Mole Concept Cheatsheet

Cheatsheet Content

### The Mole: Definition - **Definition:** A unit of measurement for amount of substance. - Represents a specific number of particles (atoms, molecules, ions, electrons, etc.). - **Avogadro's Number ($N_A$):** $6.022 \times 10^{23}$ particles/mol. - **Key Idea:** 1 mole of any substance contains Avogadro's number of particles. ### Molar Mass ($M$) - **Definition:** The mass of one mole of a substance. - **Units:** grams per mole (g/mol). - **For Elements:** Numerically equal to the atomic mass on the periodic table (e.g., C: 12.01 g/mol). - **For Compounds:** Sum of the atomic masses of all atoms in the chemical formula. - **Example:** Molar mass of $H_2O$: - H: $2 \times 1.008$ g/mol = $2.016$ g/mol - O: $1 \times 15.999$ g/mol = $15.999$ g/mol - Total: $2.016 + 15.999 = 18.015$ g/mol ### Mole Calculations #### 1. Moles from Mass - **Formula:** $n = \frac{m}{M}$ - $n$: moles (mol) - $m$: mass (g) - $M$: molar mass (g/mol) - **Example:** How many moles are in 20 g of $H_2O$? - $M(H_2O) = 18.015$ g/mol - $n = \frac{20 \text{ g}}{18.015 \text{ g/mol}} \approx 1.11 \text{ mol}$ #### 2. Moles from Number of Particles - **Formula:** $n = \frac{\text{Number of Particles}}{N_A}$ - **Example:** How many moles are $1.204 \times 10^{24}$ molecules of $CO_2$? - $n = \frac{1.204 \times 10^{24}}{6.022 \times 10^{23} \text{ molecules/mol}} \approx 2.00 \text{ mol}$ #### 3. Moles from Volume (for Gases at STP) - **STP (Standard Temperature and Pressure):** $0^\circ C$ ($273.15$ K) and 1 atm. - **Molar Volume at STP:** 1 mole of any ideal gas occupies 22.4 L. - **Formula:** $n = \frac{V}{22.4 \text{ L/mol}}$ - $V$: volume (L) - **Example:** How many moles are in 5.6 L of $O_2$ at STP? - $n = \frac{5.6 \text{ L}}{22.4 \text{ L/mol}} = 0.25 \text{ mol}$ #### 4. General Gas Law (Ideal Gas Law) - **Formula:** $PV = nRT$ - $P$: pressure (atm, Pa, kPa) - $V$: volume (L, $m^3$) - $n$: moles (mol) - $R$: ideal gas constant ($0.0821 \frac{\text{L} \cdot \text{atm}}{\text{mol} \cdot \text{K}}$ or $8.314 \frac{\text{J}}{\text{mol} \cdot \text{K}}$) - $T$: temperature (K) - **Use:** For gases not at STP. ### Percent Composition by Mass - **Definition:** The percentage by mass of each element in a compound. - **Formula:** $$ \text{% Element} = \frac{\text{mass of element in 1 mole of compound}}{\text{molar mass of compound}} \times 100\% $$ - **Example:** % H in $H_2O$: - Mass of H in 1 mol $H_2O = 2 \times 1.008 = 2.016$ g - Molar mass of $H_2O = 18.015$ g/mol - % H = $\frac{2.016 \text{ g}}{18.015 \text{ g}} \times 100\% \approx 11.19\%$ ### Empirical & Molecular Formulas #### Empirical Formula - **Definition:** The simplest whole-number ratio of atoms in a compound. - **Steps:** 1. Convert mass or % of each element to moles. 2. Divide all mole values by the smallest mole value. 3. If not whole numbers, multiply by a small integer to get whole numbers. #### Molecular Formula - **Definition:** The actual number of atoms of each element in a molecule. - **Relationship:** Molecular Formula = $(Empirical Formula)_n$ - **Steps:** 1. Determine the empirical formula. 2. Calculate the empirical formula mass (EFM). 3. Determine the molecular formula mass (MFM) (usually given). 4. Calculate $n = \frac{\text{MFM}}{\text{EFM}}$. 5. Multiply the subscripts in the empirical formula by $n$.