CHEMENG Comprehensive Reviewer: Electrochemistry & Nuclear Chemistry

Flashcards covering key definitions, reaction types, formulas, and concepts across Course Units 3 and 4: Electrochemistry and Nuclear Chemistry.

What is electrochemistry?

The interconversion of electrical energy and chemical energy, encompassing processes where spontaneous redox reactions produce electricity or electrical energy forces nonspontaneous reactions.

How are oxidation and reduction defined in terms of electron transfer and oxidation numbers?

Oxidation is the loss of electrons accompanied by an increase in oxidation number, whereas reduction is the gain of electrons accompanied by a decrease in oxidation number.

How do oxidizing agents and reducing agents differ during a redox reaction?

An oxidizing agent accepts electrons and undergoes reduction, causing another species to be oxidized. A reducing agent donates electrons and undergoes oxidation, causing another species to be reduced.

What are the standard oxidation number rules for free elements and monatomic ions?

The oxidation number of an uncombined free element is always $0$, while the oxidation number of a monatomic ion equals the ion's net electrical charge.

What are the additional steps required when balancing a redox reaction in a basic medium compared to an acidic medium?

Balance the reaction first under acidic conditions using $\text{H}_2\text{O}$ and $\text{H}^+$, then neutralize each $\text{H}^+$ by adding an equal number of $\text{OH}^-$ to both sides of the equation, combine $\text{H}^+$ and $\text{OH}^-$ into $\text{H}_2\text{O}$, and cancel identical water molecules from both sides.

How do voltaic (galvanic) cells and electrolytic cells differ in spontaneity, energy transformation, and electrode signs?

A voltaic cell is spontaneous, converts chemical energy to electrical energy, and has a negative anode and positive cathode. An electrolytic cell is nonspontaneous (requires external power), converts electrical energy to chemical energy, and has a positive anode and negative cathode.

What fundamental reaction occurs at the anode and cathode in all electrochemical cells?

Oxidation always occurs at the anode, and reduction always occurs at the cathode ("AN OX, RED CAT").

What is the function of a salt bridge in an electrochemical cell?

It maintains electrical neutrality by allowing inert electrolyte ions to migrate between half-cells (anions toward the anode, cations toward the cathode); electrons travel exclusively through the external wire, not through the salt bridge.

How is a standard cell potential ($E^\circ_{\text{cell}}$) calculated using tabulated reduction potentials?

$E^\circ_{\text{cell}} = E^\circ_{\text{cathode,red}} - E^\circ_{\text{anode,red}}$, where both potentials are taken directly from standard reduction potential tables without multiplying by stoichiometric coefficients.

What formula relates standard Gibbs free energy change ($\Delta G^\circ$) to standard cell potential ($E^\circ$)?

$\Delta G^\circ = -nFE^\circ$, where $n$ is the number of moles of electrons transferred in the balanced reaction and $F$ is Faraday's constant ($96,500\,\text{C/mol }e^-$).

What is the derived base-10 shortcut of the Nernst equation at $25^\circ\text{C}$ ($298.15\,\text{K}$)?

$E = E^\circ - \left(\frac{0.05916\,\text{V}}{n}\right)\log_{10}(Q)$, where $Q$ is the reaction quotient and $n$ is the number of electrons transferred.

Why does a concentration cell generate an electric potential despite having identical half-cell electrodes?

It generates a potential purely from a difference in electrolyte concentrations; while $E^\circ = 0$, the cell potential at $25^\circ\text{C}$ is $E = \left(\frac{0.05916\,\text{V}}{z}\right)\log_{10}\left(\frac{C_{\text{high}}}{C_{\text{low}}}\right)$.

How is the equilibrium constant ($K$) calculated from the standard cell potential ($E^\circ$) at $25^\circ\text{C}$?

$$\log_{10}(K) = \frac{nE^\circ}{0.05916\,\text{V}}$$

What is the distinction between active electrolysis and passive electrolysis?

In active electrolysis, the electrodes chemically participate in the redox reactions (such as a sacrificial dissolving anode); in passive electrolysis, inert electrodes conduct current without being chemically consumed.

What formula calculates the mass ($m$) deposited during electrolysis based on Faraday's law?

$m = \frac{ItM}{zF}$, where $I$ is current in amperes, $t$ is time in seconds, $M$ is molar mass in $\text{g/mol}$, $z$ is moles of electrons required per mole of product, and $F$ is Faraday's constant ($96,500\,\text{C/mol }e^-$).

What is the difference between a primary electrochemical cell and a secondary electrochemical cell?

A primary cell is non-rechargeable because its chemical reactants are irreversibly consumed, whereas a secondary cell is rechargeable because an external electrical current can reverse the discharge reaction.

What are the components of a lead-acid (lead storage) battery?

It utilizes a lead ($\text{Pb}$) anode, a lead dioxide ($\text{PbO}_2$) cathode, and a sulfuric acid ($\text{H}_2\text{SO}_4$) electrolyte solution, delivering approximately $2\,\text{V}$ per cell ($12\,\text{V}$ for six in series).

What are the chemical components of a commercial alkaline battery?

It contains a zinc ($\text{Zn}$) anode, a manganese dioxide ($\text{MnO}_2$) cathode material, and an alkaline potassium hydroxide ($\text{KOH}$) paste or gel electrolyte.

