Essential Chemistry Formulas and Constants

General Chemistry Formulas and Constants

Constants

• Avogadro's number ($N_A$): $6.022 \times 10^{23}$
• Calorie (cal): $1 \text{ cal} = 4.184 \text{ J}$
• Atomic mass unit (amu): $1 \text{ amu} = 1.660539 \times 10^{-24} \text{ g}$
• Ideal Gas Constant (R): $0.0821 \frac{\text{L} \cdot \text{atm}}{\text{mol} \cdot \text{K}}$
• Kilogram (kg): $1 \text{ kg} = 2.205 \text{ lb}$
• Molar volume at STP: $22.4 \text{ L}$
• Inch (in.): $1 \text{ in.} = 2.54 \text{ cm (exactly)}$

Standard Temperature and Pressure (STP)

• Temperature: $0 \text{°C}$
• Pressure: $1 \text{ atm}$

Unit Conversions

• Volume: $1 \text{ mL} = 1 \text{ cm}^3$
• Pressure:
  • $1 \text{ atm} = 760 \text{ mmHg}$
  • $1 \text{ atm} = 14.7 \text{ psi}$
  • $1 \text{ atm} = 101325 \text{ Pa}$
  • $1 \text{ atm} = 760 \text{ torr}$

Temperature Conversions

• Fahrenheit to Celsius: $\text{°C} = (\text{°F} - 32) / 1.8$
• Celsius to Fahrenheit: $\text{°F} = 1.8(\text{°C}) + 32$
• Celsius to Kelvin: $\text{K} = \text{°C} + 273$

Gas Laws

• Combined Gas Law: $\frac{P<em>1V</em>1}{T<em>1} = \frac{P</em>2V<em>2}{T</em>2}$
  • Also frequently seen as: $\frac{P<em>1V</em>1}{n<em>1T</em>1} = \frac{P<em>2V</em>2}{n<em>2T</em>2}$ (When moles are considered)
• Charles's Law (Constant P, n): $\frac{V<em>1}{T</em>1} = \frac{V<em>2}{T</em>2}$
• Boyle's Law (Constant T, n): $P<em>1V</em>1 = P<em>2V</em>2$
• Ideal Gas Law: $PV = nRT$
• Dalton's Law of Partial Pressures:
  • Total pressure: $P<em>{\text{total}} = P</em>A + P<em>B + P</em>C + \dots$
  • Partial pressure of component A: $P<em>A = X</em>A P<em>{\text{total}}$ where $X</em>A$ is the mole fraction of A.
• Kinetic Energy of a particle: $KE = \frac{1}{2}mv^2$

Stoichiometry and Solutions

• Percent Yield: \text{% Yield} = \frac{\text{actual}}{\text{theoretical}} \times 100\%
• Percent by Mass of an Element:
  • \text{% by mass element} = \frac{\text{mass of element in compound}}{\text{total mass of compound}} \times 100\%
• Moles, Mass, and Molar Mass:
  • $\text{moles} = \frac{\text{mass (g)}}{\text{MM (g/mol)}}$
• Molarity (M):
  • $M = \frac{\text{moles}}{\text{L of solution}}$
• Dilution Equation: $M<em>1V</em>1 = M<em>2V</em>2$
• Percent Concentration (Mass/Volume):
  • \text{% concentration} = \frac{\text{mass of solute (grams)}}{\text{volume of solution (mL)}} \times 100\%
• Parts per Million (ppm):
  • $\text{ppm} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 10^6$
• Parts per Billion (ppb):
  • $\text{ppb} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 10^9$
• Percent Concentration (Volume/Volume):
  • \text{% concentration} = \frac{\text{volume of solute}}{\text{volume of solution}} \times 100\%

Acids and Bases

• pH: $\text{pH} = -\log [\text{H}^+]$
  • $[\text{H}^+] = 10^{-\text{pH}}$
• pOH: $\text{pOH} = -\log [\text{OH}^-]$
  • $[\text{OH}^-] = 10^{-\text{pOH}}$
• Relationship between pH and pOH: $14 = \text{pH} + \text{pOH}$
• Ion-product constant for water ($K_w$):
  • $K<em>w = [\text{H}</em>3\text{O}^+][\text{OH}^-] = 1 \times 10^{-14}$ (at $25 \text{°C}$)
• Equilibrium Constant ($K_{\text{eq}}$) for a reaction $aA + bB \rightleftharpoons cC + dD$
  • $K_{\text{eq}} = \frac{[C]^c[D]^d}{[A]^a[B]^b}$
• Acid Dissociation Constant ($K<em>a$) for weak acid $HA(aq) + H</em>2O(l) \rightleftharpoons H_3O^+(aq) + A^-(aq)$
  • $K<em>a = \frac{[H</em>3O^+][A^-]}{[HA]}$
• Normality (N):
  • $N = \frac{\text{Eq}}{\text{L}}$
• Equivalent (Eq) for acid or base:
  • 1 \text{ Eq (acid or base)} = \frac{\text{MM of acid or base (g)}}{\text{# of H or OH per formula unit}}