Chemistry 9701/51 — October/November 2013

Cambridge A-Level · Planning, Analysis and Evaluation · worked solutions for every part, with the mark scheme

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Topics Analysis, Conclusions and Evaluation · Planning

Q1Analysis, Conclusions and EvaluationPlanningFree sample

Ammonium nitrate, $\text{NH}_4\text{NO}_3$ , is soluble in water (approximately $2.5\text{ mol}/100\text{ g}$ at $25\text{ }^\circ\text{C}$ ). The molar enthalpy of solution of a solid is defined as the enthalpy change when one mole of the solid is dissolved in water.

\text{NH}_4\text{NO}_3(\text{s}) \rightleftharpoons \text{NH}_4^+(\text{aq}) + \text{NO}_3^-(\text{aq}) \quad \Delta H_{\text{soln}} = +26.5\text{ kJ mol}^{-1}

(a)

(i)

Predict how the temperature of water, initially at $25\text{ }^\circ\text{C}$ , would change as ammonium nitrate is dissolved. Explain this prediction in terms of lattice energy and the enthalpy of hydration of ions.

Prediction of the temperature change:

Explanation:

DifficultyMedium-Easy

Worked solution

Answer

Prediction: The temperature would decrease.

Explanation: The lattice enthalpy (lattice formation enthalpy) is more negative/exothermic than the sum of the enthalpies of hydration of the ions. Therefore, the overall enthalpy change of solution is endothermic, causing the temperature of the surroundings (the water) to decrease.

Final answer

Temperature decreases; lattice enthalpy is more exothermic than the sum of hydration enthalpies.

Detailed explanation

Background Concept

When an ionic solid dissolves in water, two main enthalpy changes occur: the breaking of the ionic lattice (lattice dissociation enthalpy, endothermic) and the hydration of the resulting gaseous ions (hydration enthalpy, exothermic). The overall enthalpy of solution is the sum of these two values. If the endothermic lattice breaking requires more energy than is released by hydration, the overall process is endothermic, and the temperature of the solution falls.

Understanding the Question

You are asked to predict the temperature change when ammonium nitrate dissolves in water at 25 °C, and to explain this using lattice energy and hydration enthalpy. The question provides the enthalpy of solution as +26.5 kJ mol⁻¹, indicating an endothermic process.

Approach

Since ΔH_soln is positive, the process is endothermic. An endothermic process absorbs heat from the surroundings, meaning the temperature of the water will decrease. To explain this in terms of lattice and hydration enthalpies, recall that ΔH_soln = ΔH_lattice_dissociation + ΔH_hydration. For ΔH_soln to be positive, the endothermic lattice dissociation enthalpy must be greater in magnitude than the exothermic hydration enthalpy. Equivalently, the exothermic lattice formation enthalpy (often just called 'lattice enthalpy' in some contexts) is more negative than the sum of the hydration enthalpies.

Step-by-Step Reasoning

Prediction: The given ΔH_soln is +26.5 kJ mol⁻¹. A positive enthalpy change means the reaction is endothermic. Endothermic processes absorb thermal energy from the surroundings, so the temperature of the water will decrease.
Explanation: The enthalpy of solution is the sum of the energy required to break the ionic lattice and the energy released when the ions are hydrated. For the overall process to be endothermic, the energy required to break the lattice must exceed the energy released by hydration. In terms of exothermic/negative values, the lattice enthalpy (the energy released when the lattice forms) is more negative/exothermic than the sum of the enthalpies of hydration. Thus, the net energy change is endothermic.

Key Takeaways

A positive enthalpy of solution indicates an endothermic process where the temperature of the solvent decreases. This occurs when the lattice dissociation energy is greater than the hydration energy released.

Common Mistakes

Stating that 'lattice energy is higher' without specifying whether you mean the endothermic dissociation value or the exothermic formation value. Always clarify the sign or direction (e.g., 'more negative' or 'more exothermic').
Confusing the system and surroundings: the solution (system) absorbs heat, so the temperature of the water (surroundings initially) decreases.

