Worked Examples
Learn by watching a problem solved properly — every step shown and checked.
Easy
Balancing the Combustion of Methane
Walk through balancing the methane combustion equation and prove it is balanced by counting atoms on each side…
Boyle's Law in a Syringe
Use Boyle's law to find the compressed volume of gas in a syringe when the pressure rises from 1.00 atm to 2.5…
Preparing a Dilute Solution from Stock
Use the dilution equation M1V1 = M2V2 to find how much 1.00 M stock is needed to make 250.0 mL of 0.100 M solu…
Identifying the Hydroxyl Group in Ethanol
Identify the functional group in CH3CH2OH, name the compound, and classify it.…
Carbon-14 Dating of an Ancient Sample
A sample holds one-eighth of its original carbon-14; count the half-lives to find the age of the artifact.…
Predicting Ion Charges: Ca and Cl
Predict the ion charges of calcium and chlorine from their positions and noble-gas configurations.…
Le Chatelier Shifts in Ammonia Synthesis
Predict the direction of equilibrium shift for the ammonia synthesis reaction under four common stresses.…
Calculating the Molar Mass of Carbon Dioxide
Build the molar mass of CO2 from standard atomic weights by adding one carbon atom and two oxygen atoms.…
Molarity of a Salt Solution
Convert 5.84 g of NaCl to moles with the molar mass, then divide by the solution volume to get molarity.…
How Many Molecules Are in 36.0 g of Water?
Convert a measured mass of water to moles, then to an actual molecule count using molar mass and Avogadro's nu…
Naming Butane and Its Branched Isomer
Name the straight-chain alkane CH3CH2CH2CH3 and its branched isomer (CH3)2CHCH3 using IUPAC rules.…
Percent Composition of Water
Compute the mass percent of hydrogen and oxygen in H2O from atomic weights and confirm the percentages sum to …
pH of a Strong Acid Solution
A straightforward strong-acid pH calculation: 0.010 M HCl dissociates completely, so [H+] equals the acid conc…
Is the H-F Bond Polar?
Compute the electronegativity difference in HF and classify the bond as polar covalent with the correct partia…
Counting Subatomic Particles in the 23Na+ Ion
Count protons, neutrons, and electrons in the 23Na+ ion using the atomic number, mass number, and charge.…
Oxidation States in the Zinc-Copper Redox Reaction
Assign oxidation states in the zinc-copper redox reaction and identify which species is oxidized, reduced, and…
Significant Figures in Lab Calculations
Apply the significant-figure rules for multiplication and addition to two typical lab calculations.…
Converting Mass Units with Dimensional Analysis
Convert 2.50 kg to grams and 5.00 lb to kilograms using dimensional analysis with explicit unit cancellation.…
Medium
pH of an Acetic Acid/Acetate Buffer
Apply the Henderson-Hasselbalch equation to a buffer with equal concentrations of acetic acid and acetate.…
Calorimetry: Heat Lost by Cooling Coffee
Calculate the heat released as 250.0 g of coffee cools from 90.0 to 60.0 degC using q = mc deltaT.…
Standard Cell Potential of the Daniell Cell
Build the Daniell cell Zn|Zn2+||Cu2+|Cu, identify anode and cathode, and compute the standard cell potential.…
Freezing Point of an Antifreeze Solution
Calculate the freezing point of a 2.00 molal ethylene glycol solution using the freezing point depression equa…
Gibbs Free Energy: Is This Reaction Spontaneous?
Decide spontaneity at 298 K for a reaction with delta H = -120 kJ and delta S = -0.200 kJ/K using delta G = de…
ICE Table: Equilibrium Concentrations of H2, I2, and HI
Set up an ICE table for H2 + I2 ⇌ 2HI and solve for the equilibrium concentrations using Kc = 50.2.…
Moles of Helium in a Balloon (Ideal Gas Law)
Find the moles and mass of helium in a 2.00 L balloon at 1.00 atm and 298 K using the ideal gas law.…
Structural Isomers of Butane
Draw and name every distinct structural isomer of C4H10, showing why there are exactly two.…
Average Atomic Mass of Chlorine from Isotope Data
Combine chlorine's two isotope masses and their natural abundances into a weighted average atomic mass.…
Molar Solubility of Silver Chloride from Ksp
Calculate the molar solubility of silver chloride from its Ksp, and convert to milligrams per liter.…
Lewis Structure of Water
Draw the Lewis structure of water: 8 valence electrons, two bonds, two lone pairs, bent geometry.…
Limiting Reactant: Sandwiches, Then Hydrogen and Oxygen
A sandwich analogy makes the limiting reactant intuitive, then the same logic is applied to hydrogen burning i…
Partial Pressures in an N2/O2 Mixture
Apply Dalton's law to a 0.60 mol N2 / 0.40 mol O2 mixture at 2.00 atm total pressure.…
pH of a Weak Acid Solution
Set up the Ka expression for 0.10 M acetic acid, solve for [H+] with the small-x approximation, and check it.…
Determining a Rate Law from Experimental Data
Use three initial-rate trials to find the order in each reactant, write the rate law, and solve for the rate c…
Stoichiometry of Iron Rusting: Fe to Fe2O3
From 11.2 g of iron reacting with oxygen, use the balanced equation and molar masses to find the mass of iron(…
Strong Acid–Strong Base Titration: HCl with NaOH
Titrate 25.00 mL of 0.100 M HCl with 0.100 M NaOH: find the equivalence volume, the pH partway through, and th…
Predicting Trends: Sodium vs Magnesium
Compare atomic radius and first ionization energy of Na and Mg using effective nuclear charge reasoning.…
VSEPR Shape of Methane
Apply VSEPR to methane: four bonding pairs, no lone pairs, giving a tetrahedral shape at 109.5 degrees.…
Hard
Temperature Needed to Double a Reaction Rate
Use the two-point Arrhenius equation to find the temperature needed to double a reaction rate when Ea is known…
Hydrogen from Water Electrolysis: Faraday's Law
Use Faraday's law to find the volume of hydrogen gas produced by electrolyzing water at 2.00 A for one hour.…
Electron Configuration of Iron (Fe, Z = 26)
Build iron's ground-state electron configuration subshell by subshell and condense it to noble-gas shorthand.…
Hess's Law: Enthalpy of Formation of Methane
Use standard enthalpies of formation to find the enthalpy change for the formation of methane.…