MCAT High-Yield Reference Sheets

The equations, constants, and facts worth memorizing cold — organized by section. Use these for quick review and to build flashcards.

⚗️ MCAT Chem/Phys Equations & Constants

Kinematics & Mechanics

v = v_0 + at
x = x_0 + v_0 t + \tfrac{1}{2}at^2
v^2 = v_0^2 + 2a\,\Delta x
a_c = \dfrac{v^2}{r} (centripetal acceleration)
Projectile: horizontal a_x = 0, vertical a_y = -g
Range maximized at launch angle 45^\circ

Newton's Laws & Forces

F_{net} = ma (Newton's 2nd law)
F_g = mg (weight)
F_g = \dfrac{G m_1 m_2}{r^2} (universal gravitation)
f_s \le \mu_s N ; f_k = \mu_k N (friction)
F_{spring} = -kx (Hooke's law)
Newton's 3rd law: equal and opposite reaction forces

Work, Energy & Power

W = Fd\cos\theta
KE = \tfrac{1}{2}mv^2
PE_g = mgh ; PE_{spring} = \tfrac{1}{2}kx^2
W_{net} = \Delta KE (work–energy theorem)
P = \dfrac{W}{t} = Fv (power)
p = mv ; J = F\,\Delta t = \Delta p (impulse)
Mechanical energy conserved if no nonconservative work

Fluids

\rho = \dfrac{m}{V} ; P = \dfrac{F}{A}
P = P_0 + \rho g h (gauge/hydrostatic pressure)
F_{buoy} = \rho_{fluid}\, V_{disp}\, g (Archimedes)
A_1 v_1 = A_2 v_2 (continuity)
P_1 + \tfrac{1}{2}\rho v_1^2 + \rho g y_1 = P_2 + \tfrac{1}{2}\rho v_2^2 + \rho g y_2 (Bernoulli)
Poiseuille: flow Q \propto r^4 (resistance dominated by radius)

Thermodynamics & Gases

Q = mc\,\Delta T ; Q = mL (phase change)
\Delta U = Q - W (first law)
\Delta G = \Delta H - T\Delta S
\Delta G < 0 spontaneous ; \Delta G > 0 nonspontaneous
\Delta G = -RT\ln K ; \Delta G = \Delta G^\circ + RT\ln Q
PV = nRT (ideal gas)
Combined: \dfrac{P_1 V_1}{T_1} = \dfrac{P_2 V_2}{T_2}

Electrostatics & Circuits

F = \dfrac{k q_1 q_2}{r^2} (Coulomb's law)
E = \dfrac{F}{q} = \dfrac{kQ}{r^2} ; V = \dfrac{kQ}{r}
V = IR (Ohm's law)
P = IV = I^2 R = \dfrac{V^2}{R}
Series: R_{eq} = R_1 + R_2 + \cdots
Parallel: \dfrac{1}{R_{eq}} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \cdots
C = \dfrac{Q}{V} ; U_C = \tfrac{1}{2}CV^2

Waves & Sound

v = f\lambda ; f = \dfrac{1}{T}
\beta = 10\log\dfrac{I}{I_0} (sound level, dB)
Doppler: f' = f\dfrac{v \pm v_{obs}}{v \mp v_{src}}
Open pipe: f_n = \dfrac{nv}{2L} (n = 1,2,3,\dots)
Closed pipe: f_n = \dfrac{nv}{4L} (n = 1,3,5,\dots)
Intensity I \propto \dfrac{1}{r^2} (point source)

Optics

n_1\sin\theta_1 = n_2\sin\theta_2 (Snell's law)
n = \dfrac{c}{v} (index of refraction)
\dfrac{1}{f} = \dfrac{1}{d_o} + \dfrac{1}{d_i} (thin lens/mirror)
m = -\dfrac{d_i}{d_o} = \dfrac{h_i}{h_o} (magnification)
P = \dfrac{1}{f} (lens power, diopters; f in m)
\sin\theta_c = \dfrac{n_2}{n_1} (total internal reflection)

Acids, Bases & Equilibrium

pH = -\log[H^+] ; pOH = -\log[OH^-]
pH + pOH = 14 (at 25^\circC)
K_a K_b = K_w = 1.0\times10^{-14}
pK_a + pK_b = 14
Henderson–Hasselbalch: pH = pK_a + \log\dfrac{[A^-]}{[HA]}
Buffer optimal when pH \approx pK_a (equal HA and A^-)

Electrochemistry

\Delta G = -nFE ; \Delta G^\circ = -nFE^\circ
Nernst: E = E^\circ - \dfrac{RT}{nF}\ln Q
At 25^\circC: E = E^\circ - \dfrac{0.0592}{n}\log Q
E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode}
Spontaneous (galvanic) cell: E^\circ_{cell} > 0
Oxidation at anode, reduction at cathode (OIL RIG)

Kinetics & Spectroscopy

Rate = k[A]^m[B]^n (order = m + n)
1st order: \ln[A] = \ln[A]_0 - kt ; t_{1/2} = \dfrac{\ln 2}{k}
Arrhenius: k = A\,e^{-E_a/RT}
Catalyst lowers E_a; does not change \Delta G or K
Beer–Lambert: A = \varepsilon b c (absorbance)

Key Constants

R = 8.314\ \text{J/(mol}\cdot\text{K)} = 0.0821\ \text{L}\cdot\text{atm/(mol}\cdot\text{K)}
F = 96{,}485\ \text{C/mol} (Faraday constant)
g = 9.8\ \text{m/s}^2
c = 3.00\times10^8\ \text{m/s}
N_A = 6.022\times10^{23}\ \text{mol}^{-1}
K_w = 1.0\times10^{-14} (at 25^\circC)
k = 8.99\times10^9\ \text{N}\cdot\text{m}^2/\text{C}^2