CHM261 Exam 2 Study Guide: Solutions, Redox, and Quantum Mechanics

Comprehensive practice flashcards for CHM261 Exam 2 covering solution chemistry, net ionic reactions, titration stoichiometry, redox numbers and activity series, and quantum mechanics.

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

An empirical formula is the simplest, lowest whole-number mathematical ratio of atoms present in a compound (such as $\text{CH}_2\text{O}$), whereas a molecular formula gives the actual number of atoms of each element in a single molecule of a compound (such as $\text{C}_6\text{H}_{12}\text{O}_6$) and is always a whole-number multiple of the empirical formula.

Why is $\text{C}_5\text{H}_{10}\text{O}_5$ classified as a molecular formula rather than an empirical formula?

Because its subscripts share a common factor of $5$ and can be mathematically reduced down to the simpler whole-number ratio $\text{CH}_2\text{O}$. An empirical formula cannot be reduced any further.

What are the two primary analytical functions of mass spectrometry mentioned in the study guide?

It is used to determine the precise molecular weights of compounds and to measure the relative natural abundances of isotopes.

In combustion analysis, how are the quantities of carbon and hydrogen determined?

All carbon is converted to $\text{CO}_2$, where the mass gained by the $\text{CO}_2$ trap isolates the exact amount of carbon. All hydrogen is converted to $\text{H}_2\text{O}$, where the mass gained by the water trap yields the hydrogen content.

Why can oxygen content not be measured directly via combustion analysis, and how is its mass determined?

Oxygen cannot be measured directly because oxygen gas is continuously supplied from an external source to burn the sample. Its mass must be calculated by subtracting the masses of carbon and hydrogen from the original sample mass.

How do unsaturated, saturated, and supersaturated solutions differ in solute capacity?

An unsaturated solution can dissolve additional solute; a saturated solution contains the maximum possible amount of dissolved solute at dynamic equilibrium at a specific temperature; and a supersaturated solution has been heated to force extra solute to dissolve beyond saturation.

How is molarity ($M$) defined, and what is its formula?

Molarity is defined as the moles of solute per liter of total solution: $M = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}}$

How many grams of sodium nitrate ($\text{NaNO}_3$, molar mass = $84.99\,\text{g/mol}$) are needed to prepare $500\,\text{mL}$ of a $0.250\,\text{M}$ solution?

$10.62\,\text{g}$. Step 1: Convert volume: $500\,\text{mL} \times \frac{1\,\text{L}}{1000\,\text{mL}} = 0.500\,\text{L}$. Step 2: Calculate moles: $\text{Moles} = 0.250\,\text{M} \times 0.500\,\text{L} = 0.125\,\text{mol}$. Step 3: Convert moles to mass: $\text{Mass} = 0.125\,\text{mol} \times 84.99\,\text{g/mol} = 10.62\,\text{g}$.

What is the dilution equation, and what fundamental principle does it demonstrate?

The dilution equation is $M_1 \times V_1 = M_2 \times V_2$. It demonstrates that when solvent is added to a concentrated solution, the total moles of solute remain constant while the volume increases, decreasing the concentration.

What is the final concentration of $\text{HNO}_3$ when $45\,\text{mL}$ of a $4.0\,\text{M}$ solution is diluted with pure water to a total volume of $200\,\text{mL}$?

$0.90\,\text{M}$. Rearranging the dilution equation gives: $M_2 = \frac{M_1 \times V_1}{V_2} = \frac{4.0\,\text{M} \times 45\,\text{mL}}{200\,\text{mL}} = 0.90\,\text{M}$.

How do strong electrolytes, weak electrolytes, and nonelectrolytes differ in aqueous dissociation and conductivity?

Strong electrolytes dissociate completely into ions and conduct electricity strongly; weak electrolytes dissociate only partially into ions and conduct electricity poorly; nonelectrolytes dissolve as intact, uncharged molecules, producing no ions and conducting no electricity.

Why does a solution of calcium nitrate ($\text{Ca}(\text{NO}_3)_2$) conduct electricity more strongly than solutions of ethanol ($\text{C}_2\text{H}_5\text{OH}$) or acetic acid ($\text{CH}_3\text{COOH}$)?

