Chemistry: Atoms First 2e & General Chemistry Midterm Review

Comprehensive practice flashcards covering measurements, unit conversions, subatomic particles, chemical formulas, molarity, light, spectroscopy, Bohr model, quantum theory, electron configurations, and periodic trends.

What three components are contained in a scientific measurement?

A numerical value, a unit, and a degree of uncertainty.

What are the SI base units and symbols for length, mass, time, temperature, and amount of substance?

Length: meter ($\text{m}$); Mass: kilogram ($\text{kg}$); Time: second ($\text{s}$); Temperature: kelvin ($\text{K}$); Amount of substance: mole ($\text{mol}$).

What numerical power of 10 is represented by each of the metric prefixes kilo ($k$), centi ($c$), milli ($m$), micro ($\mu$), nano ($n$), and pico ($p$)?

kilo ($k$): $10^3$; centi ($c$): $10^{-2}$; milli ($m$): $10^{-3}$; micro ($\mu$): $10^{-6}$; nano ($n$): $10^{-9}$; pico ($p$): $10^{-12}$.

How is the volume of an irregular object measured using water displacement?

$$V_{\text{object}} = V_{\text{final}} - V_{\text{initial}}$$

What is the formula for density, and why is density classified as an intensive property?

Density is $d = \frac{m}{V}$. It is an intensive property because it does not depend on the amount of substance present.

What three sources produce exact numbers that contain no uncertainty?

1. Counting (e.g., $12\,\text{eggs}$); 2. Definitions (e.g., $1\,\text{ft} = 12\,\text{in}$); 3. Defined conversions (e.g., $1\,\text{in} = 2.54\,\text{cm}$).

What is the round-to-even rule used when rounding a measurement where the first removed digit is exactly 5 followed only by zeros?

If the retained digit is even, leave it unchanged. If the retained digit is odd, increase it by 1.

What are the rules for rounding results in addition/subtraction versus multiplication/division calculations?

For addition and subtraction, round the answer to the fewest decimal places found in the original measurements. For multiplication and division, round the answer to the fewest significant figures found in the original measurements.

How do accuracy and precision differ in scientific measurements?

Accuracy is the closeness of a measurement to the accepted or true value, whereas precision is the closeness of repeated measurements to one another.

What are the equations for converting between Celsius (T_{\text{^\circ C}}) and Fahrenheit (T_{\text{^\circ F}}) temperatures?

T_{\text{^\circ F}} = \frac{9}{5}(T_{\text{^\circ C}} + 32) and T_{\text{^\circ C}} = \frac{5}{9}(T_{\text{^\circ F}} - 32)

What is the equation for converting temperature in Celsius (T_{\text{^\circ C}}) to kelvin ($T_{\text{K}}$)?

T_{\text{K}} = T_{\text{^\circ C}} + 273.15

What are the locations, relative charges, and approximate masses of protons, neutrons, and electrons?

Proton: Nucleus, relative charge $+1$, mass $1\,\text{amu}$. Neutron: Nucleus, relative charge $0$, mass $1\,\text{amu}$. Electron: Outside nucleus, relative charge $-1$, mass approximately $0\,\text{amu}$.

How are atomic number ($Z$), mass number ($A$), and neutron count related?

Atomic number ($Z$) equals the number of protons ($Z = \text{number of protons}$). Mass number ($A$) equals total protons plus neutrons ($A = \text{protons} + \text{neutrons}$). Therefore, $\text{neutrons} = A - Z$.

How is one atomic mass unit ($\text{amu}$) defined?

One atomic mass unit is defined as one-twelfth the mass of a carbon-12 atom ($1\,\text{amu} = 1.6605 \times 10^{-24}\,\text{g}$).

What formula is used to calculate average atomic mass from isotopic abundances?

$$\text{average atomic mass} = \sum (\text{fractional abundance})(\text{isotope mass})$$

What is the difference between a molecular formula and an empirical formula?

A molecular formula shows the actual number of each type of atom in one molecule, while an empirical formula shows the simplest whole-number ratio of atoms.

What are isomers?

Isomers are compounds that have the same molecular formula but different arrangements of atoms, resulting in different physical and chemical properties.

What is Avogadro's number ($N_{\text{A}}$) and what does it represent?

$N_{\text{A}} = 6.022 \times 10^{23}\,\text{particles/mol}$. It represents the exact number of particles contained in one mole of a substance.

Why is the mass of an ionic compound called formula mass rather than molecular mass?

Because ionic compounds do not contain separate molecules; they form large crystal structures made of ions, so their mass is correctly termed formula mass.

What is the definition and equation for molarity ($M$)?

Molarity measures solution concentration as moles of solute per liter of solution: $M = \frac{\text{moles of solute}}{\text{liters of solution}}$.

What is the dilution equation, and what quantity remains constant during dilution?

The dilution equation is $M_1 V_1 = M_2 V_2$. The number of moles of solute stays constant during dilution while solvent is added.

What is the relationship between the speed of light ($c$), wavelength ($\lambda$), and frequency ($\nu$)?

$c = \lambda \nu$, where $c = 2.998 \times 10^8\,\text{m/s}$. Wavelength and frequency are inversely related.

What was the 'ultraviolet catastrophe' in classical physics?

The incorrect prediction by classical physics that hot objects would emit an unlimited amount of ultraviolet energy, which Planck resolved by proposing that energy is quantized.

What is Planck's quantum theory equation for energy?

$E = n h \nu$, where $E$ is energy, $n$ is a positive integer ($1, 2, 3, \dots$), $h$ is Planck's constant ($6.626 \times 10^{-34}\,\text{J}\cdot\text{s}$), and $\nu$ is frequency.

