Chemistry 9701/51 — October/November 2012

Background Concept

The chemical formula of an ionic compound gives the simplest whole-number ratio of atoms (or ions) present in the compound. By manipulating this ratio, we can determine the molar ratio of any constituent atoms per mole of another constituent. This is a fundamental skill in empirical formula and stoichiometry work.

Understanding the Question

The question asks for the number of moles of oxygen atoms that combine with exactly one mole of lead atoms in three specific lead oxides: PbO, Pb₃O₄, and PbO₂. This is a straightforward stoichiometric conversion from the empirical formula to a per-mole basis for a specific element.

Approach

Divide the subscript of oxygen by the subscript of lead in each formula to find the moles of O per mole of Pb.

Step-by-Step Reasoning

• For PbO: 1 O / 1 Pb = 1. The ratio is 1 : 1.
• For Pb₃O₄: 4 O / 3 Pb = 1.333... The ratio is 1 : 1.33.
• For PbO₂: 2 O / 1 Pb = 2. The ratio is 1 : 2.

Key Takeaways

Chemical formulas directly provide atom ratios. Converting to a per-mole basis for a specific element is a fundamental skill in empirical formula and stoichiometry work.

Common Mistakes

• Forgetting to divide by the lead subscript (e.g., saying Pb₃O₄ has 4 moles of O per mole of Pb instead of 4/3 = 1.33).
• Writing the ratio as O : Pb instead of Pb : O when the question asks for O per Pb.

Things to Be Careful About

• Ensure the ratio is expressed as "moles of oxygen per mole of lead" as requested. Pb₃O₄ gives 4/3 = 1.33, not 3/4 = 0.75.

Background Concept

A graph plotting the moles of one element against the moles of another in a series of compounds with the same ratio will produce a straight line passing through the origin. The gradient (slope) of this line is equal to the molar ratio of the y-axis element to the x-axis element.

Understanding the Question

You need to sketch three graphs showing the relationship between moles of oxygen (y-axis) and moles of lead (x-axis) for PbO, Pb₃O₄, and PbO₂. Each graph must be clearly labelled with axes and the compound name.

Approach

Use the molar ratios calculated in part (a) to determine the gradient of each line. Draw three straight lines from the origin with these gradients.

Step-by-Step Reasoning

1. Axes: Label the y-axis "Moles of oxygen atoms" and the x-axis "Moles of lead atoms". Mark the origin as (0, 0).
2. Gradients: From part (a), the moles of O per mole of Pb are:
   • PbO: 1 (gradient = 1)
   • Pb₃O₄: 1.33 (gradient = 1.33)
   • PbO₂: 2 (gradient = 2)
3. Lines: Draw three straight lines starting from the origin. The line with the steepest slope corresponds to PbO₂, the middle to Pb₃O₄, and the least steep to PbO. Label each line clearly with its chemical formula.

Key Takeaways

Linear graphs through the origin are a powerful way to visualise stoichiometric ratios. The gradient directly gives the molar ratio of the variables plotted.

Common Mistakes

• Drawing curves instead of straight lines.
• Forgetting to label the axes with both the quantity and the unit (or just the quantity if units are implied, but here "moles" is the unit).
• Incorrectly ordering the lines (e.g., putting PbO as the steepest).

Things to Be Careful About

• Ensure the lines are straight and pass through the origin (0,0). A line not passing through the origin would imply a constant amount of oxygen regardless of lead, which is chemically incorrect for these oxides.

Background Concept

The reduction of a metal oxide by hydrogen gas requires a setup where hydrogen is generated, purified (if necessary, though not strictly required for this level), passed over the heated oxide, and any excess hydrogen is safely managed. Hydrogen is highly flammable and forms explosive mixtures with air, so safety is paramount.

Understanding the Question

You must draw a diagram showing:
(i) How hydrogen is prepared (reagents named).
(ii) How the lead oxide is heated.
(iii) How excess hydrogen is dealt with safely.
All using standard school/college laboratory equipment.

Approach

1. Generation: Use a reactive metal (Mg, Al, Zn, Fe) and a dilute acid (HCl, H₂SO₄) in a flask.
2. Reaction: Pass the gas through a hard glass tube containing the oxide, heated by a Bunsen burner.
3. Safety: Burn off the excess hydrogen at the end of the tube or collect it.

