Chem/Phys Equations and Techniques Flashcards
Translational motion
∆x = vot + 1/2at2
(Vƒ)2 = (Vo)2 + 2ad
Vƒ = Vo + at
Frictional force
fmax = μ Ν
- N= normal force
- u= coefficient of friction
μk < μs always
Uniform circular motion
Fc = mac = mv2 /r
ac= v2 /r
Momentum, Impulse
I = F Δt = ΔM
- applied force x time
M = mv
- mass x velocity
Impulse is the change of momentum of an object when the object is acted upon by a force for an interval of time. So, with impulse, you can calculate the change in momentum, or you can use impulse to calculate the average impact force of a collision. A longer collision or impact time translates to a smaller force.
Work
W = F d cosθ
W = ∆KE
W = -P∆V
Joules
Energy (conservation)
ET = Ek + Ep
Spring Force, Work
F = -kx
W = kx2 /2
Current, Resistivity, Resistance
I = Q/t
- Current = quantity of charge / time
R = ρL/A
- resistivity = p (resistivity of wire) x Length of wire / cross sectional area of wire
V = IR
- Voltage = current x resistance
Resistors (series)
Req = R1 + R2 . . .
Resistors (parallel)
1/ Rtot = 1/ R1 + 1/ R2
Capacitors in Ser.
1/ Ceq = 1/ C1 + 1/ C2 + 1/ C3
Capacitors in parallel
Ceq = C1 + C2 . .
Sound
dB = 10 log10 (I/I0)
- I = intensity
- Io = minimum threshold of human hearing
beats = Δ ƒ
Thermodynamics and changing phases
Q = mc Δ T (MCAT)
- c= specific heat
- The specific heat is the amount of heat necessary to change the temperature of 1.00 kg of mass by 1.00ºC.
Q = mL
- m= mass
- L = specific latent heat
- the amount of energy required to change the state of 1 kilogram (kg) of a material without changing its temperature. … latent heat of vaporisation - the amount of energy needed to boil or condense the material at its boiling point.
Coulomb’s Law:
F = k∙(q1q2/r2)
This law quantifies the force between two electrically charges particles. The electrical force (F) of repulsion or attraction between the particles is proportional to the product of the charges (q) and is inversely proportional to the square of the distance between them (r2). In this equation, k is Coulomb’s constant.
Kinetic and potential energy
Ek = 1/2 mv2
Ep = mgh
Ρressure
Pressure under water
P = F/A
ΔΡ = ρgΔh
p = fluid density
Specific Gravity
SG = ρ substance / ρ water (relative density)
ρ of water= 1 g/cm3 = 103 kg/m3
Density
Buoyant force
ρ = mass / volume
Fb = ρgV
- density of the fluid, gravity, volume of the object
If an object has a specific gravity of .92 (like ice), 92% of the object will be submerged in water
Optics power and magnification, total magnification
Power = 1/ i + 1/ o = 1/ f = 2/r
- f = focal length
- the power of a converging lens is positive and that of the diverging lens is negative.
M = magnification = - i/o
- image/object
mtotal= m1 x m2….
Gibbs Free Energy (standard and nonstandard)
Gas constant R=
ΔG = ΔH - TΔS
- if H is positive and S is negative, ∆G always positive
- if H is negative and S is positive, ∆G always negative (spontaneous)
ΔG° = -RTln Keq
- R = 8.3145 J/(mol x K)
Dopplers effect
Higher frequency when coming towards you, lower when going away
fo = observed
v = speed of sound waves
vo = observer velocity
vs = source velocity
fs = actual frequency of sound waves
Bernouilli’s Equation
Bernoulli’s principle: Within a horizontal flow of fluid, points of higher fluid speed will have less pressure than points of slower fluid speed.
P1+ 1/2ρv12 + ρgh1 = P2 + 1/2ρv22 + ρgh2
This equation allows you to analyze a fluid as it moves through a tube and relates the velocity of the fluid to its pressure. For a horizontal tube that changes in diameter, regions where the fluid is moving fast will be under less pressure than regions where the fluid is moving slow. Bernoulli’s equation applies principles of energy conservation to a flowing fluid. In this equation, P is the hydrostatic pressure, ρ is the density of the liquid, v is the velocity, g is gravitational acceleration (9.8 m/s2), and h is the height of the liquid in meters.
parallel plate capacitor equation
Electric field equation
C = ε(A/d)
E = V/d
Voltage = electric field x displacement
Capacitor work
W = 1/2 CV2
- capactitance
- V = potential difference, voltage
Physics math
Radians to degrees
root 3, root 2
area of circle, circumference
Angle θ may be given in radians (R) where 1 revolution = 2πR = 360°
Estimate square root 3 as 1.7 and root 2 as 1.4
Cross-sectional area of a tube = area of a circle = πr2 where π can be estimated as 3.14 and r is the radius of the circle; circumference = 2πr
Units to memorize
Both work and energy are measured in joules where 1 joule (J) = 1 N × 1 m . {Imperial units: the foot-pound , CGS units: the dyne-centimeter or erg }
The SI unit for power is the watt (W) which equals one joule per second (J/s) = volts × amperes.
