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Chemistry Essentials

Atomic structure, periodic trends, chemical bonding, stoichiometry, thermochemistry, equilibrium, acid-base chemistry, electrochemistry, and organic chemistry basics.

Key Concepts & Laws

Core principles governing the composition, structure, and transformations of matter.

Atomic Structure

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.

Periodic Trends

Atomic radius: decreases across, increases down.
Ionization energy: increases across, decreases down.
Electronegativity: increases toward F (top-right).

Chemical Bonding

Ionic: electron transfer (NaCl).
Covalent: electron sharing (\(\text{H}_2\text{O}\)).
Metallic: electron sea model.
VSEPR predicts molecular geometry.

Stoichiometry

Mole concept: \(1\;\text{mol} = 6.022 \times 10^{23}\) entities.
Balance equations, identify limiting reagents.
Percent yield: \(\frac{\text{actual}}{\text{theoretical}} \times 100\%\)

Thermochemistry

Enthalpy: \(\Delta H = q_p\) (heat at const. pressure)
Hess's law: \(\Delta H\) is path-independent.
$$\Delta H^\circ_{\text{rxn}} = \sum \Delta H^\circ_f(\text{products}) - \sum \Delta H^\circ_f(\text{reactants})$$

Chemical Equilibrium

Law of mass action: \(K = \frac{[\text{products}]}{[\text{reactants}]}\)
Le Châtelier's principle: system opposes changes.
$$\Delta G^\circ = -RT \ln K$$

Acid-Base Chemistry

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: $$\text{pH} = \text{p}K_a + \log\!\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)$$

Electrochemistry

Standard cell potential: \(E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}\)
Nernst equation: $$E = E^\circ - \frac{RT}{nF}\ln Q$$ \(\Delta G^\circ = -nFE^\circ\)

Organic Chemistry Basics

Hydrocarbons: alkanes, alkenes, alkynes.
Functional groups: −OH, −COOH, −NH\(_2\), C=O.
Isomers: structural, geometric, optical (chirality).

Problems

12 problems covering the full breadth of essential chemistry.

1
Easy

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?

Show Hint
Cr is [Ar] 3d\(^5\) 4s\(^1\) (not 3d\(^4\) 4s\(^2\)) — half-filled d subshell stability. Cu is [Ar] 3d\(^{10}\) 4s\(^1\) — fully-filled d subshell stability. Consider which electron is removed third for each element.
2
Easy

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?

Show Hint
Across a period: radius decreases, IE increases. The O anomaly: O has a paired electron in one 2p orbital, making it easier to remove (electron-electron repulsion) compared to N's half-filled 2p\(^3\).
3
Medium

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?

Show Hint
Count valence electrons. \(\text{XeF}_4\): 36 e\(^-\), square planar (2 lone pairs), nonpolar. \(\text{IF}_5\): 42 e\(^-\), square pyramidal (1 lone pair), polar. \(\text{SF}_6\): 48 e\(^-\), octahedral (0 lone pairs), nonpolar.
4
Medium

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?

Show Hint
Molar masses: \(\text{Fe}_2\text{O}_3 = 159.7\;\text{g/mol}\), \(\text{CO} = 28.01\;\text{g/mol}\), \(\text{Fe} = 55.85\;\text{g/mol}\). Convert to moles, use stoichiometric ratios to find the limiting reagent (the one that runs out first).
5
Hard

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?

Show Hint
\(\Delta H^\circ = \sum \Delta H^\circ_f(\text{products}) - \sum \Delta H^\circ_f(\text{reactants})\). Remember \(\text{O}_2\) has \(\Delta H^\circ_f = 0\). Molar mass of ethanol = 46.07 g/mol. Divide the molar enthalpy by molar mass for per-gram value.
6
Hard

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?

Show Hint
Let \(x\) = pressure of \(\text{N}_2\text{O}_4\) that dissociates. \(K_p = \frac{(2x)^2}{1 - x} = \frac{4x^2}{1 - x}\). Solve the quadratic. \(\Delta G^\circ = -RT\ln K_p\). Le Châtelier: shifting right with heat means the forward reaction is endothermic (heat is a "reactant").
7
Medium

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?

Show Hint
(a) ICE table: \(K_a = \frac{x^2}{0.1 - x} \approx \frac{x^2}{0.1}\). (b) Henderson-Hasselbalch: \(\text{pH} = \text{p}K_a + \log\!\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)\). (c) HCl converts acetate to acetic acid: recalculate concentrations and re-apply H-H.
8
Hard

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.

Show Hint
Zn is oxidized (anode), Cu\(^{2+}\) is reduced (cathode). \(E^\circ_{\text{cell}} = 0.34 - (-0.76) = 1.10\;\text{V}\). Nernst: \(E = E^\circ - \frac{0.0257}{n}\ln Q\) with \(n = 2\) and \(Q = [\text{Zn}^{2+}]/[\text{Cu}^{2+}]\). \(\Delta G = -nFE\).
9
Easy

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?

Show Hint
Aspirin contains a carboxylic acid group (−COOH) and an ester group (−OCOCH\(_3\)). Hydrolysis of the ester produces salicylic acid and acetic acid. This is an ester hydrolysis (reverse of Fischer esterification).
10
Advanced

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?

Show Hint
\(\text{CH}_4\): London dispersion only (weak). Alcohols and water: hydrogen bonding. Water can form up to 4 H-bonds per molecule (2 donors, 2 acceptors) vs. ethanol's 2-3. Water's extensive H-bond network compensates for its lower molar mass.
11
Hard

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?

Show Hint
(a) \(K_{sp} = s^2\), so \(s = \sqrt{K_{sp}}\). (b) \(K_{sp} = s(0.1 + s) \approx 0.1s\). \(\text{NH}_3\) forms the complex ion \([\text{Ag}(\text{NH}_3)_2]^+\), removing \(\text{Ag}^+\) from solution and shifting equilibrium to dissolve more AgCl.
12
Advanced

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?

Show Hint
Adiabatic: all heat goes to raising product temperature. \(Q = [n(\text{Al}_2\text{O}_3)\,C_p + n(\text{Fe})\,C_p]\,\Delta T\). Al is more reactive (more negative \(\Delta G^\circ_f\) for \(\text{Al}_2\text{O}_3\) vs \(\text{Fe}_2\text{O}_3\)). High activation energy barrier means kinetically stable despite being thermodynamically unstable. This is why a burning magnesium strip is needed to ignite it.