CHEM/PHYS MCAT: Equations & Units — VOCABULARY Flashcards

Vocabulary flashcards covering key terms, definitions, and core formulas from the MCAT Equations & Units notes.

Displacement (d)

Change in position; a vector quantity representing the difference between final and initial position.

Initial velocity (v0)

Velocity at the start of motion (t = 0); the starting speed and direction.

Final velocity (vf)

Velocity at a later time after some interval; the speed and direction at the end.

Acceleration (a)

Rate of change of velocity; a = Δv/Δt.

Kinematic displacement formula

d = v0 t + (1/2) a t^2 (one common form) or d = (v0 + vf)t/2 (alternative form when vf is known).

Kinetic Energy (KE)

Energy of motion; KE = (1/2) m v^2.

Gravitational Potential Energy (PE_g)

Energy due to height in a gravitational field; PE_g = m g h.

Elastic Potential Energy (PE_el)

Energy stored in a spring; PE_el = (1/2) k x^2.

Total Mechanical Energy (E)

Sum of kinetic and potential energy; E = KE + PE; conserved in the absence of nonconservative work.

Conservation of energy

Ei = Ef for a closed system; total energy remains constant.

Work (W)

Energy transfer by a force over a displacement; W = F d cosθ; in one dimension, W = F d.

Work–Energy Theorem

Work done on an object equals the change in its kinetic energy: W = ΔKE.

Power (P)

Rate of doing work; P = W/Δt = F v = dW/dt.

Mechanical Advantage (MA)

Ratio of output force to input force; MA = Fout / Fin.

Efficiency (η)

Useful work output divided by total work input; η = Wout / Win.

Friction (F_f)

Force opposing motion; F_f = μ N, with μ the coefficient of friction and N the normal force.

Pressure (P)

Force per unit area; P = F/A.

Center of Mass (x_cm)

Point where the system’s mass can be considered concentrated; x_cm = (m1 x1 + m2 x2)/ (m1 + m2).

Torque (τ)

Rotational analog of force; τ = r F sinθ (units N·m).

Centripetal Force (F_c)

Net inward force keeping an object in circular motion; F_c = m v^2 / r.

Centripetal Acceleration (a_c)

Acceleration toward the circle’s center; a_c = v^2 / r.

Doppler Effect

Apparent change in frequency due to relative motion; f' = f (v ± vobs)/(v ∓ vsource).

Open pipe waves

Sound waves in an open-ended pipe; fundamental frequency f1 = v/(2L); harmonics are integer multiples of f1.

Closed pipe waves

Sound waves in a pipe closed at one end; fundamental frequency f1 = v/(4L); only odd harmonics.

Sound Level (decibels)

L = 10 log10(I/I0); a logarithmic scale for sound intensity.

Thermal expansion (α)

Linear expansion: ΔL = α L ΔT; α is the linear expansion coefficient.

Heat (Q)

Energy transfer due to temperature difference; Q = m c ΔT.

Phase change (latent heat)

Energy for phase transition at constant temperature; Q = m L (L = latent heat of fusion/vaporization).

Internal energy (U)

Total microscopic energy of a system; for an ideal gas, ΔU = Q − W and U depends on temperature (U = n C_v T in many cases).

Gibbs Free Energy (ΔG)

ΔG = ΔH − T ΔS; ΔG < 0 indicates spontaneity at constant T and P; also ΔG = −n F E°cell in electrochemistry.

Standard enthalpy of reaction (ΔH°rxn)

ΔH°rxn = ΣΔH°f(products) − ΣΔH°f(reactants).

PV work

Work associated with volume change of a gas; W = −P ΔV (sign convention: work done by the system is negative).

Internal energy of an ideal gas (U)

For many ideal-gas problems, U = n C_v T; depends only on temperature (not volume for ideal gas at constant composition).

Density (ρ)

Mass per unit volume; ρ = m/V.

Hydrostatic Pressure

P = P0 + ρ g h; pressure increases with depth in a fluid.