Ethanol is a nonelectrolyte ($0$ ions), and acetic acid is a weak acid that dissociates minimally. Calcium nitrate is a soluble strong electrolyte that dissociates completely into three ions ($1\,\text{Ca}^{2+}$ and $2\,\text{NO}_3^-$) per formula unit, yielding the highest concentration of mobile charge carriers.

What are spectator ions in an aqueous reaction?

Spectator ions are ions that appear identical and unchanged on both the reactant and product sides of a chemical equation, meaning they do not participate in the actual chemical change.

When aqueous solutions of $\text{MgSO}_4(aq)$ and $\text{Ba}(\text{NO}_3)_2(aq)$ are mixed, what is the net ionic equation and what are the spectator ions?

The net ionic equation is $\text{Ba}^{2+}(aq) + \text{SO}_4^{2-}(aq) \rightarrow \text{BaSO}_4(s)$. The spectator ions are $\text{Mg}^{2+}$ and $\text{NO}_3^-$, because nitrates remain universally soluble while barium sulfate precipitates as an insoluble solid.

If $60.0\,\text{mL}$ of $0.150\,\text{M HCl}$ is mixed with $40.0\,\text{mL}$ of $0.200\,\text{M NaOH}$, is the resulting solution acidic, basic, or neutral?

The solution is acidic. Step 1: Moles of $\text{H}^+ = 0.0600\,\text{L} \times 0.150\,\text{mol/L} = 0.0090\,\text{mol}$. Step 2: Moles of $\text{OH}^- = 0.0400\,\text{L} \times 0.200\,\text{mol/L} = 0.0080\,\text{mol}$. Step 3: There are more moles of $\text{H}^+$ than $\text{OH}^-$, leaving excess unneutralized hydronium ions.

In the titration setup shown below, what are the identity, location, and concentration status of the titrant versus the analyte/titrand?

The titrant is held in the burette and has a known concentration and measured volume. The analyte (or titrand) is held in the conical flask and has a known volume but an unknown concentration.

A $25.00\,\text{mL}$ sample of oxalic acid ($\text{H}_2\text{C}_2\text{O}_4$) requires $34.20\,\text{mL}$ of $0.125\,\text{M NaOH}$ to reach the equivalence endpoint. What is the molar concentration of the acid?

$0.0855\,\text{M}$. Step 1: Moles of $\text{NaOH} = 0.03420\,\text{L} \times 0.125\,\text{M} = 0.004275\,\text{mol}$. Step 2: Stoichiometric ratio ($1\,\text{mol H}_2\text{C}_2\text{O}_4 : 2\,\text{mol NaOH}$) gives $0.0021375\,\text{mol H}_2\text{C}_2\text{O}_4$. Step 3: Molarity $= \frac{0.0021375\,\text{mol}}{0.02500\,\text{L}} = 0.0855\,\text{M}$.

What are the oxidation number rules for pure elements, monatomic ions, oxygen, and hydrogen?

Pure elements are always $0$. Monatomic ions equal their charge ($\text{K}^+ = +1$, $\text{Cl}^- = -1$). Oxygen is $-2$ (except in peroxides like $\text{H}_2\text{O}_2$, where it is $-1$). Hydrogen is $+1$ when bonded to nonmetals and $-1$ when bonded to metals.

What is the oxidation number of each chromium (Cr) atom in sodium dichromate ($\text{Na}_2\text{Cr}_2\text{O}_7$)?

$+6$. In the tracking equation $2(\text{Na}) + 2(\text{Cr}) + 7(\text{O}) = 0$, substitute $2(+1) + 2(x) + 7(-2) = 0$. This simplifies to $2 + 2x - 14 = 0$, $2x = 12$, yielding $x = +6$.

How are oxidation, reduction, reducing agents, and oxidizing agents defined in redox chemistry?

Oxidation is the loss of electrons (oxidation number increases). Reduction is the gain of electrons (oxidation number decreases). A reducing agent undergoes oxidation and supplies electrons; an oxidizing agent undergoes reduction and accepts electrons.