Step-by-Step Reasoning

• Hydrogen generation: A conical flask with a thistle funnel (or dropping funnel) and delivery tube. Inside: magnesium (or zinc/aluminium/iron) and dilute hydrochloric acid (or dilute sulfuric acid). The reaction is: Mg + 2HCl → MgCl₂ + H₂.
• Reaction: The delivery tube connects to a hard glass tube (combustion tube) placed horizontally. The tube contains the lead oxide sample. A Bunsen burner heats the tube where the oxide is located. The reaction is: PbO + H₂ → Pb + H₂O.
• Excess hydrogen: The outlet from the hard glass tube is directed to a Bunsen burner flame. The excess hydrogen burns safely: 2H₂ + O₂ → 2H₂O. Alternatively, it could be led away from the apparatus or collected in a gas syringe, but burning is the most common school method.
• Labels: Clearly label the flask, reagents, hard glass tube, lead oxide, Bunsen burners, and the flow of gas.

Key Takeaways

Apparatus diagrams for gas-solid reactions must clearly show generation, reaction, and safety/disposal. Labeling reagents and apparatus is crucial for full marks.

Common Mistakes

• Forgetting to name the reagents in the hydrogen generator (e.g., just saying "acid" without specifying dilute, or not naming the metal).
• Not showing how excess hydrogen is dealt with (a common safety requirement).
• Drawing a closed system where gas has nowhere to go (explosion risk).

Things to Be Careful About

• Ensure the diagram shows a flow of gas from generation to reaction to disposal. Do not draw a closed system. Label all key components and reagents.

Background Concept

To determine the empirical formula of an oxide, you need the masses (or moles) of the metal and the oxygen. In a reduction experiment, the initial mass is the oxide, and the final mass is the metal. The difference is the mass of oxygen. The molar volume of a gas at a given temperature and pressure (24.0 dm³ mol⁻¹ at 25°C) allows conversion between moles and volume.

Understanding the Question

You must design the experiment:
(i) Choose a suitable mass of oxide (1-25 g).
(ii) Describe how to ensure the reaction is complete.
(iii) Calculate the minimum volume of H₂ needed (assuming PbO for calculation).
(iv) Explain how to use the data to identify the oxide.

Approach

1. Select a mass that gives a manageable volume of gas (not too small to measure accurately, not too large to be unsafe or impractical).
2. Describe the "heating to constant mass" technique.
3. Use stoichiometry and the ideal gas equation (or molar volume) to find the H₂ volume.
4. Outline the data processing: mass loss → moles O; final mass → moles Pb → ratio.

Step-by-Step Reasoning

(i) Suitable mass: A mass between 1 g and 25 g is appropriate. Too small (<1 g) gives a small mass loss that is hard to measure accurately on a standard balance. Too large (>25 g) requires a large volume of hydrogen and a large apparatus. Let's choose 2.0 g for the calculation.

(ii) Completeness: To ensure all the oxide is reduced, you must heat to constant mass. This means heating the sample, cooling it (in a desiccator to prevent re-oxidation), weighing it, then reheating, cooling, and weighing again. If the mass is the same, no more oxygen is being removed, so the reaction is complete.

(iii) Calculation (for 2.0 g PbO):

• Molar mass of PbO = 207.0 + 16.0 = 223.0 g mol⁻¹.
• Moles of PbO = 2.0 / 223.0 = 0.00897 mol.
• Equation: PbO + H₂ → Pb + H₂O. Ratio is 1:1.
• Moles of H₂ required = 0.00897 mol.
• Volume of H₂ = moles × molar volume = 0.00897 × 24.0 = 0.215 dm³ = 215 cm³.
  (If you chose a different mass, e.g., 5.0 g, volume = 538 cm³. The mark is for the method and units.)

(iv) Reaching a conclusion:

• Moles of Pb = final mass of lead / 207.0.
• Mass of O = initial mass of oxide - final mass of lead.
• Moles of O = mass of O / 16.0.
• Calculate the ratio moles Pb : moles O by dividing both by the smaller value.
• Compare the resulting ratio (e.g., 1 : 1.33) to the theoretical ratios calculated in part (a) to identify the oxide.

Key Takeaways

Heating to constant mass is a standard technique to ensure complete reaction. Calculating gas volumes requires careful use of molar mass and molar volume. Data processing involves converting masses to moles and finding simplest whole-number ratios.

Common Mistakes

• Choosing a mass that is too small (e.g., 0.1 g) or too large (e.g., 100 g).
• Forgetting to cool in a desiccator (lead can re-oxidise in air if cooled openly).
• Calculation errors in the volume (e.g., forgetting to convert dm³ to cm³ or using the wrong molar volume).
• Not describing how to process the data to get the ratio (just saying "compare masses").