Things to Be Careful About

Use the exact terminology from the mark scheme: 'lattice enthalpy is more negative/exothermic than the sum of the enthalpies of hydration'.
Ensure your prediction directly matches the sign of the given ΔH_soln.

Techniques used

predict temperature change from enthalpy termscompare lattice enthalpy and hydration enthalpy

(ii)

In the space below, sketch a graph to show your prediction of temperature change with concentration. Use two labelled axes and include an origin.

DifficultyMedium-Easy

Worked solution

Answer

Final answer

See diagram

Detailed explanation

Background Concept

When plotting experimental or predicted data, the independent variable (concentration) goes on the x-axis and the dependent variable (temperature change or temperature) goes on the y-axis. The origin (0,0) must be included if the variables can logically be zero. For temperature change, at zero concentration, the change is zero. For absolute temperature, at zero concentration, the temperature is the initial temperature (25 °C).

Understanding the Question

You must sketch a graph showing the predicted relationship between temperature change (or temperature) and concentration of ammonium nitrate, based on your answer in part (a)(i). The graph must have two labelled axes and include an origin.

Approach

Since the temperature decreases as concentration increases, the graph of 'temperature change' (as a positive magnitude of decrease) will slope upwards from the origin, or the graph of 'temperature' will slope downwards from 25 °C. Choose one consistent representation and ensure axes are correctly labelled.

Step-by-Step Reasoning

Axes selection: Let the x-axis be 'concentration' (or 'concentration of ammonium nitrate') and the y-axis be 'temperature change' (or 'temperature').
Origin: If plotting 'temperature change' (as a positive value representing the fall), the origin (0,0) is correct because at zero concentration, there is zero temperature change. If plotting 'temperature', the y-intercept should be 25 °C at zero concentration.
Shape: As concentration increases, the temperature falls more. Thus, 'temperature change' (magnitude of fall) increases with concentration (upward slope from origin), or 'temperature' decreases with concentration (downward slope from 25 °C).
Labels: Ensure both axes have clear labels with units or descriptive names, and the origin is marked.

Key Takeaways

Sketch graphs must clearly show the relationship predicted. Consistency between the y-axis variable (temperature vs. temperature change) and the slope direction is critical.

Common Mistakes

Forgetting to include the origin when plotting 'temperature change'.
Mixing up the axes (putting temperature on the x-axis).
Not labelling the axes with appropriate terms or units.

Things to Be Careful About

The question asks for a 'sketch graph', so exact scaling is not required, but the correct trend (slope direction) and intercepts must be shown.
Ensure the origin is explicitly included as requested.

Techniques used

sketch a graph from a predictionlabel axes and origin

(b)

If you were to carry out an experiment to investigate how the temperature change of the solution varies as the concentration changes name,

(i)

the independent variable,

DifficultyEasy

Worked solution

Answer

Independent variable: Concentration (of ammonium nitate) / concentration change.

Final answer

Concentration

Detailed explanation

Background Concept

In an experiment, the independent variable is the one that is deliberately changed or controlled by the experimenter to test its effect on the dependent variable. Here, the goal is to investigate how temperature change varies as concentration changes.

Understanding the Question

You are asked to name the independent variable in an experiment designed to see how temperature change varies with concentration.

Approach

The question explicitly states the aim: 'investigate how the temperature change... varies as the concentration changes'. The variable being changed is the concentration.

Step-by-Step Reasoning

The experiment varies the concentration of ammonium nitrate solutions.
Therefore, the independent variable is the concentration (or concentration change) of the ammonium nitrate solution.

Key Takeaways

The independent variable is what you change; the dependent variable is what you measure.

Common Mistakes

Stating 'mass of ammonium nitrate' as the independent variable. While mass is changed, the ultimate variable of interest being plotted against temperature change is concentration. Mass is a means to achieve different concentrations.

