Reactivity: How Much, How Fast, and How Far? — Free IB Chemistry HL Practice Questions

1FoundationMCQCalculating equilibrium constants (Kc)1 markPaper 1~2 min

For the esterification reaction

\text{CH}_3\text{COOH}(\text{l}) + \text{C}_2\text{H}_5\text{OH}(\text{l}) \rightleftharpoons \text{CH}_3\text{COOC}_2\text{H}_5(\text{l}) + \text{H}_2\text{O}(\text{l})

, a student mixes

2.0\ \text{mol}

of ethanoic acid with

2.0\ \text{mol}

of ethanol in a

1.0\ \text{dm}^3

flask. At equilibrium,

1.2\ \text{mol}

of ethyl ethanoate is present. What is the value of

K_c

?

Solutions

2MasteryMCQCalculating equilibrium constants (Kc)1 markPaper 1~2 min

A 1.00 dm³ flask initially contains 0.100 mol of

\text{PCl}_5(\text{g})

only. The system reaches equilibrium according to

\text{PCl}_5(\text{g}) \rightleftharpoons \text{PCl}_3(\text{g}) + \text{Cl}_2(\text{g})

, at which point

[\text{Cl}_2] = 0.040 \text{ mol dm}^{-3}

. What is the value of

K_c

?

Solutions

3MasteryMCQCalculating equilibrium constants (Kc)1 markPaper 1~2 min

In the Haber process,

\text{N}_2(g) + 3\text{H}_2(g) \rightleftharpoons 2\text{NH}_3(g)

, a student places

0.20\ \text{mol}

of

\text{N}_2

and

0.60\ \text{mol}

of

\text{H}_2

in a

1.0\ \text{dm}^3

container at

400\ \text{°C}

. At equilibrium,

[\text{NH}_3] = 0.20\ \text{mol dm}^{-3}

. What is the equilibrium concentration of

\text{H}_2

?

Solutions

4FoundationMCQCalculating equilibrium constants (Kc)1 markPaper 1~2 min

A student investigates the equilibrium

\text{PCl}_5(\text{g}) \rightleftharpoons \text{PCl}_3(\text{g}) + \text{Cl}_2(\text{g})

. She places

0.20\ \text{mol}

of

\text{PCl}_5

in a

1.0\ \text{dm}^3

container and allows the system to reach equilibrium, at which point

0.12\ \text{mol}

of

\text{PCl}_5

remains. What is the value of

K_c

?

Solutions

5FoundationMCQStoichiometry and mole-to-mole ratios1 markPaper 1~2 min

In the Haber process,

\text{N}_2\text{(g)} + 3\text{H}_2\text{(g)} \rightarrow 2\text{NH}_3\text{(g)}

. A chemical engineer charges a closed reactor with

2.0\ \text{mol}

of

\text{N}_2

and

5.0\ \text{mol}

of

\text{H}_2

. What is the maximum amount, in mol, of

\text{NH}_3

that can be produced?

Solutions

6MasteryMCQConcentration, volume, and number of particles1 markPaper 1~2 min

A student dissolves

4.00\ \text{g}

of NaOH(s) in distilled water and makes the solution up to

250.0\ \text{cm}^3

in a volumetric flask. A

25.0\ \text{cm}^3

aliquot is titrated against hydrochloric acid of unknown concentration; the endpoint is reached after adding

22.5\ \text{cm}^3

of HCl(aq). What is the concentration of the hydrochloric acid, in

\text{mol dm}^{-3}

?