In the reaction $\text{Zn}(s) + \text{Cu}^{2+}(aq) \rightarrow \text{Zn}^{2+}(aq) + \text{Cu}(s)$, which species is oxidized, which is reduced, and which is the reducing agent?

$\text{Zn}(s)$ is oxidized ($0$ to $+2$), $\text{Cu}^{2+}(aq)$ is reduced ($+2$ to $0$), and $\text{Zn}(s)$ is the reducing agent because it loses electrons and causes the reduction of copper ions.

What does a metal's position on the activity series indicate regarding single displacement reactions?

A metal ranked higher on the activity series is more easily oxidized (more strongly reducing) and can displace any metal ion located beneath it on the list.

A $10.00\,\text{mL}$ sample of $\text{I}_3^-$ requires $24.55\,\text{mL}$ of $0.102\,\text{M Na}_2\text{S}_2\text{O}_3$ to reach the starch endpoint via $2\,\text{S}_2\text{O}_3^{2-}(aq) + \text{I}_3^-(aq) \rightarrow \text{S}_4\text{O}_6^{2-}(aq) + 3\,\text{I}^-(aq)$. What is the molar concentration of $\text{I}_3^-$?

$0.125\,\text{M}$. First, calculate titrant amount: $0.102\,\text{M} \times 24.55\,\text{mL} = 2.5041\,\text{mmol S}_2\text{O}_3^{2-}$. Convert to analyte: $2.5041\,\text{mmol} \times \frac{1\,\text{mol I}_3^-}{2\,\text{mol S}_2\text{O}_3^{2-}} = 1.25\,\text{mmol I}_3^-$. Calculate concentration: $\frac{1.25\,\text{mmol}}{10.00\,\text{mL}} = 0.125\,\text{M}$.

What is the mathematical relationship between the energy ($E$), frequency ($\nu$), and wavelength ($\lambda$) of light?

$E = h\nu = \frac{hc}{\lambda}$. Energy is directly proportional to frequency and inversely proportional to wavelength. High-energy light has a shorter wavelength and higher frequency; low-energy light has a longer wavelength and lower frequency.

How do constructive and destructive wave interference differ?

In constructive interference, crests align with crests, combining to amplify wave amplitude or brightness. In destructive interference, crests align with troughs, causing the waves to cancel each other out to produce dimmer or dark regions.

Why is the de Broglie wavelength ($\lambda = \frac{h}{mv}$) detectable for electrons but undetectable for macroscopic objects?

Because macroscopic objects have huge masses ($m$) relative to subatomic particles, their calculated wavelengths are vanishingly small and impossible to detect. In contrast, an electron's tiny mass yields an observable wavelength visible through diffraction patterns.

What does the Heisenberg Uncertainty Principle state regarding electron motion?

It states that it is fundamentally impossible to simultaneously know both the exact position and the exact momentum of a subatomic particle, meaning electrons do not move along fixed, predictable orbits.

What physical meaning is assigned to the square of the wave function ($\psi^2$)?

While the wave function $\psi$ represents the mathematical amplitude of an electron wave, its square ($\psi^2$) represents the probability density of finding that electron in a given region of three-dimensional space.

What property of an electron orbital is defined by each of the four quantum numbers ($n$, $l$, $m_l$, $m_s$)?

$n$ (principal) defines the shell/energy level and size; $l$ (angular momentum) determines the geometric orbital shape ($s, p, d, f$); $m_l$ (magnetic) describes the spatial orientation; and $m_s$ (spin) describes the intrinsic electron spin ($+1/2$ or $-1/2$).

If an electron shell has principal quantum number $n = 4$, what are the allowed values of $l$ and the total number of individual orbitals?

The allowed values for $l$ range from $0$ to $n - 1$, giving $l = 0, 1, 2, 3$ (corresponding to $s, p, d, f$ subshells). The total number of individual orbitals is $n^2 = 4^2 = 16$ orbitals (one $4s$, three $4p$, five $4d$, and seven $4f$).