Current is measured in amperes = coulombs/sec. The units of resistance are ohms, symbolized by Ω (omega), where 1 ohm = 1 volt/ampere.
The SI unit for pressure is the pascal (1 Pa = 1 N/m2 ). Other units are: 1.00 atm = 1.01 × 105 Pa = 1.01 bar = 760 mmHg = 760 torr.
The SI unit for the magnetic induction vector B is the tesla where 1 T = 1 N/(A)(m) = 104 gauss.
Boyle’s Law:
Pressure and volume
PV = constant,
P1V1 = P2V2
Avogadro’s Law:
V1/n1 = V2/n2
Dalton’s Law of Partial Pressures:
PTotal = P1 + P2 …
Photon Energy:
Planck’s constant
E = hf
E= hc/ λ
Planck’s constant = 6.62607015 × 10−34
Snell’s Law:
n1sinθ1 = n2sinθ2
Snell’s Law describes the change in direction of a light ray as it moves from a medium with one refractive index (n1) to another medium with a different refractive index (n2). The angle (sinθ1) of incidence towards the surface and the angle (sinθ2) of refraction are measured relative to a surface normal.
Lens Equation:
1/f = 1/o + 1/i
for a convex lens the focal length will always be positive
for a concave lens the focal length will always be negative.
Van der Waals equation (real gases)
What do a and b mean?
P = RT/(V-b) - a/V2
V = molar volume
The a and b are called van der Waals constants: The constant a provides a measure of the average attraction of the molecules, whereas constant b adjusts for the volume occupied by the gas particles
Graham’s rate of effusion of gases
Quantum numbers
Electronic configuration rules
Solutions equations
molarity
molality
mole fraction
mass percent
ppm
Freezing point depression
m = molality = moles solute/ kg solvent
k = constant
Boiling point elevation
Osmotic pressure
πV = nRT
Phase diagram for water
It has a negative slope due to the fact that when ice melt, the molar volume decreases. Ice actually melt at lower temperature at higher pressure.
Large Keq
Indicate reaction has almost gone to completion
Buffer solution equation
(for pOH)
pOH = pKb + log [HB]/[[B]
pH equations
pH = -log[H+] pOH = -log[OH]
pKa = -log[Ka] pKb = -log[Kb]
pH + pOH = 14 pKa + pKb = 14
Ka x Kb = Kw = [OH][H+] = 10-14 (at 298K)
1st law of thermodynamics
Conservation of energy: energy can neither be created nor destroyed, only transformed or moved
In Closed Systems:
∆U = Q - W
change in internal energy = heat transfer into system - work performed by the system
if system performs work, loses energy to environment
positive value if work is done on the system
Doesn’t apply in open systems
Standard temp and pressure vs standard conditions
Arrhenius acid and base
Lewis acid and base
Bronsted Lowry acid and base
Rate determining step
Slowest elementary step in reaction
First step is rate determining
Pascal’s Law
Force and area
F1/A1 = F2/A2
Molar heat of solution, vaporization, fusion
Total entropy change
+ entropy change is increase in disorder
All spontaneous change occurs with an increase in entropy of the universe. The sum of the entropy change for the system and the surrounding must be positive(+) for a spontaneous process.
Cell potential
key difference between electrode potential and cell potential is that electrode potential refers to the ability of an electrode in a cell to get reduced or oxidized whereas cell potential is the difference between the electrode potentials of the electrodes present in an electrochemical cell.
Anode
Electrode where oxidation occurs, half reaction with more negative reduction potential
Cathode
Electrode where reduction occurs, more positive half reaction reduction potential
Le Chateliers Principle
Pressure
Pressure of a liquid
F/A
density x mass x height
Linear and volumetric expansion
Center of mass
1 Joule =
N x m
Torque
When to use Joules, Watts, Newtons
Newtons is force
Joules is work (N x m), kinetic and potential energy
Power is watts (J/s)
Frequency of a wave
Speed of a wave (not in a vacuum)
Speed of light is in a vacuum
F = 1/T (Hz)
- Period (T) is number of seconds per cycle; inverse of frequency
v = wavelength x frequency
c = fλ
Magnetic Force
F = qvBsin0
Acid and base dissociation constants
PRODUCTS OVER REACTANTS (excluding water)
Michaelis-Mentin
Km
Vmax
Equation
Km is the concentration of substrate which permits the enzyme to achieve half Vmax. An enzyme with a high Km has a low affinity for its substrate, and requires a greater concentration of substrate to achieve Vmax.
Vmax is the maximum rate that can be observed in the reaction
Capacitance
energy of a capacitor
C= q/V
- charge over voltage
C = εA/d
- area of plates over length
E = 1/2 * C * V² (also work eq)
Power
P = W/t
P = Fv
P = I2R
Watts = J/s
Concave vs. Convex lens focal point (+/-)
Focal point is positive for convex lens, negative for concave lens
Absorbance