Solutions

7FoundationMCQStoichiometry and mole-to-mole ratios1 markPaper 1~2 min

Complete combustion of ethene proceeds according to the equation:

\text{C}_2\text{H}_4\text{(g)} + 3\text{O}_2\text{(g)} \rightarrow 2\text{CO}_2\text{(g)} + 2\text{H}_2\text{O(l)}

A

0.50\ \text{mol}

sample of ethene undergoes complete combustion in excess oxygen. Which of the following gives the amount, in mol, of

\text{CO}_2

produced and the amount, in mol, of

\text{O}_2

consumed? A —

0.50

—

1.0

B —

1.0

—

1.5

C —

1.0

—

1.5

D —

1.0

—

1.5

(Replacing table format with standard options below)

Solutions

8FoundationMCQStoichiometry and mole-to-mole ratios1 markPaper 1~2 min

In the reaction

2\text{NaOH(aq)} + \text{H}_2\text{SO}_4\text{(aq)} \rightarrow \text{Na}_2\text{SO}_4\text{(aq)} + 2\text{H}_2\text{O(l)}

, a student mixes

0.40\ \text{mol}

of NaOH with

0.25\ \text{mol}

of

\text{H}_2\text{SO}_4

. Which reactant is limiting, and what amount, in mol, of

\text{Na}_2\text{SO}_4

is produced?

Solutions

9FoundationMCQCollision theory and activation energy1 markPaper 1~2 min

When a few drops of potassium iodide solution are added to a solution of hydrogen peroxide, the rate of decomposition according to

\text{2H}_2\text{O}_2\text{(aq)} \rightarrow \text{2H}_2\text{O(l)} + \text{O}_2\text{(g)}

increases dramatically. Which statement best explains this observation in terms of collision theory?

Solutions

10MasteryMCQFactors affecting reaction rates: Concentration, temperature, surface area, catalysts1 markPaper 1~2 min

The reaction between marble chips (calcium carbonate) and excess hydrochloric acid is first order with respect to HCl. A student monitors the volume of

\text{CO}_2

produced over time and determines the initial rate from the gradient of the curve at

t = 0

. The experiment is repeated with the concentration of HCl doubled, all other conditions remaining constant. What is the expected ratio of the new initial rate to the original initial rate?

Solutions

11MasteryMCQFactors affecting reaction rates: Concentration, temperature, surface area, catalysts1 markPaper 1~2 min

In an experiment, the time for a sulfur precipitate to obscure a cross is measured for the reaction between sodium thiosulfate solution and dilute hydrochloric acid at two temperatures. At

20\ ^\circ\text{C}

the time is

120\ \text{s}

, and at

30\ ^\circ\text{C}

the time is

60\ \text{s}

. Using the Arrhenius equation with

R = 8.31\ \text{J K}^{-1}\text{mol}^{-1}

, what is the approximate activation energy for this reaction?

Solutions

12FoundationMCQCollision theory and activation energy1 markPaper 1~2 min

For the reaction

\text{N}_2\text{(g)} + 3\text{H}_2\text{(g)} \rightarrow 2\text{NH}_3\text{(g)}

, the activation energy for the forward reaction is

+335 \ \text{kJ mol}^{-1}

and

\Delta H = -92 \ \text{kJ mol}^{-1}

. What is the activation energy for the reverse reaction?

Solutions

13ChallengeSAQ-LCalculating equilibrium constants (Kc)7 marksPaper 2~11 min

The esterification reaction between ethanol and ethanoic acid reaches equilibrium in a closed system:

\text{C}_2\text{H}_5\text{OH}(l) + \text{CH}_3\text{COOH}(l) \rightleftharpoons \text{CH}_3\text{COOC}_2\text{H}_5(l) + \text{H}_2\text{O}(l)

A student prepares a mixture by adding

0.500\,\text{mol}

of ethanol and

0.500\,\text{mol}

of ethanoic acid to a

1.00\,\text{dm}^3

flask. The flask is sealed and allowed to reach equilibrium at

298\,\text{K}

. At equilibrium, the concentration of ethyl ethanoate is

0.333\,\text{mol}\,\text{dm}^{-3}

.