Weight (Fg)

Force of gravity on a mass; Fg = m g = ρ V g.

Pascal’s Principle

Pressure applied to any part of an enclosed fluid is transmitted undiminished to every part of the fluid.

Poiseuille’s Law

Q = (π ΔP r^4)/(8 η L) for laminar flow in a tube; relates flow rate to pressure difference, radius, viscosity, and length.

Bernoulli’s Equation

P + ½ ρ v^2 + ρ g h = constant along a streamline.

Coulomb’s Law

F = k q1 q2 / r^2; electric force between point charges.

Electric Field (E)

E = F/q = k Q / r^2; field due to charges; direction follows force on positive test charge.

Electric Potential Energy (U)

U = q V; energy associated with a charge in an electric potential.

Electric Potential (Voltage, V)

Work per unit charge to move a test charge; measured in Volts (V).

Current (I)

Rate of electric charge flow; I = ΔQ/Δt.

Ohm’s Law

V = I R; relation among voltage, current, and resistance.

Series circuits

Resistances add: Req = R1 + R2 + …; same current flows through all components; voltages add: Vtotal = V1 + V2 + …

Capacitance (C)

C = Q/V; ability of a system to store charge per unit voltage; measured in Farads (F).

Parallel/Series Capacitance

Parallel: Ceq = C1 + C2 + …; Series: 1/Ceq = 1/C1 + 1/C2 + …

potential Energy in a capacitor

• Energy is stored in the electric field between the plates.

• A capacitor resists changes in voltage by holding energy.

• Larger capacitance or higher voltage → more stored energy.

• Dielectrics (insulators between plates) increase capacitance → more energy can be stored at the same voltage.

Electrochemical EMF (E°cell)

EMF of a cell; E°cell = E°cathode − E°anode; related to spontaneous redox reaction.

Gibbs equation for electrochemistry

ΔG = −n F E°cell; connects Gibbs energy change to cell potential.

Parallel circuits (voltage/current behavior)

Voltage is the same across all branches in parallel; currents add: I_total = I1 + I2 + …

Henderson–Hasselbalch equation

pH = pKa + log([A−]/[HA]); relates pH to ratio of conjugate base to weak acid.

pH vs pOH

pH = −log[H+];

pOH = −log[OH−]; in water at 25°C, pH + pOH = 14.

Acids and Bases: Ka and Kb

Ka is acid dissociation constant; Kb is base dissociation constant; larger value indicates stronger acid/base.

Osmotic Pressure

π = i M R T; i is van’t Hoff factor, M is molar concentration, R is gas constant, T is temperature.

Snell’s Law

n1 sin θ1 = n2 sin θ2; describes refraction of light between media.

Photon Energy

E = h f; energy of a photon with frequency f.

Thin Lens Equation

1/f = 1/do + 1/di (sign conventions apply); relates focal length, object distance, and image distance.

Magnification (m)

m = −di/do; ratio of image height to object height; negative indicates inversion.

Optical Power (P, diopters)

P = 1/f; measure of lens’ ability to bend light; units diopters.

Wave speed relation

v = f λ; speed of a wave equals frequency times wavelength.

Period (T)

Time for one complete cycle; T = 1/f.

SI base units (examples)

Newton (N) = kg·m/s^2; Joule (J) = N·m; Watt (W) = J/s; Coulomb (C) = A·s; Volt (V); Ohm (Ω); Farad (F); Siemens (S); Pascal (Pa).

freezing point depression

concept: more solutes lower freezing points (salt on icy road melts the ice)

BUT increased boiling point

Dilution Formula

Dilution Formula M1V1=M2V2M

• M1M_1M1​ = initial molarity

• V1V_1V1​ = initial volume

• M2M_2M2​ = final molarity

• V2V_2V2​ = final volume

Faraday's constant is: the charge of 1 mole of electrons:

• look out for problems in electrochemistry problems, electrolytic cells, electroplating, and physiology (Nernst equation).