational force in cases where objects are distant from Earth's surface
F = [G(m1)(m2)]/r^2
Magnetic force
F = iLBsinθ; F = qvBsinθ (right hand rule) charged particle in a B field forced into moving path.
Spring forces; Hooke's Law
F = kΔx, where -k = spring stiffness and Δx = distance spring has deformed from rest position.
Work
F(dCos(angle)), or P(deltaV). Also W = delta E (KEf - KEi) (sign must be + when E is gained and - when E is lost)
Newton's Second Law
F=ma or F=mg
Rydberg formula
Formula that predicts wavelength of light emitted by electron moving from one energy level to another. hc/(lamda)=R[1/n1^2 - 1/n2^2] where R = 2.18x10^-18 J, and n2 is always > n1
percent yield
(actual yield/theoretical yield) x 100
Ohm's Law
(delta)V = IR, where I = current through conductor in amperes (A), V is voltage across conductor in volts (ΔV = voltage drop: difference in electric potential), and R = resistance of conductor in Ohms (Ω).
Displacement if final velocity is unknown
(initial velocity x time) + 1/2(a)(time^2)
Van't Hoff's Law
(pi) = iMRT, where i = Van't Hoff constant (# of particles/mol of dissolved substrate), M = TOTAL conc. of solutes, R = ideal gas constant, T = temp in K
Cos of 45 degrees
(square root of 2)/2
Sin of 45 degrees
(square root of 2)/2
Cos of 30 degrees
(square root of 3)/2
Sin of 60 degrees
(square root of 3)/2
average velocity
(v initial + v final)/2
Kinetic energy
KE=1/2mv^2
Equilibrium constant formula
Keq = [products]^coefficients/[reactants]^coefficients. (Should not include solids or pure liquids!).
Affinity of enzyme for substrate
Km (a concentration) = [S] @ 1/2Vmax, where [S] = conc. of substrate
Solubility constant: for AB(s) --> aA(aq) + bB(aq),
Ksp = [A]^a([B]^b). (Ksp is an equilibrium constant). (Note: pure solids are not included bc we can't change their concentrations.)
Mechanical advantage equation for ramps
MA = (incline length/incline height). MA MUST be >1!
Celsius to Fahrenheit
Multiply by 9/5, then add 32
Conservation of energy
Sum of Ei = Sum of Ef. PEi + KEi = PEf + KEf. ghi + 1/2vi^2 = ghf + 1/2vf^2. Where i = initial and f = final.
Michaelis-Menten equation
V = (Vmax[S])/(Km + [S])
Equation for mole fraction of a gas? Partial pressure of a gas?
Xgas = ngas/ntotal = Pgas/Ptotal, so Pgas = (Xgas)(Ptotal)
Area under the curve (AUC)
Y(X)
Displacement if acceleration is unknown
[(Vi + Vf)/2]*t
# of structural isomers for alkanes
[2^(n-4)] + 1, where n = # of C's
What is the Van Der Waals equation?
[P + a/(V^2)m][Vm - b] = RT, where a is a constant for each gas, Vm = a gas's molar volume, and b is subtracted to reflect the actual volume taken up by gas particles.
Displacement (d)
average velocity x time
Pythagorean Theorem
a²+b²=c²
Velocity (v)
displacement/time
Horizontal displacement
dx = Vx(t)
Frequency of light (f)
f = c/λ where c = speed of light: ~3x10^8 m/s and λ = wavelength in m
Static or kinetic friction (ff = fs or fk)
f_friction = µN, where N = normal force: F perpendicular to surface object rests upon, and μ = coefficient of static or kinetic friction.
Reaction quotient (Q)
formula same as Keq, but rxn doesn't have to be at equilibrium. When Q = Keq, rxn is at equilibrium. If Q < Keq, ratio of products to reactants is lower than when at equilibrium (rxn proceeds -->). If Q > Keq, ratio of products : reactants is greater than at equilibrium (rxn proceeds <--).
change in energy (ΔE) between orbitals
hc/λ = R[1/n1^2 - 1/n2^2] where h = 6.626x10^-34 J, c = 3x10^8 m/s, λ = wavelength, R = 2.18x10^-18 J, and n2 is always > n1
Final velocity (Vf)
initial velocity + (acceleration* time)
Arrhenius equation
k = Ae^-(Ea/RT), where k = rate constant, A = frequency of collisions between reactants, Ea = activation energy, R = ideal gas constant, T = temp. in K
Normal force that acts on an object on an incline
mgcosθ
Gravitational force that acts on an object on an incline
mgsinθ
Fahrenheit to Celsius
subtract 32, then multiply by 5/9
formal charge
v.e.'s - 1/2 bonding e-'s - lone pair e-'s (should - actually has)
Displacement for free fall
y = 1/2g(t^2)
speed of light (c)
~3.00 x 10^8 m/s
potential torque
Ʈ = (mg)(d)(sin90^o)
Torque
Ʈ = rFsinθ
Gibbs free energy (ΔG)
ΔG = (ΔH) - T(ΔS), where ΔH = change in enthalpy, and ΔS = change in entropy
Standard free energy change (ΔG^o in kcal/mol)
ΔG^o = -lnKeq (When ΔG < 0, Keq > 1. When ΔG > 0, Keq < 1).
