Atomic structure, periodic trends, chemical bonding, stoichiometry, thermochemistry, equilibrium, acid-base chemistry, electrochemistry, and organic chemistry basics.
Core principles governing the composition, structure, and transformations of matter.
Quantum numbers \((n, l, m_l, m_s)\) define electron states. Electron configuration follows Aufbau principle, Hund's rule, and Pauli exclusion. Example: Fe → [Ar] 3d&sup6; 4s².
Atomic radius: decreases across, increases down.
Ionization energy: increases across, decreases down.
Electronegativity: increases toward F (top-right).
Ionic: electron transfer (NaCl).
Covalent: electron sharing (\(\text{H}_2\text{O}\)).
Metallic: electron sea model.
VSEPR predicts molecular geometry.
Mole concept: \(1\;\text{mol} = 6.022 \times 10^{23}\) entities.
Balance equations, identify limiting reagents.
Percent yield: \(\frac{\text{actual}}{\text{theoretical}} \times 100\%\)
Enthalpy: \(\Delta H = q_p\) (heat at const. pressure)
Hess's law: \(\Delta H\) is path-independent.
$$\Delta H^\circ_{\text{rxn}} = \sum \Delta H^\circ_f(\text{products}) - \sum \Delta H^\circ_f(\text{reactants})$$
Law of mass action: \(K = \frac{[\text{products}]}{[\text{reactants}]}\)
Le Châtelier's principle: system opposes changes.
$$\Delta G^\circ = -RT \ln K$$
Brønsted-Lowry: proton donors/acceptors.
\(\text{pH} = -\log[\text{H}^+]\) \(\text{pOH} = -\log[\text{OH}^-]\)
\(K_w = [\text{H}^+][\text{OH}^-] = 10^{-14}\) at 25°C.
Buffer: $$\text{pH} = \text{p}K_a + \log\!\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)$$
Standard cell potential: \(E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}\)
Nernst equation: $$E = E^\circ - \frac{RT}{nF}\ln Q$$
\(\Delta G^\circ = -nFE^\circ\)
Hydrocarbons: alkanes, alkenes, alkynes.
Functional groups: −OH, −COOH, −NH\(_2\), C=O.
Isomers: structural, geometric, optical (chirality).
12 problems covering the full breadth of essential chemistry.
Write the full electron configuration and orbital diagram for Cr (\(Z = 24\)) and Cu (\(Z = 29\)). Explain why their configurations are exceptions to the Aufbau principle. Which has a higher third ionization energy, and why?
Rank the following in order of increasing atomic radius: Na, Mg, Al, Si. Then rank in order of increasing first ionization energy. Explain any anomalies. Why does the first ionization energy of O dip below that of N?
Draw the Lewis structure, predict the molecular geometry (VSEPR), bond angles, and polarity for: (a) \(\text{XeF}_4\) (b) \(\text{IF}_5\) (c) \(\text{SF}_6\). How many lone pairs are on the central atom in each case? Which are polar molecules?
Iron(III) oxide reacts with carbon monoxide: \(\text{Fe}_2\text{O}_3 + 3\text{CO} \rightarrow 2\text{Fe} + 3\text{CO}_2\). If you start with 150 g of \(\text{Fe}_2\text{O}_3\) and 80 g of CO: (a) Identify the limiting reagent. (b) Calculate the mass of iron produced. (c) If only 78 g of iron is obtained, what is the percent yield?
Using standard enthalpies of formation, calculate \(\Delta H^\circ\) for the combustion of ethanol: \(\text{C}_2\text{H}_5\text{OH(l)} + 3\text{O}_2\text{(g)} \rightarrow 2\text{CO}_2\text{(g)} + 3\text{H}_2\text{O(l)}\). Given: \(\Delta H^\circ_f [\text{C}_2\text{H}_5\text{OH(l)}] = -277.7\;\text{kJ/mol}\), \(\Delta H^\circ_f [\text{CO}_2\text{(g)}] = -393.5\;\text{kJ/mol}\), \(\Delta H^\circ_f [\text{H}_2\text{O(l)}] = -285.8\;\text{kJ/mol}\). How much heat is released per gram of ethanol?
For the reaction \(\text{N}_2\text{O}_4\text{(g)} \rightleftharpoons 2\text{NO}_2\text{(g)}\), \(K_p = 0.148\) at 25°C. Starting with 1.00 atm of pure \(\text{N}_2\text{O}_4\): (a) Set up an ICE table and calculate the equilibrium partial pressures. (b) Calculate \(\Delta G^\circ\) for this reaction. (c) If the temperature is raised, the equilibrium shifts right. Is the forward reaction endothermic or exothermic?
Calculate the pH of: (a) 0.1 M acetic acid (\(K_a = 1.8 \times 10^{-5}\)), (b) a buffer made from 0.1 M acetic acid and 0.15 M sodium acetate, (c) the buffer in (b) after adding 0.01 mol of HCl to 1 L of solution. Why is the pH change small?
A galvanic cell is constructed with Zn|Zn\(^{2+}\)(0.10 M) and Cu|Cu\(^{2+}\)(1.0 M). Given: \(E^\circ(\text{Zn}^{2+}/\text{Zn}) = -0.76\;\text{V}\), \(E^\circ(\text{Cu}^{2+}/\text{Cu}) = +0.34\;\text{V}\). (a) Identify the anode and cathode. (b) Calculate \(E^\circ_{\text{cell}}\). (c) Use the Nernst equation to find the cell potential under the given conditions. (d) Calculate \(\Delta G\) for the cell reaction.
Identify the functional groups present in aspirin (acetylsalicylic acid: \(\text{C}_9\text{H}_8\text{O}_4\)). Draw its structural formula. If aspirin hydrolyzes in water, what two products are formed? What type of reaction is this?
Explain why the boiling point order is: \(\text{CH}_4\) (\(-161\)°C) < \(\text{CH}_3\text{OH}\) (65°C) < \(\text{H}_2\text{O}\) (100°C) < \(\text{C}_2\text{H}_5\text{OH}\) (78°C). Wait — ethanol has a higher molar mass than water but a lower boiling point. Explain using intermolecular force analysis. How many hydrogen bonds can each molecule form?
The solubility product of AgCl is \(K_{sp} = 1.77 \times 10^{-10}\). (a) Calculate the molar solubility of AgCl in pure water. (b) Calculate the molar solubility in 0.1 M NaCl solution (common ion effect). (c) By what factor does the solubility decrease? (d) What happens if you add \(\text{NH}_3\text{(aq)}\) to the saturated AgCl solution?
Thought Experiment: Consider the thermite reaction: \(2\text{Al(s)} + \text{Fe}_2\text{O}_3\text{(s)} \rightarrow 2\text{Fe(l)} + \text{Al}_2\text{O}_3\text{(s)}\). This reaction is so exothermic (\(\Delta H \approx -852\;\text{kJ/mol}\)) that it produces molten iron. (a) Calculate the adiabatic flame temperature assuming \(C_p(\text{Al}_2\text{O}_3) \approx 79\;\text{J/(mol}\!\cdot\!\text{K)}\) and \(C_p(\text{Fe}) \approx 25\;\text{J/(mol}\!\cdot\!\text{K)}\). (b) Why does aluminum reduce iron oxide but not the reverse? Relate to the activity series and \(\Delta G\). (c) This reaction is used to weld railroad tracks. Why is it hard to ignite despite being thermodynamically favorable?