مراجعة شاملة للوحدة الاولى | بكالوريا 2026

Unit One: Monitoring Chemical Reactions over Time

This lesson reviews the main ideas in Unit One: redox reactions, progress tables, limiting reactants, graph interpretation, experimental monitoring methods, reaction rates, and kinetic factors. Much of the unit builds on earlier knowledge. Success depends on using data correctly, understanding experimental protocols, and practising with exercises.

1. Redox Reactions and Half-Equations

Exercises may provide redox couples, a complete reaction equation, or reactants from which the equation must be constructed. In each case:

• Identify the actual reactants first. Ions that do not participate are spectator ions.
• Write the oxidation and reduction half-equations, then combine them to obtain the overall reaction.
• In an acidic aqueous medium, balance each half-equation as follows:
  1. Balance the main element other than oxygen and hydrogen.
  2. Balance oxygen using water.
  3. Balance hydrogen using (H^+), or (H_3O^+) when hydronium is specified in the exercise or redox couples.
  4. Balance electrical charge by adding electrons to the side with the greater positive charge.
• An oxidant gains electrons; a reductant loses electrons.
• Before adding the half-equations, multiply them as needed so that the numbers of electrons are equal and cancel.

2. The Progress Table and Amount of Substance

The progress table is central to the unit. Calculations of concentrations, masses, gas volumes, rates, and limiting reactants depend on it.

• Products begin at zero if initially absent and increase according to their stoichiometric coefficients.
• Reactants decrease according to their coefficients.
• In these aqueous reactions, water is treated as being in excess and is generally not treated as a limiting reactant.
• At the final state, the amount of the limiting reactant is zero. If both reactants are exhausted together, the initial mixture is stoichiometric.

Common amount-of-substance relationships include:

• Solid: (n = \frac{m}{M})
• Solution: (n = CV)
• Gas: (n = \frac{PV}{RT}), or (n = \frac{V}{V_m}) when molar volume is used
• Liquid organic compound: (n = \frac{\rho V}{M})

Use consistent units. In particular, distinguish between the total reaction-mixture volume and the gas volume.

Mixture Volumes and Purity

• A solid added to a solution does not normally add to the solution volume; use the volume of the solution as the mixture volume.
• When two solutions are mixed, the total volume is generally the sum of their volumes.
• In a self-decomposition reaction, there is one reactant, so the mixture volume is the volume of that solution. The teacher describes this as a case where the same substance acts as both oxidant and reductant.
• If a solid sample is impure, only its pure portion reacts. Use the pure mass in the progress table, then compare it with the impure sample mass to calculate the purity percentage.

• For a commercial solution, the teacher gives the relation [ P = \frac{C_0M}{10d}, ] where (C_0) is the solution concentration, (M) is the molar mass, and (d) is the density. Rearrange the relation when the unknown is the concentration.

• Distinguish the concentration of the whole solution from the concentration of a particular species. The concentration of an ion in the mixture depends on its amount and may reflect the stoichiometric coefficient of the dissolved compound.

3. Finding the Limiting Reactant and (x_{\max})

The limiting reactant is consumed completely and stops the reaction. If both reactants are consumed in stoichiometric proportions, the mixture is stoichiometric.

Using Calculations

1. If all initial quantities are known, calculate a candidate (x_{\max}) for each reactant by setting that reactant’s final amount to zero.
2. If the candidate values are equal, the mixture is stoichiometric.
3. If they differ, the smaller candidate is the actual (x_{\max}); the reactant that produced it is limiting.
4. If some reactant data are missing, use the available data and final amounts to establish which reactant remains in excess. Do not simply assume that the unknown reactant is limiting; justify the conclusion using the table or other information.

Using Graphs

• From a graph of reaction progress (x) against time, read (x_{\max}) at the plateau.

• From a graph of a reactant’s amount, use [ x_{\max} = \frac{n_0 - n_f}{\nu}, ] where (\nu) is that reactant’s stoichiometric coefficient. If the amount reaches zero, (n_f = 0).

• If the graph shows another quantity, such as mass, concentration, or gas volume, convert it to an amount of substance or relate it to (x) using the progress table.

• Read the initial and final states from the direction of change and the role of each species: reactants decrease, while products increase. Do not assume that a marked point is the final state without checking the graph.

4. Deriving Relationships and Matching Graphs

To derive a relationship between two quantities in the progress table:

1. Write an expression for the first quantity using the progress table.
2. Write an expression for the second quantity. For example, concentration is (n/V_{\text{total}}), mass is (nM), and gas volume can be related to (n).
3. Rearrange the second expression to isolate (x).
4. Substitute that expression for (x) into the first quantity’s expression.

For a straight-line graph, compare the derived theoretical relationship with the line equation (y = ax + b):

• (a) is the slope.
• (b) is the vertical-axis intercept.
• Matching the graph’s slope and intercept to the theoretical expression can reveal unknown quantities such as total volume or initial amount.

5. Methods for Temporal Monitoring

For each method, know when it can be used, its experimental conditions and protocol, and how to derive the relationship between the measured quantity and (x).