How do increasing light brightness and increasing light frequency uniquely affect ejected electrons in the photoelectric effect?

Increasing brightness increases the number of photons and can eject more electrons, but does not increase photon energy. Increasing frequency increases the energy of each photon and makes ejected electrons move faster.

What experimental evidence supports the wave behavior versus particle behavior of light?

Wave behavior is demonstrated by interference and diffraction. Particle behavior is demonstrated by the photoelectric effect, photons, and quantized energy.

What is the Rydberg equation used to calculate hydrogen emission wavelengths?

$\frac{1}{\lambda} = R_\infty \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$, where $R_\infty = 1.097 \times 10^7\,\text{m}^{-1}$, $n_2 > n_1$, and $\lambda$ is in meters.

What equation describes the energy ($E_n$) of an electron in energy level $n$ for a hydrogen-like ion?

$E_n = -\frac{k Z^2}{n^2}$, where $k = 2.179 \times 10^{-18}\,\text{J}$ and $Z$ is the nuclear charge.

In electron energy transitions, what do the signs of energy change ($\Delta E > 0$ vs $\Delta E < 0$) signify?

$\Delta E > 0$ indicates that the atom absorbs energy and the electron moves upward ($n_{\text{low}} \rightarrow n_{\text{high}}$). $\Delta E < 0$ indicates that the atom emits energy and the electron moves downward ($n_{\text{high}} \rightarrow n_{\text{low}}$).

What equation gives the radius ($r$) of a Bohr orbit for a hydrogen-like atom or ion?

$r = \frac{n^2}{Z} a_0$, where $a_0 = 5.292 \times 10^{-11}\,\text{m}$ is the Bohr radius.

What are the major limitations of the Bohr model?

The Bohr model works accurately only for one-electron species (such as $\text{H}$, $\text{He}^+$, $\text{Li}^{2+}$, $\text{Be}^{3+}$) and fails for multi-electron atoms because it does not account for electron-electron interactions.

What is the De Broglie wavelength equation for a moving particle?

$\lambda = \frac{h}{m v} = \frac{h}{p}$, where $h$ is Planck's constant ($6.626 \times 10^{-34}\,\text{J}\cdot\text{s}$), $m$ is mass in kilograms, $v$ is velocity in $\text{m/s}$, and $p$ is momentum.

What is Heisenberg's uncertainty principle equation for position and momentum?

$\Delta x \cdot \Delta p_x = (\Delta x)(m \Delta v) \ge \frac{\hbar}{2}$, where $\hbar = \frac{h}{2\pi} \approx 1.055 \times 10^{-34}\,\text{J}\cdot\text{s}$.

What are the four quantum numbers, their allowed values, and their physical meanings?

1. Principal ($n$): $1, 2, 3, \dots$ (shell, energy, size); 2. Angular-momentum ($l$): $0$ through $n-1$ (subshell, orbital shape); 3. Magnetic ($m_l$): $-l$ through $+l$ (orbital orientation); 4. Spin ($m_s$): $+\frac{1}{2}$ or $-\frac{1}{2}$ (electron spin).

What formula calculates the number of radial nodes in an atomic orbital?

$$\text{radial nodes} = n - l - 1$$

What are the formulas for the number of orbitals and maximum electrons in a shell $n$?

Orbitals in a shell = $n^2$; Maximum electrons in a shell = $2 n^2$.

What are the definitions of the Aufbau principle, Pauli exclusion principle, and Hund's rule?

Aufbau principle: Electrons fill the lowest-energy orbitals available first. Pauli exclusion principle: No two electrons in an atom can have the same four quantum numbers. Hund's rule: Electrons occupy equal-energy orbitals individually with parallel spins before pairing.

What are the observed ground-state electron configurations for chromium ($\text{Cr}$) and copper ($\text{Cu}$)?

Chromium ($\text{Cr}$): $[\text{Ar}] 4s^1 3d^5$; Copper ($\text{Cu}$): $[\text{Ar}] 4s^1 3d^{10}$.

When transition metals form cations, from which subshell are electrons removed first?

Electrons are removed from the highest $n$ level first, meaning $s$ electrons are removed before $d$ electrons.

What is effective nuclear charge ($Z_{\text{eff}}$), and how does it trend across a period?

$Z_{\text{eff}} = Z - \text{shielding}$. Across a period from left to right, $Z_{\text{eff}}$ increases because nuclear charge ($Z$) increases while shielding increases only slightly.

What are the general periodic trends for atomic radius, ionization energy, and metallic character across a period (left to right) and down a group (top to bottom)?

Atomic radius: Decreases left to right, increases top to bottom. Ionization energy: Increases left to right, decreases top to bottom. Metallic character: Decreases left to right, increases top to bottom.

What are isoelectronic species, and how does proton number affect their ionic radii?

Isoelectronic species are atoms or ions that contain the same number of electrons. Species with more protons have a larger nuclear charge that pulls electrons closer, resulting in a smaller radius.

What is the Beer-Lambert law formula and what does each variable represent?

$A = \varepsilon b c$, where $A$ is absorbance (unitless), $\varepsilon$ is molar absorptivity ($\text{M}^{-1}\,\text{cm}^{-1}$), $b$ is path length ($\text{cm}$), and $c$ is concentration ($\text{M}$).

How are absorbance ($A$) and transmittance ($T$) mathematically related?

$A = -\log(T)$, where transmittance $T = \frac{I}{I_0}$.

What is the definition of $\lambda_{\text{max}}$ in spectroscopy?

$\lambda_{\text{max}}$ is the wavelength of maximum absorbance, corresponding to the highest peak on an absorption spectrum graph.

What is the Modern Periodic Law?

The properties of elements are periodic functions of their atomic numbers.