MCAT Physics and Chemistry High Yield Equations

Practice flashcards covering high-yield MCAT Physics and Chemistry equations encompassing Kinematics, Forces, Energy, Waves, Optics, Circuits, Fluids, Thermodynamics, Nuclear Decay, and Gas Laws.

What is the kinematic equation for velocity with constant acceleration?

$$v = v_0 + at$$

What is the kinematic equation for displacement including acceleration?

$$x = v_0 t + \frac{1}{2} at^2$$

What is the kinematic equation for displacement using average velocity?

$$x = \left(\frac{v + v_0}{2}\right) t$$

What is the kinematic 'no-time' equation for velocity?

$$v^2 = v_0^2 + 2a\Delta x$$

What is Newton's 2nd Law?

$$F = ma$$

What is the equation for Hooke's Law?

$$F = -kx$$

What is the formula for weight due to gravity and the standard value for acceleration due to gravity?

$F_g = mg$ where $g = 9.8\,m\,s^{-2}$

What is the formula for centripetal force?

$$F_c = \frac{mv^2}{r}$$

What is the formula for friction?

$$F = \mu N$$

What is Newton's Law of Universal Gravitation?

$$F = \frac{Gm_1m_2}{r^2}$$

What is the formula for work?

$$W = Fd \cos(\theta)$$

What is the formula for kinetic energy?

$$KE = \frac{1}{2} mv^2$$

What is the formula for gravitational potential energy?

$$PE = mgh$$

What is the formula for spring potential energy?

$$PE = \frac{1}{2} kx^2$$

What is the Work-Energy Theorem?

$$W_{net} = \Delta KE$$

What is the formula for momentum?

$$p = mv$$

What are the formulas for power in a mechanical system?

$$P = \frac{W}{t} = Fv$$

What is the formula for impulse?

$$J = F\Delta t = \Delta p$$

What is the relationship between wave speed, frequency, and wavelength?

$$v = f\lambda$$

What is the formula for sound intensity in decibels?

$$\beta = 10 \log_{10}\left(\frac{I}{I_0}\right)$$

What is the Doppler effect formula for an observed frequency?

$$f' = f \left(\frac{v \pm v_{obs}}{v \mp v_{src}}\right)$$

What is the relationship between frequency and period?

$$f = \frac{1}{T}$$

What is the formula for intensity?

$$I = \frac{P}{A}$$

What is Snell's Law for light refraction?

$$n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$$

What is the formula for the index of refraction?

$$n = \frac{c}{v}$$

What is the thin lens or mirror equation?

$$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$$

What is the formula for magnification in optics?

$$m = -\frac{d_i}{d_o}$$

What is the formula for photon energy and the value for the speed of light?

$E = hf = \frac{hc}{\lambda}$ where $c = 3 \times 10^8\,m\,s^{-1}$

What is Ohm's Law?

$$V = IR$$

What is the formula for electric power in a circuit?

$$P = IV = I^2 R$$

How are resistors calculated in series?

$$R_s = R_1 + R_2 + \dots$$

How are resistors calculated in parallel?

$$\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2}$$

What is Coulomb's Law?

$$F = \frac{kq_1q_2}{r^2}$$

What is the formula for Capacitor charge?

$$Q = CV$$

What is the formula for how capacitors add in series?

$$\frac{1}{C_s} = \frac{1}{C_1} + \frac{1}{C_2}$$

What is the formula for an electric field?

$$E = \frac{kq}{r^2} = \frac{F}{q}$$

What are the formulas for density and pressure?

$\rho = \frac{m}{V}$ and $P = \frac{F}{A}$

What is Archimedes' Principle for buoyancy?

$$F_b = \rho_f V g$$

What is Bernoulli's equation?

$$P + \frac{1}{2} \rho v^2 + \rho gh = \text{constant}$$

What is the formula for hydrostatic pressure?

$$P = P_0 + \rho gh$$

What is the continuity equation for fluids?

$$A_1 v_1 = A_2 v_2$$

What is Poiseuille's law for flow?

$$Q = \frac{\pi r^4 \Delta P}{8 \eta L}$$

What is the formula for heat transfer?

$$Q = mc\Delta T$$

What is the formula for latent heat during a phase change?

$$Q = mL$$

What is the 1st Law of Thermodynamics?

$$\Delta U = Q - W$$

What is the formula for work done by a gas?

$$W = P\Delta V$$

What is the formula for Carnot efficiency?

$$e = 1 - \frac{T_c}{T_h}$$

What is the general formula for engine efficiency?

$$e = \frac{W}{Q_H}$$

What is the mass-energy equivalence formula?

$$E = mc^2$$

What is the formula for the half-life of radioactive decay?

$$t_{1/2} = \frac{0.693}{\lambda}$$

What is the formula for radioactive decay?

N(t)=N₀(1/2)^t/t_1/2

N(t)= quantity remaining

N₀= initial quantity

t = time elapsed

t_1/2= half life of substance

What is the formula for radioactive activity?

$$A = \lambda N$$

What is the Ideal Gas Law and the value of R?

$PV = nRT$ where $R = 8.314\,J\,mol^{-1}\,K^{-1}$

What is Dalton's Law of partial pressures?

$$P_{total} = P_1 + P_2 + \dots$$

What is the root-mean-square speed of a gas molecule?

$$v_{rms} = \sqrt{\frac{3RT}{M}}$$

What is the combined gas law?

$$\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$$

What is the average kinetic energy of gas molecules?

$$KE_{avg} = \frac{3}{2} RT$$

What is the formula for Gibbs Free Energy change?

$$\Delta G = \Delta H - T\Delta S$$

What is the relationship between standard free energy and the equilibrium constant?

$$\Delta G^\circ = -RT \ln(K)$$

What is the formula for non-standard Gibbs Free Energy?

$$\Delta G = \Delta G^\circ + RT \ln(Q)$$

What is Hess's Law for calculating reaction enthalpy?

$$\Delta H^\circ_{rxn} = \sum \Delta H^\circ(P) - \sum \Delta H^\circ(R)$$

How is the equilibrium constant (Keq) expressed?

$$K_{eq} = \frac{[P]^n}{[R]^m}$$

What is the relationship between Kp and Kc?

$$K_p = K_c (RT)^{\Delta n}$$

What is the formula for the solubility product constant (Ksp)?

$$K_{sp} = [A]^a [B]^b$$

What determines the direction of a reaction when comparing Q to K?

The relationship between the reaction quotient (Q) and the equilibrium constant (K)

Rate Law

k[A]^x[B]^y

first order integrated rate law

ln[A]=-kt+ln[A]₀

first order half life

t_1/2+0.693/k

2nd order integrated rate law

1/[A] = kt + 1/[A]₀

Spectroscopy Beer-Lambert law

A = εcl

Spectroscopy absorbance

A = log(l₀/l)