Comprehensive Engineering Chemistry Study Guide: Stoichiometry, Measurements, and Atomic Theory

Line Calculations, Units of Measurement, and Formatting Rules

• Measurement Basics:

  • A measurement compares an unknown amount to a known standard (such as the SI system).

  • A number without a unit is incomplete and meaningless. Always write the unit next to the number.

  • Units are placed in square brackets when showing dimensions: $[v] = \text{m}\,\text{s}^{-1}$.

• Rules for Writing Units and Numbers:

  • Always put a space between the number and the unit (write $5.0\,\text{kg}$, not $5.0\text{kg}$).

  • Write numbers and units in normal upright text, but italicize math variables (e.g., $m = 5.0\,\text{kg}$, where $m$ is italicized).

  • Do not use more than one slash in a unit; write $9.8\,\text{m}\,\text{s}^{-2}$ instead of $9.8\,\text{m/s/s}$.

  • Percentages and angle degrees do not need a space ($10\%$, $30^\circ$), but temperature units do need a space ($25\,^\circ\text{C}$, $77\,^\circ\text{F}$).

  • Do not add an "s" to make units plural (write $10\,\text{kg}$, never $10\,\text{kgs}$).

  • The unit mole is always written as $\text{mol}$.

  • The Kelvin temperature scale does not use a degree circle ($300\,\text{K}$, never $300\,^\circ\text{K}$).

  • Always put a space or dot between unit symbols with negative powers. For example, write $9.8\,\text{m}\,\text{s}^{-2}$. If you skip the space and write $9.8\,\text{ms}^{-2}$, it reads as reciprocal milliseconds, which changes the value by a factor of one million.

• Common Metric Prefixes:

  • Nano- ($\text{n}$): $10^{-9}$

  • Micro- ($\mu$): $10^{-6}$

  • Milli- ($\text{m}$): $10^{-3}$

  • Centi- ($\text{c}$): $10^{-2}$

  • Kilo- ($\text{k}$): $10^{3}$

  • Mega- ($\text{M}$): $10^{6}$

• Converting Units (The Factor-Label Method):

  • Step 1: Find the conversion relationship (e.g., $1\,\text{ft} = 12\,\text{in}$, $1\,\text{m} = 100\,\text{cm}$).

  • Step 2: Build a fraction equal to 1 where the unit you want to eliminate is on the opposite side (top or bottom).

  • Step 3: Multiply the values so the unwanted units cancel out, leaving only the desired unit.

Temperature Scales and Conversions

• Formulas for Reading a Specific Temperature:

  • Fahrenheit from Celsius: $T(^\circ\text{F}) = 1.8 \times T(^\circ\text{C}) + 32$

  • Celsius from Fahrenheit: $T(^\circ\text{C}) = \frac{T(^\circ\text{F}) - 32}{1.8}$

  • Kelvin from Celsius: $T(\text{K}) = T(^\circ\text{C}) + 273.15$

  • Rankine from Fahrenheit: $T(^\circ\text{R}) = T(^\circ\text{F}) + 459.67$

• Difference Between Temperature Readings and Temperature Changes:

  • Reading a single point on a thermometer requires using the full formula with the offset number (like adding 32).

  • Measuring a change in temperature ($\Delta T$) only compares the size of the degree steps:

  • A change of $1\,^\circ\text{C}$ equals a change of $1.8\,^\circ\text{F}$.

  • A change of $1\,\text{K}$ equals a change of $1\,^\circ\text{C}$.

Significant Figures (Sig Figs)

• What Are Significant Figures?:

  • They represent all the digits you are sure about in a measurement, plus one last digit that is an estimate.

• Simple Rules for Counting Sig Figs:

  • Any number that is not zero counts ($42$ has 2 sig figs; $3.14$ has 3 sig figs).

  • Zeros at the beginning never count; they are just place holders ($0.0052$ has 2 sig figs).

  • Zeros between non-zero numbers always count ($405$ has 3 sig figs).

  • Zeros at the end only count if there is a written decimal point ($4.00$ has 3 sig figs; $400$ without a decimal is ambiguous and technically counts as 1 sig fig).

• Calculation Rules:

  • Adding and Subtracting: Round the final answer so it matches the least number of decimal places from the starting values.

  • Multiplying and Dividing: Round the final answer so it matches the starting number that has the fewest total sig figs.

  • Intermediate Steps: Keep all numbers in your calculator until the very end to avoid rounding errors.

Types of Matter and Separation Methods

• How Matter is Grouped:

  • Mixtures: Two or more substances combined physically that can be separated without breaking chemical bonds.

  • Homogeneous (Solutions): Blended evenly throughout so you cannot see separate parts (e.g., salt dissolved in water, clean air).

  • Heterogeneous: Not blended evenly; you can see different regions or phases (e.g., oil mixed with water, sand in water).

  • Pure Substances: Have a fixed chemical identity and cannot be separated physically.

  • Elements: Made of only one type of atom (e.g., $\text{Fe}$, $\text{O}_2$, $\text{He}$).

