AP Unit 1 Problems

A sample contains 0.125 mol Al₂O₃. Use M = 101.96 g mol⁻¹, N_A = 6.022 × 10²³ mol⁻¹ and 1 u ≈ 1.66054 × 10⁻²⁴ g.

1. Determine the sample mass and number of oxygen atoms. Explain why the oxygen counting factor is 3.
2. State the average mass represented by one Al₂O₃ formula unit in u, and the mass of one mole of formula units in g. Show how the supplied u-to-gram factor and Avogadro’s constant connect these quantities. Evaluate the claim “101.96 u and 101.96 g mol⁻¹ are the same units.”

Equal-mass samples of Ne (20.18 g mol⁻¹) and Ar (39.95 g mol⁻¹) are compared. Without choosing a sample mass, find the ratio N_Ne/N_Ar and justify it.

An element has only two isotopes in the sample: 10.0 u and 11.0 u. Its measured average mass is 10.80 u. Determine both relative abundances and describe which spectrum peak should be taller.

A singly charged elemental spectrum has peaks at 24, 25 and 26 u with counts 79, 10 and 11, respectively. A student claims that 25 u is the average because it is the central peak. Evaluate the claim and calculate the weighted average using these mass estimates.

A pure compound contains 40.0% C, 6.71% H and 53.3% O by mass. Use 12.01, 1.008 and 16.00 g mol⁻¹. Find its empirical formula and explain why percentages can be treated as gram masses here.

Two samples contain 0.500 g Mg with 0.329 g O, and 1.00 g Mg with 0.658 g O. A student says this proves both are pure MgO. State what the data support and propose a testable follow-up question.

A 10.00 g mixture contains only NaCl and KCl. Their chlorine mass fractions are 0.6066 and 0.4755. Analysis finds 5.542 g Cl. Determine the mass of each salt.

A 5.00 g sample labeled “pure compound X” contains less oxygen by mass than the formula of X predicts. A student reports an exact purity from this datum alone. Evaluate the conclusion and specify one assumption that would make a purity calculation possible.

Use phosphorus-31, with atomic number Z = 15 and mass number 31.

1. Give the full ground-state configurations for P and P³⁻. Create labeled orbital-box diagrams showing occupancy and spin in the three 3p orbitals for each species. Use one box per orbital and arrows for individual electrons.
2. Make a table for a proton, neutron and electron: give each particle’s charge in elementary-charge units (+1, 0 or −1) and location in the atomic model. Then give the proton, neutron and electron counts of ³¹P³⁻ and use them to verify its net charge. Explain which counts change when neutral ³¹P gains three electrons.

For a simplified pair of opposite charges, the nucleus charge magnitude doubles and separation also doubles. Find the ratio F_new/F_old. Then explain why this result cannot alone calculate an actual multielectron atom’s ionization energy.

A student writes Fe²⁺ as [Ar]4s²3d⁴ from neutral Fe = [Ar]4s²3d⁶. Evaluate the model and write the correct configuration. Explain why simply moving two places left in the periodic table fails here.

An idealized neutral-element PES has three peaks at decreasing binding energies with populations 2, 2 and 4. A proposed model gives 1s²2s⁴2p². Evaluate it and identify a consistent atom.

Two idealized PES plots have the same populations 2:2:6 and belong to Ne and Mg²⁺. Plot B places every corresponding peak at greater binding energy than plot A. Assign the species and justify with electron count, proton count and shielding.

Compare the first ionization energies of Mg and Ca using their valence configurations [Ne]3s² and [Ar]4s². Then compare radii of Na⁺ and Mg²⁺. Give causal explanations.

An unknown third-period main-group element has successive ionization energies 580, 1820, 2750 and 11,600 kJ mol⁻¹. Identify its likely valence count and group. Predict whether its atomic radius is larger or smaller than Mg in the same period, and explain.

Define the electron-addition enthalpy as the change for X(g) + e⁻ → X⁻(g). Negative values mean energy is released.

1. Two anonymous atoms have values −200 and +50 kJ mol⁻¹. Which electron addition is more energetically favorable? Explain why an electronegativity trend cannot supply an exact electron-addition enthalpy.
2. S and Cl are next to one another in period 3, with valence configurations 3s²3p⁴ and 3s²3p⁵. Predict which first electron addition is generally more energetically favorable. Explain using nuclear attraction, the shared shell and comparable core shielding.
3. Measured first-addition values are F: −322 kJ mol⁻¹ and Cl: −348 kJ mol⁻¹. F receives the added electron in a compact 2p shell; Cl receives it in a larger 3p shell. Explain how electron–electron repulsion can account for this exception to a simple down-group prediction. Do these data imply that F is less electronegative than Cl?

Use the familiar main-group monatomic-ion model for binary compounds. K and Na are in group 1, Ca and Mg in group 2, O in group 16 and F in group 17. In this question, “oxide” means the monatomic oxygen ion, not peroxide or superoxide.

1. Predict each element’s typical ion charge from its periodic position and valence-electron count. Explain the electron loss or gain represented by those charges.
2. Use your predicted charges to write neutral formulas for potassium oxide and calcium fluoride. Show the charge balance, then predict the analogous formulas using Na instead of K and Mg instead of Ca.
3. State why this charge-prediction model is useful but does not assign one universal charge to every element in every compound.

1. A student argues that K should be less likely than Na to lose an electron because K has more protons. Evaluate the argument using electronic structure, and state one limit of predicting reactions from this trend.
2. Consider two isolated H atoms approaching to form H₂. In a qualitative electrostatic bonding model, identify the valence-electron/nucleus attractions involving both nuclei and the repulsions between like charges. Explain why shared electrons can stabilize a bonded arrangement, but why bringing the nuclei ever closer does not keep making it more stable. Evaluate the claim that an H–H bond consists only of each electron attracting its original nucleus.