Conductimetry

• Conductimetry is suitable when ions are present in the reaction mixture.
• Keep the temperature constant because ionic conductivities depend on temperature.

• Kohlrausch’s law sums the contributions of all ions present, including spectator ions: [ \sigma = \sum_i \lambda_i[i]. ]

• To derive conductivity as a function of progress:

  1. Write Kohlrausch’s law for all ions.
  2. Express each ion concentration as its amount of substance divided by the total volume.
  3. Obtain each amount from the progress table.
  4. Substitute and collect the constant term and the terms involving (x).
• Conductance (G) is related to conductivity through the cell geometry. The lesson writes (G = K\sigma), with the cell constant based on plate area and separation. Pay attention to units and convert centimetres to metres when required.
• A conductivity–time graph can provide the initial and final conductivity. A straight-line graph can also be analysed by matching its slope and intercept to the derived relationship.

Titration

Keep the main reaction and the titration reaction separate:

• The main reaction is the reaction being monitored. Its progress table, limiting reactant, rate, and half-life are considered.
• The titration reaction is used to measure the amount of a selected reactant or product in a sample. It is treated as fast and does not use the main reaction’s progress table.

Typical procedure:

1. Divide the reaction mixture into equal-volume samples. The number of samples is (V_{\text{total}}/V_0), where (V_0) is the volume of one sample.
2. Quench each sample to stop or strongly slow the main reaction. Chemical quenching involves adding cold water and ice to the sample; physical quenching involves placing it in an ice-water bath.
3. Titrate the sample with a solution of known concentration, adding it until the equivalence point is reached.
4. At equivalence, use the stoichiometric proportions of the titration reaction to relate the amounts of its reactants.
5. To derive a relationship with the main reaction’s progress (x), obtain the amount of the measured species from the main reaction’s progress table. For a single sample, account for the fact that it contains only a fraction of the total mixture.

Quenching does not change the equivalence volume because the amount of the species in the sample is conserved during titration. Its purpose is to halt the main reaction while the sample is analysed.

Pressure Measurement

• This method requires a gas and, in the setup described, constant temperature and volume.

• Use the ideal-gas law: [ P = \frac{nRT}{V}. ] Obtain (n) from the progress table and substitute it to relate pressure to (x).

• If the recorded pressure includes a nonzero initial pressure (P_0), distinguish the gas’s pressure contribution from the total measured pressure. The gas contribution is (P_t - P_0).

• Use consistent units for pressure, volume, temperature, and (R).

Gas-Volume Measurement

• This method requires a gas and, in the setup described, constant pressure and temperature.
• Determine the gas volume from the information given. It may be stated directly, found by subtracting the reaction-mixture volume from the flask volume, or equal to the flask volume if the mixture volume is negligible.
• Relate gas volume to the amount of gas formed using the ideal-gas law or molar volume, then obtain that amount from the progress table.

6. Reaction Rates and Graph Tangents

The reaction rate is distinct from the rate of disappearance or formation of an individual species:

• Reaction rate: (v = \frac{dx}{dt})
• Volumetric reaction rate: (v_{\text{vol}} = \frac{1}{V_{\text{total}}}\frac{dx}{dt})
• A species’ disappearance rate is written with a negative sign; its formation rate is positive.
• The rate for a species and the reaction rate are related through that species’ stoichiometric coefficient.

When a graph gives a quantity other than (x):

1. Write the requested rate formula.
2. Derive a relationship between (x) and the quantity plotted on the graph.
3. Differentiate that relationship with respect to time.
4. Substitute the derivative into the rate formula.
5. Find the derivative from the slope of the tangent at the required time. Calculate the tangent’s slope as the change in vertical coordinate divided by the change in time.

7. Kinetic Factors

• Increasing temperature increases the reaction rate, attributed to more effective collisions. It makes the reaction reach its final state sooner but does not change the final extent or final composition in the examples discussed.
• Increasing the concentration of a non-limiting reactant increases the rate but does not change the final extent in the cases described.
• Dilution lowers concentrations and slows the reaction, so the final state takes longer to reach. In the pressure-measurement setup discussed, dilution also changes the available gas space: the teacher explains that the gas volume decreases and the final pressure can therefore be higher. When interpreting a graph, distinguish the reaction’s slower progress from any change in the measured final pressure.

8. Study and Exam Advice

The teacher recommends using difficult tests to identify gaps rather than judging progress only by the score. Review questions that were not understood, practise applying the methods to exercises, and use the detailed lessons and experimental-protocol summaries for further study. A difficult test is presented as an opportunity to learn, not as a prediction of the final baccalaureate result.

Speakers and Sources

• Salma is the physics teacher and main speaker.
• Brief, indistinct off-camera voices are audible during a short interruption; they are not identified in the subtitles.
• The speaker references Unit One exercise data and graphs, including an example associated with a past baccalaureate exercise, as well as her other detailed lessons and experimental-protocol summaries on her YouTube channel. No other named speaker or guest is identified.