(a)

Calculate the equilibrium constant,

K_c

, for this reaction at

298\,\text{K}

. [3 marks]

(b)

Explain why

K_c

has no units for this reaction. [2 marks]

(c)

When the experiment is repeated at

350\,\text{K}

,

K_c

decreases to

3.2

. Deduce and explain whether the forward reaction is exothermic or endothermic. [2 marks]

Solutions

14MasterySAQ-SChemical equilibrium and Le Chatelier’s Principle5 marksPaper 2~8 min

Consider the following equilibrium system in a closed container:

2\text{NO}_2(g) \rightleftharpoons \text{N}_2\text{O}_4(g) \qquad \Delta H = -58\,\text{kJ mol}^{-1}

Nitrogen dioxide (

\text{NO}_2

) is a brown gas, while dinitrogen tetroxide (

\text{N}_2\text{O}_4

) is colourless. A sealed flask containing a mixture of these gases at equilibrium has a pale brown colour. The flask is placed in an ice-water bath (

0\,°\text{C}

) and the colour becomes much lighter. The flask is then transferred to a boiling water bath (

100\,°\text{C}

) and the colour becomes much darker.

(a)

Explain why the colour becomes lighter when the flask is cooled to

0\,°\text{C}

. [2 marks]

(b)

Calculate the equilibrium concentration of

\text{N}_2\text{O}_4

at

25\,°\text{C}

, given that the equilibrium concentration of

\text{NO}_2

is

0.040\,\text{mol dm}^{-3}

and

K_c = 6.8\,\text{dm}^3\,\text{mol}^{-1}

.

K_c = \frac{[\text{N}_2\text{O}_4]}{[\text{NO}_2]^2}

[3 marks]

Solutions

15ChallengeSAQ-LCalculating equilibrium constants (Kc)7 marksPaper 2~11 min

Hydrogen iodide decomposes according to the equation:

2\text{HI}(g) \rightleftharpoons \text{H}_2(g) + \text{I}_2(g)

A

2.00\,\text{dm}^3

flask is filled with

0.600\,\text{mol}

of

\text{HI}(g)

and sealed. The system is heated to

700\,\text{K}

and allowed to reach equilibrium. At equilibrium,

[\text{I}_2] = 0.0500\,\text{mol}\,\text{dm}^{-3}

.

(a)

Calculate the equilibrium constant,

K_c

, for this reaction at

700\,\text{K}

. [3 marks]

(b)

(i) Explain why

K_c

would change if the experiment were repeated at

500\,\text{K}

. [1]
(ii) Explain why

K_c

would NOT change if the volume of the flask were halved at constant temperature. [1 mark]

(c)

It is known that

K_c

for this reaction increases as temperature increases. Using this information and your calculated value of

K_c

, deduce whether the forward reaction is endothermic or exothermic, and determine the sign of

\Delta H^\circ

. Justify your answer. [2 marks]

Solutions

16ChallengeSAQ-LCalculating equilibrium constants (Kc)9 marksPaper 2~14 min

Phosgene (

\text{COCl}_2

) is an important industrial chemical used in the production of polyurethane plastics. It is produced by the reaction:

\text{CO}(g) + \text{Cl}_2(g) \rightleftharpoons \text{COCl}_2(g) \quad \Delta H < 0

A

5.00\,\text{dm}^3

reactor is charged with

2.00\,\text{mol}

of

\text{CO}(g)

and

1.50\,\text{mol}

of

\text{Cl}_2(g)

at

400\,°\text{C}

. At equilibrium, the concentration of

\text{COCl}_2

is

0.200\,\text{mol dm}^{-3}

.

