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Flashcards · AP® Chemistry · Unit 1

Unit 1: Atomic Structure and Properties flashcards

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1.1 Moles and Molar Mass

What is a mole, and how many particles does it contain?
The mole is a counting unit chemists use because particles cannot be counted directly. 1 mol of anything contains 6.022 × 10²³ of its particles (atoms, molecules or formula units). This number is Avogadro's number, N_A = 6.022 × 10²³ mol⁻¹.
What is molar mass, and how do you find it for a compound?
Molar mass, M, is the mass of one mole of a substance in g mol⁻¹. Add the average atomic masses from the periodic table, counting every atom in the formula. Example: CO₂ = 12.01 + 2(16.00) = 44.01 g mol⁻¹.
How are the average mass of one particle in amu and the molar mass related?
They have the same number. A particle with an average mass of 18.02 amu has a molar mass of 18.02 g mol⁻¹. This is why the periodic table's average atomic mass can be read directly as g mol⁻¹.
How do you convert a mass into a number of particles?
Always go through moles. First n = m / M (n in mol, m in g, M in g mol⁻¹). Then N = n × N_A. Example: 9.01 g of water ÷ 18.02 g mol⁻¹ = 0.500 mol, and 0.500 × 6.022 × 10²³ = 3.01 × 10²³ molecules.
How do you count atoms of one element inside a sample of a compound?
Find the number of formula units or molecules (N = n × N_A), then multiply by the subscript of that element, remembering brackets. Ca(NO₃)₂ contains 2 N and 6 O per formula unit. 1 mol O₂ contains 2 mol O atoms.
Do equal masses of two substances contain equal numbers of particles?
No. Equal mass does not mean equal particles, because molar masses differ. To compare particle numbers, convert each mass to moles and compare the moles.
When converting between moles and particles, when do you multiply and when do you divide by N_A?
Moles → particles: multiply by N_A. Particles → moles: divide by N_A. Check that units cancel to the unit you want; if they do not, the setup is wrong.
What assumptions sit behind a mass-to-moles calculation, and how should you round?
The sample is pure (all the mass is the substance in the formula), and average atomic masses assume the natural mix of isotopes. Keep full calculator values and round once at the end; the answer is no more precise than the least precise measurement.

1.2 Mass Spectra of Elements

What are isotopes?
Atoms of the same element (same number of protons) with different numbers of neutrons, so they have different masses. Each atom is one isotope; no single atom has the average atomic mass.
What does a mass spectrometer do to a sample of an element?
It turns the atoms into +1 ions, separates them by mass-to-charge ratio (m/z) and counts them. For singly charged ions of one atom, m/z equals the isotope's mass in amu.
How do you read the mass spectrum of a single element?
Number of peaks = number of isotopes. Position of each peak (m/z) = isotope mass in amu. Peak height = relative abundance. Height tells you how many; position tells you how heavy.
How do you calculate average atomic mass from a mass spectrum?
Use a weighted average: average = Σ (mass × fraction). Turn % into a fraction by dividing by 100. Example: chlorine, 0.7576 × 34.969 + 0.2424 × 36.966 = 35.45 amu.
How do you turn relative peak heights into fractional abundances?
Divide each height by the sum of all heights (not by the tallest). Heights 100 and 50 give 100/150 = 66.7% and 50/150 = 33.3%.
How do you find isotope abundances from an average atomic mass with two isotopes?
Let x be the fraction of isotope 2, so isotope 1 is (1 − x). Solve m₁(1 − x) + m₂x = average for x. The fractions must add to 1.
What quick check catches a wrong average atomic mass?
The answer must lie between the lightest and heaviest isotope masses, and closer to the more abundant one. An answer outside the range of isotope masses is always wrong; a simple (unweighted) mean is a common error.

1.3 Elemental Composition of Pure Substances

What is the law of definite proportions?
Every pure sample of a compound has the same mass ratio of its elements. Pure water is always 11.19% H and 88.81% O by mass. Different compounds of the same elements have different ratios (H₂O₂ is 5.93% H).
How do you calculate the percentage by mass of an element in a compound?
% element = (atoms in formula × atomic mass) ÷ M × 100. Example: carbon in CO₂ = 12.01 ÷ 44.01 × 100 = 27.29%.
What is an empirical formula?
The lowest whole-number ratio of atoms in a compound. C₆H₁₂O₆ → CH₂O; N₂O₄ → NO₂. Mass composition fixes the empirical formula only: C₂H₂ and C₆H₆ have identical percentages.
How do you find an empirical formula from percentage composition?
Assume 100 g so each % becomes grams. Convert each mass to moles by dividing by atomic mass (not atomic number). Divide every mole value by the smallest. If the ratio is not whole, multiply all values to make it whole.
A mole ratio comes out as 1 : 1.5 or 1 : 1.33. What should you do?
Do not round. Multiply the whole ratio: .50 → × 2; .33 or .67 → × 3; .25 or .75 → × 4; .20, .40, .60, .80 → × 5. P 1.000 : O 2.500 becomes P₂O₅.
In a metal + oxygen experiment, how do you get the mass of oxygen?
Oxygen mass = product mass − metal mass. The method assumes the reaction is complete and all the mass gain is oxygen. Using the product's mass as the oxygen mass is a common mistake.
What is the difference between a molecule and a formula unit?
Molecular substances (H₂O, CO₂) are made of separate molecules. Substances like NaCl or SiO₂ are atoms or ions held in a fixed ratio in a lattice, described by a formula unit. NaCl is not a molecule.

