DGD #6 (mardi le 27 octobre)

Summary

The instructor reviews a 2019 midterm to show which topics and problem-solving approaches are relevant to the upcoming test and final exam. The main advice is to practise with older exams, keep units and signs consistent, and check whether answers make chemical sense—not just whether a calculator produced them.

Course and exam scope

• The upcoming test covers material from readings 8–10. Some questions on the old midterm came from material outside this scope, so not every old-exam question will be relevant.
• Balancing redox reactions in basic solution is reserved for the final exam. The instructor recommends watching the referenced podcast and practising past final-exam questions well in advance.
• Older exams are useful practice, although questions may use different substances or values.
• Test questions may cover thermodynamics, equilibrium, ICE tables, quadratic equations, gravimetric analysis, titration stoichiometry, and short conceptual topics.

Thermodynamics and the van ’t Hoff equation

The instructor works through a multi-part equilibrium and thermodynamics problem and explains how to check the results.

Key relationships:

[ \Delta G^\circ = -RT\ln K ]

[ \Delta G = \Delta G^\circ + RT\ln Q ]

[ \Delta G^\circ = \Delta H^\circ - T\Delta S^\circ ]

[ \ln\left(\frac{K_2}{K_1}\right) = -\frac{\Delta H^\circ}{R}\left(\frac{1}{T_2}-\frac{1}{T_1}\right) ]

Suggested approach

1. Given equilibrium constants at two temperatures, use the van ’t Hoff equation to find (\Delta H^\circ).
2. Use a known (K) and its corresponding temperature to find (\Delta G^\circ). Keep each temperature paired with the correct equilibrium constant.
3. Use (\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ) to find (\Delta S^\circ), using (\Delta G^\circ) at the same temperature.
4. To find (K) at a third temperature, first calculate (\Delta G^\circ) at that temperature, then use (\Delta G^\circ = -RT\ln K).
5. To find the temperature at which (K) reaches a target value, substitute the target (K) and unknown temperature into the van ’t Hoff equation, then solve for the reciprocal temperature.

Checks and common pitfalls

• Use kelvin in temperature-dependent equations.
• Keep units consistent. In particular, convert kilojoules to joules when using (R = 8.3145\ \mathrm{J\,mol^{-1}\,K^{-1}}).
• Check negative signs and the order of (K_1), (K_2), (T_1), and (T_2).
• Predict the expected sign when possible:
  • A liquid becoming a gas is endothermic and increases entropy.
  • If (K) increases as temperature rises, the reaction is endothermic and (\Delta H^\circ) is positive.
  • If (K) decreases as temperature rises, the reaction is exothermic and (\Delta H^\circ) is negative.
• As a sign check, (K < 1) corresponds to positive (\Delta G^\circ), while (K > 1) corresponds to negative (\Delta G^\circ).
• Keep extra precision during intermediate calculations and round the final answer to the appropriate number of significant figures.

Using (\Delta G), (K), and (Q) to find a concentration

For a reaction such as (2A \rightleftharpoons B + 2C), the instructor demonstrates how to use a given (\Delta G), equilibrium constant, and known concentrations to determine an unknown concentration.

1. Calculate (\Delta G^\circ) from the given equilibrium constant using (\Delta G^\circ = -RT\ln K).
2. Convert all energy values to consistent units.
3. Rearrange (\Delta G = \Delta G^\circ + RT\ln Q) to find (\ln Q), then exponentiate to obtain (Q).

4. Write (Q) using the reaction’s stoichiometric coefficients. For this example: [ Q = \frac{[B][C]^2}{[A]^2} ]

5. Substitute the known concentrations and solve for the unknown concentration, taking the square root if the unknown is squared.

6. Check that the result is physically plausible and has appropriate significant figures.

A concentration far outside the scale of the other given concentrations may indicate a calculation or unit error.