Things to Be Careful About

Use the exact term 'concentration' as it is the variable being investigated in relation to temperature change.

Techniques used

identify independent variable

(ii)

the dependent variable.

DifficultyEasy

Worked solution

Answer

Dependent variable: Temperature change (or decrease in temperature).

Final answer

Temperature change

Detailed explanation

Background Concept

The dependent variable is the one that is measured or observed in response to changes in the independent variable. It 'depends' on the independent variable.

Understanding the Question

You are asked to name the dependent variable in the experiment described in part (b).

Approach

The aim is to investigate how the 'temperature change' varies. Therefore, temperature change is the measured outcome.

Step-by-Step Reasoning

The experiment measures the effect of concentration on the thermal response of the solution.
The quantity being measured is the temperature change (or the decrease in temperature).
This is the dependent variable.

Key Takeaways

Always identify what is being measured as the dependent variable.

Common Mistakes

Stating 'final temperature' instead of 'temperature change'. The prediction in (a) is about the change in temperature, so the dependent variable should be the change (final - initial), not just the final value.

Things to Be Careful About

Ensure you use the term 'temperature change' or 'decrease in temperature' to match the mark scheme and the prediction made earlier.

Techniques used

identify dependent variable

(c)

You are to plan an experiment to determine as accurately as possible how the temperature change varies when different solutions are made, each with different concentrations of ammonium nitrate. You are reminded that the approximate solubility of ammonium nitrate is $2.5\text{ mol}/100\text{ g}$ at $25\text{ }^\circ\text{C}$ .

The following information gives some of the hazards associated with ammonium nitrate.

Ammonium nitrate $\text{NH}_4\text{NO}_3$ . Contact with combustible material may cause fire. Explosive when mixed with combustible material.
Do not allow the salt to become contaminated with organic matter and do not grind it.
Solutions should be diluted to less than $0.5\text{ mol dm}^{-3}$ for disposal.

You should use only standard apparatus found in a school or college laboratory. Draw a diagram of the apparatus and experimental set up you would use showing clearly the following:

(i) the apparatus used, such as the reaction vessel, and how the thermometer will be positioned in order to measure the temperature of the solution as accurately as possible,
(ii) how the apparatus will be insulated.

Label each piece of apparatus used, indicating its size or capacity and both the temperature range and the precision of the thermometer.

DifficultyMedium

Worked solution

Answer

Labels and specifications:

Reaction vessel: Polystyrene cup or beaker, capacity 250 cm³ (or between 25 and 250 cm³).
Insulation: Polystyrene cup (inherently insulating) or surrounded by insulation; covered with a lid (e.g., cardboard or plastic lid with a hole for the thermometer) to minimize heat loss.
Thermometer: Positioned vertically in the solution, not touching the bottom or sides. Range: 0–50 °C (must include 25 °C). Precision: 0.1 °C or 0.5 °C.

Final answer

See diagram and labels

Detailed explanation

Background Concept

To accurately measure temperature changes in solution (calorimetry), it is crucial to minimize heat exchange with the surroundings. This is achieved by using insulated containers (like polystyrene cups), lids to prevent heat loss via evaporation or convection, and precise thermometers. The apparatus must be clearly labelled with capacities and instrument specifications.

Understanding the Question

You must draw and label a diagram of the apparatus and experimental setup for measuring temperature changes. Requirements include: reaction vessel with thermometer positioned accurately, insulation with a lid, and thermometer specifications (range including 25 °C, precision 0.1–0.5 °C).

Approach

Draw a standard simple calorimeter: a cup with a lid, containing liquid and a thermometer. Label all components, specify the cup's volume (ensuring it's large enough for the experiment, e.g., 250 cm³), describe the insulation, and state the thermometer's range and precision.

