MCAT Equations Flashcards
Instantaneous Displacement (Assuming constant linear acceleration)
X = Xo + Vo + 1/2AT^2
Instantaneous Velocity (Assuming constant linear acceleration)
V = Vo + AT
Instantaneous Velocity Squared (Assuming constant linear acceleration)
V^2 = Vo^2 + 2AX
Average Velocity (Assuming constant linear acceleration)
Vavg = 1/2(V + Vo)
Total Displacement (m)
Xtot = VavgT
Initial Vertical Velocity (Projectile Motion)
Vvert = Vsin(theta)
Initial Horizontal Velocity (Projectile Motion)
Vhor = Vcos(theta)
True of False: Acceleration in the horizontal direction effects acceleration in the vertical direction?
FALSE they are independent of one another
Peak Height of a Projectile (m)
Vosin(?) = root(2(gh)) or H=(Vsin(theta)^2)/2g
Force (N)
F = MA
Gravitational force exerted by one object on another object
F = G(Mm/r^2)
How does the gravitational force change as an object doubles it’s distance from another object?
By a factor of 4 (2^2)
Normal force against an object on an inclined plane
Fn = mgcos(theta)
Vector sum of the weight and normal force on an inclined plane
Ftot = mgsin(theta)
True or False: Any object on an inclined plane will accelerate at a rate that is some fraction of Mg?
TRUE: mgsin(90) = 1 and mgsin(0) = 0
Angular Velocity (m/s)
w = V/r
Frequency (Number of full rotations per second) (Angular Motion)
f = w/2pi
Centripetal Acceleration (m/s^2)
Ac = V^2/r
Centripetal Force (N)
Fc = MV^2/r
True or False: Centripetal Force always faces toward the center of the circle?
True: Centrifugal force faces outward
Force of Static Friction (N)
Fs lessthanorequalto MUsFnormal
Force of Kinetic Friction (N)
Fk = MukFnormal
True or False: The coefficient of static friction is usually greater than the coefficient of kinetic friction?
True = an object is easier to push when moving
Force on a compressible object like a spring (Hook’s Law) (N)
F = -k(delta)x
Torque (N*m)
T = FL (L is the lever arm)
Kinetic Energy of an object
Ek = 1/2MV^2
Gravitational potential Energy of an object
Ep = mgh
Elastic Potential Energy
Epe = 1/2k(delta)X^2
What are the two possible types of energy transfer?
Work and Heat
What is the definition of work?
The transfer of energy via force
What is the definition of heat?
The transfer of energy via normal flow from high to low
Work done by all forces other than friction
W = Fdcos(theta) (d is in the direction of displacement)
Total Work (When there is neither heat nor friction)
W = (delta)U + (delta)K
Total Change in Energy (Measured in Joules N*m)
(delta)E = W + q (q equals heat)
Power (Measured in Watts J/s)
P = (delta)E/t
Instantaneous Power due to force
P = Fvcos(theta)
Momentum (kg*m/s)
p = mv
Elastic Collision (Energy is conserved)
Einitial = Efinal (Scalar)
Inelastic Collision (Momentum is conserved)
MinintialVinitial = MfinalVfinal (Vector)
True or False: Reverse collisions approximate inelastic collisions?
TRUE: Initial momentum is equal to final momentum
Impulse
J = (delta)p
Impulse as a factor of Force
J = Favg(delta)t
Average force (N) from change in momentum
(delta)mv = Favg(delta)t
True or False: Ideal machines change the amount of work?
FALSE: Ideal machines do not change work
Density
p = m/V (kg/m^3)
What is the density of water?
1000kg/m^3 or 1g/cm^3
Specific Gravity
S.G. = p(substance)/p(water)
Pressure
P = F/A (N/m^2 or Pa)
Pressure of fluid at a given depth
P = pgy (y is the depth below the surface)
Pressure of fluid at a given depth open to the air
P = pgy + 101,000Pa
Bouyant Force
Fb = p(fluid)Vg (where V is the volume displaced)
Bulk Flow of a Fluid
Q = Av
Fluid Constant (K)
K = P + pgh + 1/2pv^2
Maximum Velocity of Fluid
v = (root)2gh
Modulus of Elasticity
Modulus = Stress/Strain
True or False: Waves require a medium in which to move?