1.4 Composition of Mixtures

What is the difference between a pure substance and a mixture?
A pure substance contains one type of particle (atoms, molecules or formula units). A mixture contains two or more types, in proportions that can vary, so it has no formula. NaCl is pure even though it has two elements; salt plus sand is a mixture.
How does the elemental composition of a mixture differ from that of a pure compound?
A pure compound always has the same mass percent of each element. A mixture's mass percent depends on how much of each component it holds; for two components it lies between the two pure values (a weighted average, not the midpoint).
How do you find the purity of a sample from elemental analysis?
Mass of compound = mass of element ÷ mass fraction of that element in the compound. Purity (%) = mass of compound ÷ mass of sample × 100. Example: 25.0 g of impure MgO containing 12.0 g Mg is 79.6% MgO.
What does a calculated purity above 100% tell you?
The one-step method assumed the impurity contains none of the analysed element. A purity over 100% signals that the impurity does contain it, or a data error. Losses of the element during analysis make purity look too low.
How do you analyse a two-component mixture in which both parts contain the analysed element?
Set up two equations: a + b = total moles of the element (adjusted for subscripts), and M₁a + M₂b = total mass of the sample. Solve simultaneously. A single-step purity calculation does not work here.
Why is element percent not the same as compound percent?
The element is only part of the compound's mass. 40.8% Cl in a sample does not mean 40.8% KCl; divide the chlorine mass by the mass fraction of Cl in KCl to get the KCl mass.
How can repeated analyses show whether a sample is pure or a mixture?
A pure compound gives the same mass percent every time. If samples from one bottle give 31%, 36% and 28% Ca, the composition varies, so it is a mixture.

1.5 Atomic Structure and Electron Configuration

What is the structure of an atom in the shell model?
A small positive nucleus (protons and neutrons) surrounded by negative electrons, held together by electrostatic attraction. Electrons occupy shells (n = 1, 2, 3 …) split into subshells s, p, d, f, which hold 2, 6, 10 and 14 electrons.
What does Coulomb's law say, and how do you use it to compare attractions?
F ∝ q₁q₂ / r². Doubling a charge doubles the force; doubling the distance quarters it (1/r², not 1/r). Halving the distance makes the force 4 times larger. Always name both charge and distance when ranking.
In what order do subshells fill in a ground-state configuration?
Lowest energy first (Aufbau): 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p. The s, p, d and f blocks of the periodic table show the order. Arsenic is [Ar]4s²3d¹⁰4p³; do not forget the d block.
How do you write the electron configuration of a transition-metal cation?
Remove electrons from the largest n first, so 4s empties before 3d. Fe²⁺ is [Ar]3d⁶, not [Ar]4s²3d⁴. Zn²⁺ is [Ar]3d¹⁰. The proton number never changes in an ion.
What is the difference between core and valence electrons?
Core electrons are inside the noble-gas core; valence electrons are in the highest occupied shell. K is [Ar]4s¹, with one valence electron.
What is core charge and how do you estimate it?
The approximate positive charge an outer electron feels: core charge ≈ protons − core electrons. It is an estimate because shielding is not perfect; use it for comparisons only. Na ≈ +1, Mg ≈ +2.
Why is a 3s electron harder to remove from Mg than from Na?
Mg has a core charge of about +2 against +1 for Na, at a similar distance from the nucleus, so by Coulomb's law the attraction on the 3s electron is greater in Mg.