Things to Be Careful About

• The calculation in (iii) assumes PbO. If you chose a different mass, show the full working for that mass. Units are required for the volume (dm³ or cm³).
• In (ii), "heating until no more mass change" is acceptable, but "heating to constant mass" is the precise technical term.

Background Concept

Safety in chemistry is about identifying hazards (substances or conditions that can cause harm) and implementing precautions (actions to minimise the risk). Common hazards in reduction experiments include flammable gases (hydrogen), toxic metals/oxides (lead), corrosive reagents (acids), and hot equipment.

Understanding the Question

You must state one hazard from the experiment and describe a specific precaution to minimise the risk. The question provides a table of hazards (lead oxides are toxic, hydrogen is explosive).

Approach

Select a hazard (hydrogen explosion is the most critical) and link it to a standard safety procedure for hydrogen reduction experiments.

Step-by-Step Reasoning

• Hazard: Hydrogen is highly flammable and forms explosive mixtures with air (4-74% by volume). If air is present in the apparatus when hydrogen is ignited or heated, an explosion can occur.
• Precaution: Before heating the lead oxide or lighting the flame to burn excess hydrogen, you must expel the air from the apparatus. This is done by allowing hydrogen to flow through the system for a few minutes (often tested by collecting a test tube of gas and doing a "pop test" to ensure it's pure hydrogen).
• Alternative hazards/precautions:
  • Lead/lead oxide is toxic/harmful by inhalation. Precaution: Use a fume cupboard or wear a mask/respirator.
  • Dilute acids are corrosive/irritants. Precaution: Wear chemically resistant gloves and eye protection.
  • The hard glass tube becomes very hot. Precaution: Allow to cool before handling, or use heat-resistant gloves/tongs.

Key Takeaways

Always link a specific hazard to a specific, practical precaution. Vague answers like "be careful" do not score.

Common Mistakes

• Stating a hazard not related to the experiment (e.g., "electricity is dangerous").
• Giving a vague precaution (e.g., "wear safety glasses" for hydrogen explosion).
• Not mentioning the specific action (e.g., "expel air" rather than just "be careful with hydrogen").

Things to Be Careful About

• The mark scheme accepts multiple valid hazard/precaution pairs. Choose the most prominent one (hydrogen explosion is usually the best choice for this type of experiment). Ensure the precaution directly addresses the hazard.

Background Concept

A well-designed data table should include all raw measurements, intermediate calculations, and final derived values needed to reach the conclusion. Units are essential for recorded data, while calculated mole ratios are dimensionless.

Understanding the Question

You need to draw up a table to record data and calculate values to determine the formula of the oxide graphically (or by ratio). The table must have appropriate headings and units.

Approach

The table needs columns for the initial mass (oxide), final mass (lead), the difference (oxygen), the moles of each, and the final ratio. Include units where appropriate.

Step-by-Step Reasoning

1. Mass of lead oxide (g): Initial mass of the sample before reduction. Unit: grams (g).
2. Mass of lead (g): Final mass of the solid after reduction to constant mass. Unit: grams (g).
3. Mass of oxygen (g): Calculated by subtracting the mass of lead from the mass of lead oxide (col 1 - col 2). Unit: grams (g).
4. Moles of lead: Calculated by dividing the mass of lead by the atomic mass of lead (207.0 g mol⁻¹). No units (or mol, but often left blank for ratios).
5. Moles of oxygen: Calculated by dividing the mass of oxygen by the atomic mass of oxygen (16.0 g mol⁻¹).
6. Ratio (Pb : O): Divide moles of Pb and moles of O by the smaller value to get the simplest whole-number ratio. No units.

Note: The question mentions "determine graphically the formula". If plotting a graph (as in part b), you might plot moles of O vs moles of Pb, and the gradient gives the ratio. The table should support this.

Key Takeaways

Data tables must be logical, include units for raw data, and show the path from raw data to final conclusion. Calculated columns should be clearly labelled.

Common Mistakes

• Forgetting units in the headings (e.g., "Mass of lead" instead of "Mass of lead (g)").
• Including unnecessary columns or missing key calculated columns (like moles of oxygen).
• Not showing how the calculated values are derived (optional in the table, but good practice to include formulas or just clear headings).

Things to Be Careful About

• The mark scheme requires at least 5 of the 6 columns to be fully correct with units to get 2 marks. Ensure your headings are clear and units are included for mass columns. Moles columns may not need units, but the ratio definitely doesn't.