True: Think about the lack of sound in space
What happens if a wave in something of lighter density encounters something of greater density?
The reflected wave is inverted, this is not true of a wave from a higher density to a lower density.
Velocity of a wave
v = (frequency)(wavelength)
Period of a Wave
T = 1/(frequency)
Decibels of Sound
B = 10log(I/Io) This increases by ten times the log of the difference IE if it is the log of 12 it is 120 decibles which is 1200 times louder
Beat frequency
Fbeat = abs(F1-F2)
Length of a Harmonic (When both ends are nodes)
L = n(wavelength of N)/4
Length of a Harmonic (When one end is antinode)
L = n(wavelength of N)/2 (This does not have any even numbers for harmonics)
Doppler Effect
(delta)f/f = v/c where v is the difference between the two velocities
Force (due to an electric charge)
F = kQq/r^2
Force due to an electric field
F = KQ/r^2 (N/C or V/m)
True or False: Lines of force run from positive to negative?
True (when it comes to magnetic poles they run from north to south)
Force on a charge by an electric field
F = Eq (N)
Potential Energy of a Charge in a field
U = Eqd (d is only in the direction of displacement) (Potential energy is measured in Joules)
Voltage
V = Ed (voltage is independent of charge and is J/C)
Current (i)
i = V/r (Current is measured in Amps or C/s)
True or False: Current runs opposite the flow of electrons?
True
Voltage due to current and resistance
V = iR
Capacitance
C = Q/V (charge per unit of voltage)
True or False: The thickness of plates in a capacitor will increase their ability to store charge?
False, the charge sits only on the face of the plates. Increased surface area would increase the ability to store charge.
Energy Stored in a Capacitor
E = 1/2QV or E = 1/2CV^2
Effective Resistance (in series)
R = R1 + R2 + R3…
Effective Resistance in Parallel
1/R = 1/R1 + 1/R2…
Effective Capacitance (in series)
1/C = 1/C1 + 1/C2…
Effective Capacitance (in parallel)
C = C1 + C2…
Electrical Power
P = iV or P = i^2R or P = V^2/R
Maximum Voltage (Alternating Current)
Vmax = (root(2))Vrms (root mean square means the square root of the average of the squared values)
Maximum Current (Alternating Current)
imax = (root(2))irms
True or False: Electric poles can be found separately?
True, however magnetic poles have never been found separated
True or False: Like electric fields, magnetic fields follow the inverse square law (x/r^2)
True, therefore both lose strength as a function of the square of the distance.
Force of a magnetic field on a charge
F = qvBsin(theta)
Curved path of a charge particle in a field
qbB = mv^2/r
What is the speed of light in a vacuum
3 x 10^8 m/s
Index of Refraction
N = C/V (c is the speed of light in a vacuum and V is the speed of light in the medium)
True or False: The greater the index of refraction the slower light moves through a medium?
True, nothing is faster than the speed of light in a vacuum
Angle of Reflection
Theta of Incidence = Theta of Reflection
Angle of Refraction
N1sin(Theta1) = N2sin(Theta2)
True or False: When light passes into a new medium the frequency remains the same but the wavelength changes?
True: the change in wavelength makes it shorter which slows the velocity of the wave in the new medium
Energy of a Photon
E = hF where h is plancks constant (6.63 x 10^-34)
True or False: A diverging lens acts like a convex mirror and a converging lens acts like a convex mirror?
True
Focal Length
Lfocal = 1/2r (r is the radius of curvature)
Lens Power
P = 1/f (where f is the focal length)
Lens Magnification
m = hi/ho = -di/do
Focal Length of a mirror or lens
1/f = 1/do + 1/di
Lateral Magnification of a 2 lens system
M = m1m2
Power of two lenses together
P = P1 + P2
Moles of a substance
mol = grams/atomic weight
True or False: A period is a horizontal row on the periodic table.
True, a family is a vertical column
True or False: Greater bond length means less bond strength.
