Measurements and Significant Figures

Measurements

• Physical properties are measurable without altering the substance's chemical identity; examples include color, density, and phase.
• Chemical properties describe a substance's potential to undergo changes to form new substances, for example, flammability and corrosiveness.
• Accuracy refers to how close a measurement is to the true or accepted value.
• Precision refers to how close a series of measurements are to each other.

Significant Figures Rules

• Non-zero digits are always significant; for instance, 3.1415 has five significant figures.
• Zeros located between non-zero digits are significant; 1.005 has four significant figures.
• Trailing zeros to the right of the decimal point are significant; 6.00 has three significant figures.
• Leading zeros are never significant; 0.0025 has two significant figures.
• Trailing zeros without a decimal are ambiguous; use scientific notation to clarify, as 130 could have 2 or 3.

Math with Sig Figs

• When multiplying or dividing, the result should have the same number of significant figures as the factor with the fewest significant figures
• When adding or subtracting, the answer should have the same number of decimal places as the number with the fewest decimal places

Unit conversions

• Employ conversion factors to change a quantity from one unit to another

• To convert 10.0 inches to centimeters:

  $10.0\ in \cdot \frac{2.54\ cm}{1\ in} = 25.4\ cm$

Temperature Conversion

• Celsius to Kelvin: K = °C + 273.15
• Celsius to Fahrenheit: $^\circ F = \frac{9}{5}(^\circ C) + 32$

Atoms, Molecules, and Ions

Atomic Structure

• Protons are positively charged and reside in the nucleus.
• Neutrons have no charge and are located in the nucleus.
• Electrons are negatively charged and orbit outside the nucleus.

Isotopes

• Isotopes are atoms of the same element with varying numbers of neutrons; examples include $^{12}_6C$, $^{13}_6C$, and $^{14}_6C$.

Average Atomic Mass Calculation

• Average atomic mass is calculated as the weighted average of the masses of an element's isotopes.
• The calculation formula is: $\text{Average Atomic Mass} = \sum (\text{isotope mass} \cdot \text{fractional abundance})$.

Naming Compounds

• For ionic compounds (metal + nonmetal): name the metal, then name the nonmetal with an "-ide" ending (e.g., NaCl is sodium chloride).
• For covalent compounds (nonmetal + nonmetal), utilize prefixes to denote the quantity of each element.

Prefixes for Naming Covalent Compounds

• Mono- prefix means 1.
• Di- prefix means 2.
• Tri- prefix means 3.
• Tetra- prefix means 4.
• Penta- prefix means 5.
• Hexa- prefix means 6.
• Name the first element using a prefix only if there is more than one atom.
• Name the second element with an "-ide" ending, always using a prefix; $N_2O_4$ is dinitrogen tetroxide.

Naming Acids

• Binary acids are named as hydro + nonmetal + -ic acid; HCl is hydrochloric acid.
• Oxyacids: If the polyatomic ion ends in "-ate", change to "-ic acid" (e.g., $H_2SO_4$ is sulfuric acid).
• If the polyatomic ion ends in "-ite", change to "-ous acid" (e.g., $H_2SO_3$ is sulfurous acid).

Reactions

Balancing Chemical Equations

• Step 1: Write the unbalanced equation showing reactants and products.
• Step 2: Balance elements appearing in only one reactant and one product first.
• Step 3: Treat polyatomic ions as single units when balancing.
• Step 4: Balance the remaining elements, typically hydrogen and oxygen, last.
• Step 5: Check to ensure the equation is balanced.

Stoichiometry

• Stoichiometry involves using balanced equations to determine the quantities of reactants and products in a chemical reaction.

• For example, to calculate the grams of $O_2$ needed to react with 10.0 g of $CH_4$ in the reaction $CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O$:

  $10.0\ g\ CH_4 \cdot \frac{1\ mol\ CH_4}{16.04\ g\ CH_4} \cdot \frac{2\ mol\ O_2}{1\ mol\ CH_4} \cdot \frac{32.00\ g\ O_2}{1\ mol\ O_2} = 39.9\ g\ O_2$

Limiting Reactant

• The limiting reactant is the one that is completely consumed during a reaction, determining the maximum amount of product formed.
• To identify the limiting reactant: calculate the moles of each reactant, divide each by its stoichiometric coefficient, and the reactant with the smallest result is limiting.

Percent Yield

• Percent yield measures the efficiency of a reaction, comparing actual yield to theoretical yield.

  $\text{Percent Yield} = \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \cdot 100%$