How do chemical reactions differ from nuclear reactions regarding atom identity and energy scale?

Chemical reactions rearrange valence electrons while keeping element identities constant and releasing relatively small amounts of energy; nuclear reactions alter atomic nuclei, convert elements or isotopes, and involve vastly larger energy releases.

What changes occur in mass number ($A$) and atomic number ($Z$) during alpha decay?

The parent nucleus emits an alpha particle ($^4_2\text{He}$), causing its mass number ($A$) to decrease by $4$ and its atomic number ($Z$) to decrease by $2$.

What nuclear transformation occurs during beta-minus ($\beta^-$) decay?

A neutron transforms into a proton while emitting an electron ($^0_{-1}e$ or $\beta^-$); the mass number ($A$) remains unchanged and the atomic number ($Z$) increases by $1$.

How do positron emission and electron capture alter the parent nucleus?

Both processes convert a proton into a neutron, leaving the mass number ($A$) unchanged while decreasing the atomic number ($Z$) by $1$.

What is gamma ($\gamma$) decay, and how does it affect $A$ and $Z$?

Gamma decay is the emission of a high-energy photon from an excited nucleus; it involves no change in either mass number ($A$) or atomic number ($Z$).

How is radioactive activity ($A$) related to the decay constant ($\lambda$) and sample quantity?

$A = \lambda N$, where $N$ is the number of radioactive nuclei and $\lambda$ is the decay constant in $\text{s}^{-1}$ to give activity in Becquerels ($1\,\text{Bq} = 1\,\text{decay/s}$).

What equation relates radioactive half-life ($t_{1/2}$) to the decay constant ($\lambda$)?

$$t_{1/2} = \frac{\ln(2)}{\lambda} \approx \frac{0.693}{\lambda}$$

What is the integrated first-order rate equation for radioactive decay?

$N = N_0 e^{-\lambda t}$ or $\ln\left(\frac{N}{N_0}\right) = -\lambda t$, where $N_0$ is the initial quantity of nuclei and $N$ is the quantity remaining at time $t$.

What is the basis of radiocarbon dating using carbon-14?

Living organisms maintain an equilibrium carbon-14 activity by atmospheric exchange; once an organism dies, carbon-14 intake stops and its activity decreases with a half-life of $5730\,\text{years}$, enabling determination of age via $t = \frac{\ln\left(\frac{A_0}{A}\right)}{\lambda}$.

How does the stable neutron-to-proton ($n/p$) ratio change between light and heavy nuclides?

For light stable nuclei ($Z < 20$), the stable $n/p$ ratio is close to $1.0$; as nuclei become heavier, extra neutrons are required to offset proton-proton electrostatic repulsion, pushing the stable $n/p$ ratio up to approximately $1.5$.

What are the nuclear magic numbers that convey extra nuclear stability?

The numbers $2$, $8$, $20$, $50$, $82$, and $126$ (with $28$ also recognized), which correspond to completely filled nuclear shells.

At what atomic number threshold are all known isotopes radioactive?

All isotopes with atomic numbers greater than $83$ ($Z > 83$) are radioactive.

What is mass defect ($\Delta m$) in an atomic nucleus?

The difference between the total combined rest mass of the separated individual nucleons and the actual mass of the bound nucleus: $\Delta m = [Z m_p + (A - Z) m_n] - m_{\text{nucleus}}$.

How is nuclear binding energy ($BE$) related to mass defect ($\Delta m$)?

$BE = \Delta m\,c^2$, where $\Delta m$ in kilograms multiplied by $c^2$ ($c = 3.00 \times 10^8\,\text{m/s}$) gives energy in Joules, or $\Delta m$ in atomic mass units multiplied by $931.5\,\text{MeV/u}$ gives energy in $\text{MeV}$.

Why is binding energy per nucleon ($BE/A$) the primary measure of nuclear stability?

Total binding energy grows with nucleus size, whereas binding energy per nucleon measures the average binding strength per nucleon, directly indicating how tightly bound the nucleus is.

What is the core distinction between nuclear fission and nuclear fusion?

Nuclear fission splits a heavy nucleus into lighter fragment nuclei and neutrons, whereas nuclear fusion combines two light nuclei into a heavier nucleus; both release energy when the resulting nuclides have a higher binding energy per nucleon.

How are Natural Uranium, Low Enriched Uranium (LEU), and Highly Enriched Uranium (HEU) categorized by U-235 percentage?

Natural Uranium contains about $0.711\%$ $\text{U-235}$; Low Enriched Uranium contains $0.711\%$ to $20\%$ $\text{U-235}$ (reactor-grade is about $3\text{--}5\%$); Highly Enriched Uranium contains greater than $20\%$ $\text{U-235}$.

What are the opposing roles of the moderator and the control elements in a nuclear reactor?

The moderator slows down fast neutrons to increase the probability of sustaining thermal fission, whereas control elements absorb neutrons to decrease the rate of or halt the nuclear chain reaction.

What is the step-by-step energy conversion sequence in a commercial nuclear power plant?

Nuclear binding energy released during fission produces thermal energy (heat) in water, thermal energy produces steam to drive mechanical energy in a turbine, and the turbine drives an electrical generator to output electrical energy.