Equilibrium pressure and an ICE table

For (A + 2B \rightleftharpoons C + 3D), the example begins with only (A) and (B), at equal partial pressures and a total pressure of (20\ \mathrm{atm}). Each therefore begins at (10\ \mathrm{atm}). Given the equilibrium pressure of (B), the reaction change (x) can be found and used to calculate the other equilibrium pressures.

The general ICE-table procedure is:

• Start with the initial amounts or pressures.
• Use negative changes for reactants and positive changes for products.
• Multiply (x) by each species’ coefficient in the balanced equation.
• Use the given equilibrium value to solve for (x).
• Substitute (x) to obtain all equilibrium values.
• Calculate (K_p) using product pressures over reactant pressures, each raised to its stoichiometric coefficient.
• Use the equilibrium constant to find (\Delta G^\circ).

The instructor cautions against confusing a species’ initial amount with its stoichiometric coefficient. The problem specifies the initial pressures; the coefficients determine how each species changes.

ICE tables and quadratic equations

For an example reaction (A + B \rightleftharpoons 2C), the instructor sets up equilibrium concentrations as:

[ [A]_{\mathrm{eq}} = [A]_0 - x ]

[ [B]_{\mathrm{eq}} = [B]_0 - x ]

[ [C]_{\mathrm{eq}} = [C]_0 + 2x ]

Substituting these expressions into the equilibrium-constant expression may produce a quadratic equation.

• Solve for both roots, then reject any root that gives an impossible negative concentration.
• As a check, substitute the equilibrium concentrations back into the expression for (K). The result should reproduce the given equilibrium constant.
• Report no more significant figures than the input data supports.

Gravimetric analysis and titration stoichiometry

For a gravimetric example, sodium hydroxide reacts with excess zinc nitrate to form solid zinc hydroxide.

1. Convert the mass of precipitate to moles using its molar mass.
2. Use the balanced reaction to relate moles of precipitate to moles of hydroxide. Each mole of (\mathrm{Zn(OH)_2}) corresponds to two moles of (\mathrm{OH^-}).
3. Divide the hydroxide moles by the original solution volume in litres to find ([\mathrm{OH^-}]).

Finding the hydroxide concentration is within the stated material. Calculating pH belongs to a later reading and is not part of the test’s scope.

For acid–base titrations, match the total moles of (H^+) and (OH^-):

• Multiply acid moles by the number of ionizable protons per acid molecule.
• Multiply base moles by the number of hydroxide ions per base formula unit.
• A monoprotic acid or monohydroxide base uses a factor of 1. Diprotic and triprotic acids, and bases with multiple hydroxides, require the corresponding factor.

Short conceptual questions

Students may be asked to identify:

• Brønsted acids (proton donors) and bases (proton acceptors)
• Oxidizing agents (electron acceptors) and reducing agents (electron donors)
• Oxidation states
• The precipitate formed in a precipitation reaction

For oxidation states, the instructor highlights these common rules: oxygen is generally (-2), fluorine is (-1), and hydrogen is generally (+1). Determine the remaining oxidation state so the total matches the charge of the molecule or ion.

For precipitation questions, sodium compounds and nitrates are treated as soluble in the examples. The other ions are therefore the likely candidates to form the precipitate. Balance ionic charges when writing the formula; for example, ions with charges (+2) and (-3) require a (3:2) ratio.

Exam technique and grading

• Check whether calculated signs, magnitudes, and units make sense.
• Use joules or kilojoules consistently, and include appropriate units for entropy and other quantities.
• The instructor says either kelvin or Celsius may be accepted for a temperature answer if the question does not specify a scale, although calculations require kelvin.
• Past-exam feedback can help identify where marks were lost. The instructor recommends using the feedback process if the written explanation supports a higher score.

Speakers and sources featured

• Instructor/lecturer: The video’s channel identifies the instructor as Alain St-Amant. He is the only audible speaker in the subtitles.
• Students: Unnamed students’ questions are referenced, apparently through chat; they are not individually identified.
• Materials discussed: A 2019 midterm, older exams (including final-exam examples), course readings and lecture notes, and a referenced podcast on balancing redox reactions in basic solution.