Step-by-Step Reasoning

Reaction vessel: Draw a container (e.g., a beaker or polystyrene cup). Label it with a capacity between 25 cm³ and 250 cm³ (e.g., 250 cm³).
Thermometer positioning: Draw a thermometer inserted into the solution. Ensure it is positioned vertically and does not touch the bottom or sides of the container, to measure the solution temperature accurately and avoid damage.
Insulation and lid: Show that the vessel is insulated (e.g., draw a polystyrene cup or show surrounding insulation). Add a lid (cardboard, plastic, or foil) with a small hole for the thermometer to prevent heat loss.
Thermometer specifications: Label the thermometer with a range that includes 25 °C (e.g., 0–50 °C) and a precision between 0.1 °C and 0.5 °C (e.g., 0.1 °C or 0.5 °C).

Key Takeaways

Calorimetry apparatus must be well-insulated and properly labelled. Thermometer precision and range are critical for accurate temperature change measurements.

Common Mistakes

Forgetting the lid, which allows significant heat loss via evaporation.
Placing the thermometer touching the bottom or sides, which measures the container's temperature rather than the solution's.
Specifying a thermometer range that does not include 25 °C or a precision worse than 0.5 °C.

Things to Be Careful About

The mark scheme specifically requires the container capacity to be between 25 cm³ and 250 cm³.
Thermometer precision must be stated as 0.1 °C to 0.5 °C; 'accurate' is not acceptable.
All apparatus must be labelled.

Techniques used

design experimental apparatusspecify insulation and thermometer specifications

(d)

Using the apparatus shown in (c) design an experiment to test your prediction in (a)(ii) of how the temperature change of the solution varies with solutions of different concentration.

In addition to the apparatus normally found in a laboratory you are provided with the following materials;

a supply of solid ammonium nitrate,
distilled (deionised) water.

Give a step-by-step description of how you would carry out the experiment to include;

(i) the number of experiments you would do,
(ii) the temperature measurements you would take,
(iii) the volume of water you would use,
(iv) a calculation to show the maximum mass of ammonium nitrate you could use for your volume of water in (iii) and a range of masses for the other experiments.

[ $A_r$ : H, 1.0; N, 14.0; O, 16.0]

DifficultyMedium-Hard

Worked solution

Answer

(i) Number of experiments: Carry out a minimum of 5 experiments using different masses or concentrations of ammonium nitrate.

(ii) Temperature measurements: Measure the initial temperature of the water before adding the salt, and the final maximum temperature of the solution after the salt has completely dissolved.

(iii) Volume of water: Measure a fixed volume of water, for example 50 cm³, using a measuring cylinder. This volume will fit into the 250 cm³ vessel from part (c).

(iv) Calculation for maximum mass and range:

Solubility is 2.5 mol per 100 g of water. For 50 cm³ (≈50 g) of water, the maximum moles = 1.25 mol.
Molar mass of NH₄NO₃ = 14.0 + 4(1.0) + 14.0 + 3(16.0) = 80.0 g mol⁻¹.
Maximum mass = 1.25 mol × 80.0 g mol⁻¹ = 100 g.
Use a range of masses below this maximum, for example: 10 g, 20 g, 30 g, 40 g, 50 g (or corresponding concentrations) for the 5 experiments.

Procedure: Add a measured mass of ammonium nitrate to the 50 cm³ of water in the insulated cup, stir until dissolved, and record the temperature change.

Final answer

See working for calculation; 5 experiments with masses ranging from 10g to 50g in 50cm³ water.

Detailed explanation

Background Concept

To investigate the effect of concentration on temperature change, you must prepare a series of solutions with varying concentrations while keeping other variables (like volume of water) constant. The maximum mass of solute is limited by its solubility. Ammonium nitrate has a solubility of 2.5 mol per 100 g of water at 25 °C.

Understanding the Question

You must design an experiment to test the prediction from (a)(ii). Requirements: number of experiments, temperature measurements, volume of water, and a calculation for the maximum mass of ammonium nitrate that can dissolve in that volume, plus a range of masses for the experiments.