True, also remember that energy is always required to break a bond.
Percent Yeild
% yield = actual/theoretical
How do you find the principal quantum number
It is the number of the period, transition metals are period -1 and lanthanides and actinides are period -2
How do you find the azimuthal quantum number?
The first shell number minus 1. 0 is s, 1 is p, 2 is d, and 3 is f
How do I find the magnetic quantum number
it is every integer between positive azimuthal quantum number and negative azimuthal quantum number
What is standard temperature and pressure?
0 degrees celsius and 1 atm
How many Pa are in 1 atm?
101,300Pa
Ideal Gas Law
PV = nRT (n is the number of mols of gas) (r is the ideal gas constant) (t is temperature)
How much volume does 1 mol of ideal gas take up at 1 atm?
22.4 L
Partial Pressure of a Gas
Pp = XaPtot where Xa is the mol fraction of the gas
Average Kinetic Energy of a Gas Particle
K.E. = 3/2RT
RMS Velocity of a particle
V1/V2 = root (m2/m1)
Effusion rate of particles
Rate1/Rate2 = root(m2/m1)
True or False: The volume of a real gas is greater than the volume of an ideal gas.
True, the pressure of a real gas is less than the pressure of an ideal gas. These are especially true at low temperature and high pressure.
True or False: The rate of a reaction increases with temperature?
True, the average kinetic energy is greater and therefore the molecules collide with more energy
Rate of reaction not equilibrium
Rate = K [A]^a[B]^b making sure to use concentrations to the proper exponents.
True or False: For a second order reaction, each consecutive half life is twice as long as the previous.
True
Equilibrium Constant
K = [Products]^exponents/[reactants]^exponents
How do you use the reaction quotient to determine how a reaction will proceed?
If q is equal to K the reaction is at equilibrium, if q is greater than k there are more products and it will go in reverse, if q is less than k there are more reactants and the reaction will move forward
PV work
w = P(delta)V, because constant pressure is being applied when a constant force acts over a constant areas
Energy change of a system
deltaE = w + q
True or False: Work done by the system has a negative convention, work done on the system has a positive convention
True, if work is done by the system then the change in energy is = q - w
Rest mass energy
E = mc^2
For a closed system at rest with no fields how can energy be written?
U = q + w, if volume is held constant then u = q
Change in Enthalpy
deltaH = deltaU + PdeltaV (at constant pressure)
Change in Enthalpy when volume is held constant
deltaH = q, because no work is done when both pressure and volume are constant
deltaH or a reaction
deltaHproducts - deltaHreactants
True or False: Catalysts lower the activation energy but have no effect on the enthalpy of reaction.
True, there is no change in the enthalpy of the initial and final states, enthalpy is a state function
Gibbs Free Energy
deltaG = deltaH - TdeltaS
Molarity
mol solute/volume of solution
Molality
mol solute/kg of solution
mol fraction
mol of solute/total mols of solute and solution
mass percentage
mass of solute/total mass of solution x 100
parts per million
mass of solute/total mass of solution x 10^6
Vapor Pressure (with non-volatile solute)
Pv = XaPa (mole fraction of pure product by the vapor pressure of pure product)
Vapor Pressure (with a volatile solute)
Pv = XaPa + XsPs
Heat Capacity
q = CdeltaT
Specific Heat Capacity
q = McdeltaT
Specific Heat of Water
1 Cal/g*degreesC
Boiling Point Elevation
deltaT = kbmi (m is molality and i is the vant hoff factor)
Freezing point depression
deltaT = kfmi (kf is the constant specific to freezing)
Osmotic Pressure
Pi = iMRT (M is the molarity of the solution)
pH
pH = -log[H+]
pOH
pOH = -log[OH-]
pH from Ka of weak acid
Ka = X^2/[initial undissociated]
pOH from Kb of weak acid
Kb = X^2/[Initial undissociated]
Free Energy of a Cell
deltaG = -nFEmax (where N is the number of transferred electrons and E is the voltage)
True or False: Positive Cell Potential indicates a spontaneous reaction.
True, this leads to a negative deltaG