Hess's Law (change in enthalpy for a reaction)
ΔHreaction = ΔHf products - ΔHf reactants, where Hf = heat of formation in J/mol
Slope
ΔX/ΔY
Centripetal acceleration
Δa that a centripetal F causes. a = v^2/r
Acceleration (a)
Δv/time = (v final - v initial)/time
Formal Charge example: N in NH3
5ve - (6 bonding e-'s/2) - 2 lone pair e-'s = 0
Planck's constant (h)
6.626 x 10^-34 J*s
Cos of 90 degrees
0
Sin of 0 degrees
0
Cos of 0 degrees
1
Sin of 90 degrees
1
3 power equations that relate current, resistance, and volts
1) P = IV, 2) P = I^2(R), 3) P = V^2/R
# of possible codons
4^3 = 64 codons --> 20 aa's. 4 nitrogenous bases can assume 1 of 3 positions in a codon.
Total resistance in parallel circuit example: R1 = 16, R2 = 16, R3 = 16, R4 = 16
1/16 + 1/16 + 1/16 + 1/16 = 4/16 = 1/4. Rtot = 4Ω
Cos of 60 degrees
1/2
Sin of 30 degrees
1/2
elastic potential energy
1/2kx^2, where k = spring constant in N/m, and x = distance compressed or extended.
Capacitance in series
1/C = 1/C1 + 1/C2 + 1/C3 . . . + 1/Cn
Rydberg constant (R)
2.18 x 10^-18 J
Faraday's constant
23.1 kcal/(V x mol)
Avogadro's number
A mole of any chemical substance is a quantity that contains 6.022x10^23 particles (molecules, ions, or atoms).
Capacitance in parallel
C = C1 + C2 + C3 . . . + Cn
Capacitance when there's no dielectric material
C = Ԑ_0 (A/d), where Ԑ_0 is the permittivity of free space, A is area, and d is distance
Capacitance with dielectric material
C' = (KԐ_0A)/d, where K is the dielectric constant (Ԑ_material/Ԑ_0), and C' is modified capacitance (K*Capacitance when there's no dielectric)
Specific heat of liquid water
Cwater(l) = 4.186kJ/(kg x K)
General electric fields
E = F/q, where F = Farads and q = charge
Uniform electric field
E = V/d, where V = volts and d = distance
Energy of one photon (E)
E = hf where h = 6.626x10^-34 J*s and f = frequency of light in c/λ (c = speed of light: ~3x10^8 m/s) (λ = wavelength in m)
Energy
E =KE + PE
gravitational potential energy
PEgrav = mgh (mass x gravity x height)
Ideal gas law
PV = nRT, where n = # of moles present
Heat added as it relates to specific heat, mass, and temperature
Q = mcΔT, where Q = heat added (in kJ), m = mass in kg, c = specific heat capacity in (kJ/kg*K) and T = temp in K.
How is the ideal gas constant (R) usually expressed on the MCAT?
R = 0.08Latm/molK
Center of mass in a multi-mass system
Xcenter = (m1x1 + m2x2...)/(m1 + m2...)
What is Graham's Law? What is the equation?
The rate of effusion (escape through small opening) of a smaller gas is quicker than that of a larger gas. (R1/R2) = √(M1/M2)
What is Dalton's Law?
The total pressure of a mix of gases is the sum of the partial pressures of the indv. gases. Ptotal = Pa + Pb + Pc + ...
What is the relationship between the average kinetic energy of (U) of gas particles and the temp. of the gas? What is the equation for U?
They are directly proportional. Average kinetic energy (U) = 3/2RT, where R is a constant and T = temp.
Electrostatic force
Type of electromagnetic force between 2 objects that are not moving relative to each other. F = qE, where F is experienced for particle w/ charge q in uniform electric field E.
Final velocity for free fall
Vf =√2gy
Final velocity if time is unknown
Vf^2 = Vi^2 + 2ad
Voltage, current, and resistance in a series circuit
Vtot = -(V1 + V2 + V3 . . . + Vn) Itot = I1 = I2 = I3 . . . = In Rtot = R1 + R2 + R3 . . . + Rn
Voltage, current, and resistance in a parallel circuit
Vtot = V1 = V2 = V3 . . . = Vn Itot = I1 + I2 + I3 . . . + In 1/Rtot = 1/R1 + 1/R2 + 1/R3 . . . + 1/Rn
Horizontal velocity
Vx = Vi(cosθ)
Vertical Velocity
Vy = Vi(sinθ)
Power
W/t = J/s = Watt. Or P = F(d)/t
Rydberg formula example: from n=5 to n=2
Where R = 2.18x10^-18 J: hc/(lamda)=R[1/2^2 - 1/5^2] = R[21/100] = n=2 shell is ~4.2x10^-19 J lower in energy than n=5 shell
Work energy theorem
Wnet = (delta)KE
Molarity
n(the # of moles present)/V(in L)
Snell's Law
n1sinθ1 = n2sinθ2, where n = index of refraction for a particular material, and θ = θ of refraction
Allele frequency in HW equilibrium
p + q = 1, where p = % dominant allele and q = % recessive allele
Phenotype frequency in HW equilibrium
p^2 + 2pq + q^2 = 1, where p^2 = homozygous dominant, 2pq = heterozygotes, q^2 = homozygous recessive.
Rate law of aA + bB --> cC + dD
rate = k[A]^x([B]^y), where rate is in mol/(L*s) (aka M/s), x and y must be experimentally determined, and the order of the rxn = x + y