Approach

Choose a volume of water that fits the apparatus (e.g., 50 cm³ in a 250 cm³ cup).
Calculate the maximum moles and mass of NH₄NO₃ that can dissolve in this volume using the given solubility.
Plan at least 5 experiments with masses below this maximum to generate a meaningful graph.
Specify the temperature measurements (initial and final) needed to calculate the temperature change.

Step-by-Step Reasoning

Number of experiments: To plot a reliable graph showing the relationship between concentration and temperature change, a minimum of 5 data points (experiments) is required. Use different masses or concentrations for each.
Temperature measurements: For each experiment, record the initial temperature of the water (before adding salt) and the final temperature (after dissolution is complete and the temperature has stabilized or reached a maximum/minimum). The difference gives the temperature change.
Volume of water: Use a fixed volume, e.g., 50 cm³ (measured with a measuring cylinder). This is a practical volume that fits well within a 250 cm³ calorimeter and provides a measurable temperature change.
Maximum mass calculation:
- Solubility: 2.5 mol / 100 g water.
- For 50 g (≈50 cm³) of water: moles = (2.5 / 100) × 50 = 1.25 mol.
- M_r of NH₄NO₃ = 14.0 + 4.0 + 14.0 + 48.0 = 80.0 g mol⁻¹.
- Maximum mass = 1.25 mol × 80.0 g mol⁻¹ = 100 g.
Range of masses: Choose 5 masses that are below 100 g and spread across a reasonable range, e.g., 10 g, 20 g, 30 g, 40 g, 50 g. (Ensure they are fully soluble; 50 g in 50 g water is 10 mol/100g, which exceeds solubility! Wait. 50g in 50g water is 100g/100g water, which is > 2.5 mol/100g. Let's recalculate.
- Max mass for 50 cm³ (50g) water is 100g? No. 2.5 mol per 100g water. For 50g water, max moles = 1.25 mol. Max mass = 1.25 * 80 = 100g. Wait. 100g in 50g water is 200g/100g water. Solubility is 2.5 mol/100g = 200g/100g. So 100g in 50g water is exactly the solubility limit. So masses like 10g, 20g, 30g, 40g, 50g are fine, as 50g in 50g water is 100g/100g water, which is half the solubility limit. Yes, 50g is safe.
- Correct range: 10 g, 20 g, 30 g, 40 g, 50 g (all < 100 g max).

Key Takeaways

Calculations based on solubility limits are essential to ensure the solute fully dissolves. A minimum of 5 data points is needed for a valid graph.

Common Mistakes

Calculating the maximum mass incorrectly (e.g., forgetting to scale from 100 g to 50 g of water).
Choosing masses that exceed the solubility limit, resulting in undissolved solid and inaccurate temperature readings.
Not specifying both initial and final temperature measurements.

Things to Be Careful About

The volume of water must be stated and must fit into the apparatus described in part (c).
The calculation must clearly show the steps: moles from solubility, then mass from moles and M_r.
Ensure the range of masses is realistic and below the calculated maximum.

Techniques used

design experimental procedurecalculate maximum mass from solubilityplan repeated experiments

(e)

State one hazard that must be considered when planning the experiment and describe a precaution that should be taken to keep risks from this hazard to a minimum. You may use the information in (c) if you wish.

DifficultyMedium-Easy

Worked solution

Answer

Hazard: Ammonium nitrate may cause a fire or explosion if contaminated with combustible/organic material or if ground up.

Precaution: Do not grind the salt; ensure it is not contaminated with organic matter; dilute solutions to less than 0.5 mol dm⁻³ before disposal.

Final answer

Hazard: fire/explosion from contamination or grinding. Precaution: do not grind, avoid organic contamination, dilute before disposal.

Detailed explanation

Background Concept

Ammonium nitrate is an oxidizing agent and can be explosive when mixed with combustible materials or when confined and heated. In a school laboratory, the main risks are contamination with organic matter (which can lead to fire) and the physical act of grinding the salt (which can generate heat or create fine dust that is more reactive). Disposal guidelines must also be followed to prevent environmental or safety hazards.