1.6 Photoelectron Spectroscopy

What happens in photoelectron spectroscopy (PES)?
High-energy photons knock single electrons out of gas-phase atoms or ions, from every occupied subshell. The binding energy of each electron, the energy needed to remove it, is measured.
What do the number, position and height of PES peaks tell you?
Number of peaks = number of occupied subshells. Position = binding energy (higher for electrons closer to the nucleus). Relative height ≈ number of electrons in that subshell, so heights give the configuration's superscripts.
Which way does binding energy usually increase on a PES spectrum?
Spectra often plot binding energy increasing to the left, frequently on a log scale. Always check the axis before reading which peak is the core and which is the valence.
How do you identify an element from PES peak heights?
Read the relative heights as electron counts and add them. Heights 2, 2, 6, 2, 5 give 1s²2s²2p⁶3s²3p⁵, 17 electrons: chlorine. Round height ratios to whole numbers of electrons.
Why is the 1s peak of Ne at a higher binding energy than the 1s peak of F?
Ne has one more proton, so the 1s electrons feel a larger nuclear charge (larger q in Coulomb's law). Comparing the same subshell in two elements, the difference is nuclear charge, not number of shells.
What PES evidence shows that shells contain subshells?
Within one shell, s and p electrons give separate peaks at different binding energies (for example 2s and 2p). A simple shell model would predict one peak per shell.
What are the common mistakes when reading a PES spectrum?
Thinking the tallest peak has the highest energy (height = electron count); one peak per electron (it is one per subshell); treating peaks as successive ionization energies (only the lowest peak ≈ first ionization energy); keeping a valence peak for a cation (Mg²⁺ has no 3s peak).
How do PES spectra of isoelectronic species compare?
Same number of peaks with the same relative heights, but positions shifted: the species with more protons has every peak at higher binding energy. Ca²⁺ has five peaks: 1s, 2s, 2p, 3s, 3p.

1.7 Periodic Trends

Why do element properties repeat periodically?
Valence electron configurations repeat. Elements in a group share the same outer pattern (ns¹ for group 1), and each period fills a new outer shell, ending with a filled shell at a noble gas.
How does atomic radius change across a period and down a group, and why?
Across a period it decreases: Z_eff rises while electrons are added to the same shell, so they are pulled closer. Down a group it increases: each new shell is farther out. Core shielding is about constant across a period.
How does first ionization energy change across a period and down a group?
Generally increases across a period (larger Z_eff, smaller radius) and decreases down a group (outer electron farther away and more shielded). There are dips at groups 13 and 16.
Why is the first ionization energy of Al lower than that of Mg?
Al loses a 3p electron, which is higher in energy and more shielded than Mg's 3s electron, so it is easier to remove.
Why is the first ionization energy of O lower than that of N?
O's fourth 2p electron is paired in an orbital that already holds an electron. Repulsion between the paired electrons makes it easier to remove. Name the paired-electron repulsion; "half-filled is stable" alone is not an explanation.
How do successive ionization energies reveal the number of valence electrons?
Each successive ionization energy is larger. The big jump appears when the next electron comes from an inner shell. Mg: 738, 1451, 7733 kJ mol⁻¹, so the jump after the second shows 2 valence electrons and Mg forms Mg²⁺.
How do ion sizes compare with their atoms and with each other?
Cations are smaller than their atoms (a shell is lost); anions are larger (extra repulsion, same protons). In an isoelectronic series more protons means a smaller ion; from smallest to largest: F⁻, O²⁻, N³⁻.
What is the difference between electronegativity and electron affinity?
Electron affinity is the energy change when an isolated atom gains an electron. Electronegativity is how strongly an atom attracts a shared pair in a bond. Electronegativity increases across a period and decreases down a group.

1.8 Valence Electrons and Ionic Compounds

How do you find the number of valence electrons of a main-group element?
Groups 1–2 have 1–2 valence electrons; groups 13–18 have (group − 10). Valence electrons are the outer-shell electrons beyond the noble-gas core. Helium has 2.
What decides whether two elements form an ionic compound?
How strongly each nucleus attracts valence electrons (Coulomb's law: charge and distance). A metal that holds its valence electrons weakly plus a nonmetal that attracts electrons strongly gives electron transfer and an ionic compound.
Why do metals get more reactive down a group but halogens less reactive?
Metals react by losing electrons: down a group the valence electron is farther away and more shielded, so it is lost more easily. Halogens react by gaining electrons: down a group the incoming electron is farther from the nucleus, so it is attracted less. Fluorine is the most reactive halogen.
Why do main-group ions stop at the nearest noble-gas arrangement?
Removing or adding one more electron would involve a different shell, which costs much more energy, shown by a big jump in successive ionization energies. "Wants a full shell" is not an energy explanation.
How do you write the formula of an ionic compound?
Use the smallest whole-number ratio of ions with total charge zero: (number × charge) + (number × charge) = 0. Lithium nitride is Li₃N; aluminium sulfide is Al₂S₃. Reduce the ratio: MgO, not Mg₂O₂.
What typical ion charges do main groups form?
Group 1: +1; group 2: +2; Al (group 13): +3; group 15: −3; group 16: −2; group 17: −1; group 18: none. Nonmetal ions are negative: sulfur forms S²⁻. Transition metals often form more than one ion; iron(III) means Fe³⁺.
What does "analogous compounds" mean for elements in the same group?
Elements in one group form compounds with the same formula type: Na₂O and K₂O; MgCl₂ and CaCl₂; H₂O and H₂S. Their properties are similar but change gradually, not identical.
Do subscripts in an ionic formula show the ion charges?
No. Subscripts show the ratio of ions. In Ca₃N₂ calcium is 2+ and nitrogen is 3−; 3(+2) + 2(−3) = 0.

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