  • Compounds: Made of two or more different elements chemically bonded together (e.g., $\text{H}_2\text{O}$, $\text{NaCl}$).

• Common Separation Methods:

  • Distillation: Separating liquids by boiling them at different boiling points.

  • Filtration: Passing a mixture through a barrier to catch solid particles while liquid passes through.

  • Centrifugation: Spinning a mixture rapidly so denser parts sink to the bottom (e.g., separating blood cells from plasma).

  • Chromatography: Separating substances based on how quickly they move across a stationary surface.

Inside the Atom

• Subatomic Parts:

  • Protons: Positively charged particles in the nucleus; mass is about $1\,\text{u}$.

  • Neutrons: Neutral particles (no charge) in the nucleus; mass is about $1\,\text{u}$.

  • Electrons: Very tiny, negatively charged particles in a cloud orbiting the nucleus; mass is nearly zero ($\approx 0.00055\,\text{u}$).

  • In a neutral atom, the number of protons equals the number of electrons.

• Key Terms:

  • Atomic Number ($Z$): The number of protons. This defines which element the atom is.

  • Mass Number ($A$): The total number of protons plus neutrons ($A = Z + N$).

  • Isotopes: Atoms of the same element that have the same number of protons but different numbers of neutrons.

Chemical Bonds and Formulas

• Why Atoms Bond:

  • Atoms want a full outer shell of electrons (usually 8 electrons, called the Octet Rule) to become stable.

  • Bond formation releases energy (exothermic); breaking bonds requires energy (endothermic).

• Types of Chemical Bonds:

  • Nonpolar Covalent Bond: Two non-metals share electrons equally.

  • Polar Covalent Bond: Two non-metals share electrons unequally, creating slight positive and negative ends.

  • Ionic Bond: A metal transfers one or more electrons to a non-metal, creating charged ions that attract each other.

  • Metallic Bond: Metal atoms share a free-flowing sea of loose electrons, allowing electricity and heat to pass easily.

• Formulas:

  • Empirical Formula: The simplest, lowest whole-number ratio of atoms in a molecule (e.g., $\text{CH}_2\text{O}$).

  • Molecular Formula: The real, exact count of every atom in the molecule (e.g., $\text{C}_6\text{H}_{12}\text{O}_6$).

Chemical Equations and Reactions

• Balancing Equations:

  • Atoms are neither created nor destroyed during chemical reactions (Law of Conservation of Mass).

  • Change the large numbers in front of the molecules (coefficients) to make sure the count of each atom on the left matches the right.

• Reaction Types:

  • Sequential Reactions: Step-by-step reactions where the product of one step becomes the starting ingredient for the next step.

  • Parallel Reactions: Independent reactions taking place at the same time. Never merge parallel reactions into a single combined equation.

The Mole and Counting Atoms

• What is a Mole?:

  • A mole is a chemist's counting group, just like a "dozen" means 12 items.

  • One mole contains $6.022 \times 10^{23}$ items (Avogadro's number).

  • Molar Mass ($M$): The mass in grams of one mole of a substance ($\text{g}\,\text{mol}^{-1}$). You find this by adding up the atomic masses from the periodic table.

• Core Mole Conversions:

  • Converting mass to moles:     $n = \frac{m}{M}$

  • Converting moles to number of particles:     $\text{Number of particles} = n \times N_A$

Solutions and Concentration

• Parts of a Solution:

  • Solvent: The main liquid that does the dissolving (usually water in aqueous solutions).

  • Solute: The substance that gets dissolved (present in smaller amounts).

• Ways to Measure Concentration:

  • Molarity ($M$): Moles of solute divided by total solution volume in cubic decimeters:     $M = \frac{n_{\text{solute}}}{V_{\text{solution}}}$

  • Molality ($m$): Moles of solute divided by kilograms of solvent mass:     $m = \frac{n_{\text{solute}}}{m_{\text{solvent}}}$

  • Mass Percent ($\%\,\text{w/w}$):     $\%\,\text{mass} = \frac{m_{\text{solute}}}{m_{\text{solution}}} \times 100\%$

  • Parts Per Million ($\text{ppm}$): Useful for very small trace quantities (multiplying the mass fraction by $10^6$).

Yields, Limiting Reactants, and Atom Economy

• Limiting vs. Excess Reactants:

  • Limiting Reactant: The reactant that gets used up first. It stops the reaction and limits how much product can form.

  • Excess Reactant: The ingredient that is left over when the limiting reactant runs out.

• Reaction Yields:

  • Theoretical Yield: The maximum amount of product predicted by stoichiometric calculations if everything works perfectly.

  • Actual Yield: The real amount of product measured in the lab after the experiment.

  • Percentage Yield:     $\text{Percentage Yield} = \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100\%$

• Atom Economy (Green Chemistry):

  • Measures how efficiently starting atoms end up in the desired product rather than waste:     $\text{Atom Economy} = \frac{\text{Mass of Desired Product}}{\text{Total Mass of All Reactants}} \times 100\%$

  • A higher percentage means less chemical waste.