Understanding the Question

You must state one hazard associated with ammonium nitrate (from the provided information) and describe a precaution to minimize the risk.

Approach

Read the provided hazard information. Identify a specific hazard (e.g., fire/explosion from grinding or contamination) and pair it with the corresponding precaution (e.g., do not grind, avoid contamination, dilute for disposal).

Step-by-Step Reasoning

Hazard: The information states ammonium nitrate is 'Explosive when mixed with combustible material' and 'Do not allow the salt to become contaminated with organic matter and do not grind it.' Thus, the hazard is fire or explosion due to contamination or grinding.
Precaution: To minimize this risk, do not grind the salt, ensure no organic matter is present in the apparatus, and dilute solutions to less than 0.5 mol dm⁻³ before disposal to reduce the hazard.

Key Takeaways

Always link a specific hazard to a specific, actionable precaution. Do not give generic answers like 'be careful'.

Common Mistakes

Stating a hazard not mentioned in the information (e.g., 'it is toxic') without justification.
Giving a vague precaution like 'wear safety glasses' without linking it to the specific hazard identified.

Things to Be Careful About

Use the information provided in the question. The mark scheme accepts either the grinding/contamination hazard or the disposal hazard.

Techniques used

identify hazards and propose precautions

(f)

In order to test your prediction in (a)(ii), you would need to plot a graph. In the space below, draw a table with appropriate headings, in which you would record all your experimental data and calculated values necessary for the construction of the graph. The headings must include the appropriate units.

DifficultyMedium-Easy

Worked solution

Answer

Mass of NH₄NO₃ / g	Volume of water / cm³	Initial temperature / °C	Final temperature / °C	Temperature change / °C	Concentration of NH₄NO₃ / mol dm⁻³

(Any 4-6 correct columns with units will score. Acceptable alternatives: mass of water / g for volume, temperature fall / °C for temperature change, mol / 100 g for concentration).

Final answer

See table with 4-6 columns including units

Detailed explanation

Background Concept

A data table must record all raw measurements and calculated values needed to plot the required graph. For a graph of temperature change vs. concentration, you need columns for the independent variable (concentration), the dependent variable (temperature change), and the raw data used to calculate them (mass of solute, volume/mass of solvent, initial and final temperatures).

Understanding the Question

You must draw a table with appropriate headings and units to record all experimental data and calculated values necessary for constructing the graph from part (a)(ii).

Approach

Identify the columns needed: raw data (mass of salt, volume of water, initial temp, final temp), calculated data (temperature change, concentration). Ensure every column heading includes the correct unit.

Step-by-Step Reasoning

Raw data columns:
- Mass of ammonium nitrate used (unit: g or kg).
- Volume (or mass) of water used (unit: cm³ or g).
- Initial temperature (unit: °C).
- Final temperature (unit: °C).
Calculated columns:
- Temperature change (or temperature fall) = Final - Initial (unit: °C).
- Concentration of ammonium nitrate = moles / volume in dm³ (unit: mol dm⁻³ or mol L⁻¹, or mol/100 g water).
Units: Every column heading MUST include the appropriate unit. This is a common mark-losing error.
Number of columns: The mark scheme awards 1 mark for 4 correct columns and 1 mark for 5 or 6 correct columns. Ensure at least 4-5 are included.

Key Takeaways

Data tables must be self-contained, with clear headings and units. Calculated columns must be derived from raw data.

Common Mistakes

Forgetting units in column headings (e.g., 'Concentration' instead of 'Concentration / mol dm⁻³').
Including only raw data and forgetting the calculated 'temperature change' or 'concentration' columns needed for the graph.
Having too few columns (less than 4 correct).

Things to Be Careful About

The question asks for 'appropriate headings', which in CIE marking means the quantity AND the unit (e.g., 'Temperature / °C').
Ensure the number of rows is sufficient for at least 5 experiments (plus a header row).

Techniques used

design data recording tableinclude appropriate units

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