Formulas MCAT

--- FORMULAS ONLY ---

Density (ρ = m/V)

mass divided by volume

Molarity

moles per liter

Dilution

M1V1 = M2V2

Ideal Gas Law

PV = nRT

Combined Gas Law

(P1V1)/T1 = (P2V2)/T2

Dalton’s Law

total pressure is sum of partial pressures

Mole Fraction

moles of component divided by total moles

Rate Law

rate = k[A]^m[B]^n

Equilibrium Constant

products over reactants

Gibbs Free Energy

ΔG = ΔH − TΔS

ΔG and K

ΔG° = −RT lnK

Heat equation

q = mcΔT

Coulomb’s Law

F proportional to q1q2 over r^2

Velocity

distance over time

Acceleration

change in velocity over time

Kinematic equation

v^2 = v0^2 + 2aΔx

Force

F = ma

Work

force times distance

Kinetic Energy

½mv^2

Potential Energy

mgh

Power

work over time

Pressure

force over area

Hydrostatic Pressure

ρgh

Continuity Equation

A1v1 = A2v2

Bernoulli Principle

increase velocity decreases pressure

Ohm’s Law

V = IR

Electric Power

P = IV

Series Resistance

add resistances

Parallel Resistance

inverse sum

Wave Speed

v = fλ

Snell’s Law

n1sinθ1 = n2sinθ2

Lens Equation

1/f = 1/o + 1/i

Magnification

m = −i/o

Michaelis-Menten

velocity equals Vmax[S] over Km plus S

Enzyme Efficiency

kcat over Km

Weber’s Law

ΔI over I is constant

--- UNIT CONVERSIONS ---

Liters to cubic meters

1 L = 10^-3 m^3

Milliliters to liters

1 mL = 10^-3 L

Cubic centimeters to mL

1 cm^3 = 1 mL

Meters to centimeters

1 m = 100 cm

Kilograms to grams

1 kg = 1000 g

Hours to seconds

1 hr = 3600 s

Atmospheres

1 atm = 760 mmHg

Calories to joules

1 cal = 4.184 J

Electron charge

1.6 x 10^-19 C

Gas constant

0.0821 L atm per mol K

Avogadro number

6.022 x 10^23

Speed of light

3.0 x 10^8 m/s

Celsius to Kelvin

add 273

Density of water

1 g per mL

--- PRACTICE QUESTIONS ---

Density practice: A 24 g object occupies 6 mL. What is density?

4 g/mL

Molarity practice: 3 moles in 1.5 L. What is molarity?

2 M

Dilution practice: 1 L of 2 M diluted to 1 M. Final volume?

2 L

Ideal gas practice: 2 moles at STP. Volume?

44.8 L

Combined gas practice: temperature triples at constant pressure. Volume change?

triples

Dalton law practice: pressures 1, 2, 3 atm. Total?

6 atm

Mole fraction practice: 1 mol A, 4 mol B. X_A?

0.2

Rate law practice: rate = k[A]^2, A triples. Rate change?

9 times

Equilibrium practice: K = 0.01. Which side favored?

reactants

Gibbs practice: ΔH = −20, TΔS = −30. Spontaneous?

no

Heat practice: 5 g water, ΔT = 2 C. Heat?

about 42 J

Coulomb practice: distance triples. Force change?

1/9

Velocity practice: 150 m in 30 s. Speed?

5 m/s

Acceleration practice: 10 to 30 m/s in 5 s. Acceleration?

4 m/s^2

Kinematics practice: starts at rest, a = 4, x = 5. Final velocity?

about 6.3 m/s

Force practice: 5 kg at 2 m/s^2. Force?

10 N

Work practice: 20 N over 3 m. Work?

60 J

KE practice: 1 kg at 4 m/s. KE?

8 J

PE practice: 2 kg at 5 m. PE?

100 J

Power practice: 200 J in 20 s. Power?

10 W

Pressure practice: 50 N over 10 m^2. Pressure?

5 Pa

Hydrostatic practice: depth increases 4 times. Pressure?

4 times

Continuity practice: area becomes one third. Velocity?

3 times

Bernoulli practice: velocity increases. Pressure?

decreases

Ohm law practice: 12 V across 4 ohms. Current?

3 A

Power practice: 5 A and 10 V. Power?

50 W

Series practice: 3 ohm and 7 ohm. Total?

10 ohm

Parallel practice: two 4 ohm resistors. Total?

2 ohm

Wave practice: frequency 5 Hz, wavelength 2 m. Speed?

10 m/s

Snell practice: entering denser medium. Angle?

decreases

Lens practice: object beyond focal length. Image?

real inverted

Magnification practice: m = +1. Image?

upright same size