(a)

Calculate the equilibrium constant,

K_c

, for this reaction at

400\,°\text{C}

. [3 marks]

(b)

Explain why the units of

K_c

for this reaction are

\text{dm}^3\,\text{mol}^{-1}

. [2 marks]

(c)

An engineer proposes increasing the total pressure in the reactor to increase the yield of

\text{COCl}_2

. Evaluate this proposal using Le Chatelier's principle. [2 marks]

(d)

Suggest one other change in reaction conditions that would increase the equilibrium yield of

\text{COCl}_2

. Explain your reasoning using equilibrium principles. [2 marks]

Solutions

17MasterySAQ-SStoichiometry and mole-to-mole ratios5 marksPaper 2~8 min

In the Haber process, nitrogen and hydrogen react according to:

\text{N}_2(g) + 3\text{H}_2(g) \rightarrow 2\text{NH}_3(g) \quad \Delta H = -92\,\text{kJ mol}^{-1}

A reactor is charged with

5.00\,\text{mol}

of

\text{N}_2

and

12.00\,\text{mol}

of

\text{H}_2

, which react to completion.

(a)

State the limiting reactant. [1 mark]

(b)

Calculate the amount, in mol, of

\text{NH}_3

produced. [1 mark]

(c)

Explain how increasing pressure from atmospheric to

200\,\text{atm}

affects the equilibrium position and the yield of

\text{NH}_3

. [2 marks]

(d)

Evaluate one reason why operating at pressures significantly above

200\,\text{atm}

is not used industrial practice, despite further increasing equilibrium yield. [1 mark]

Solutions

18MasterySAQ-SStoichiometry and mole-to-mole ratios6 marksPaper 2~9 min

A student performs a titration to determine the concentration of ethanoic acid in vinegar. They pipette

25.0\ \text{cm}^3

of vinegar into a conical flask and titrate with

0.500\ \text{mol dm}^{-3}

sodium hydroxide solution. The balanced equation is:

\text{CH}_3\text{COOH}(aq) + \text{NaOH}(aq) \rightarrow \text{CH}_3\text{COONa}(aq) + \text{H}_2\text{O}(l)

The average titre of NaOH used is

20.8\ \text{cm}^3

.

(a)

Calculate the concentration, in

\text{mol dm}^{-3}

, of ethanoic acid in the vinegar. [2 marks]

(b)

The vinegar label states it contains

5.00\%

ethanoic acid by mass. The density of vinegar is

1.01\ \text{g cm}^{-3}

. Show that the concentration of ethanoic acid expected from the label is

0.841\ \text{mol dm}^{-3}

. [2 marks]

(c)

The student's result is approximately half the value expected from the label. Deduce one systematic error in the titration procedure that could account for this discrepancy, and explain how it would produce a result that is too low. [2 marks]

Solutions

19MasterySAQ-SStoichiometry and mole-to-mole ratios4 marksPaper 2~6 min

Iron(III) oxide reacts with carbon monoxide in a blast furnace to produce iron:

\text{Fe}_2\text{O}_3\text{(s)} + 3\text{CO(g)} \rightarrow 2\text{Fe(s)} + 3\text{CO}_2\text{(g)}

A sample of iron ore contains

80.0\%

Fe

_2

O

_3

by mass, with the remainder being inert silica. A

500\,\text{g}

sample of this ore is processed.

(a)

Calculate theoretical yield of iron, in grams, from this sample. [2 marks]

(b)

The actual yield of iron obtained is

250\,\text{g}

. Suggest one reason, other than experimental error, why the actual yield is less than theoretical yield. [1 mark]

(c)

Calculate the minimum volume, in

\text{dm}^3

, of CO gas measured at STP (

273\,\text{K}

,

100\,\text{kPa}

) required to completely react with the Fe

_2

O

_3

in this sample. [1 mark]

Solutions

20MasterySAQ-SStoichiometry and mole-to-mole ratios5 marksPaper 2~8 min

The combustion of octane, a component of gasoline, is represented by:

2\text{C}_8\text{H}_{18}(l) + 25\text{O}_2(g) \rightarrow 16\text{CO}_2(g) + 18\text{H}_2\text{O}(g)

A car engine burns

5.00\,\text{kg}

of octane during a journey. The molar mass of octane is

114.26\,\text{g mol}^{-1}

.

(a)

Calculate the mass of carbon dioxide produced, in kg, assuming complete combustion. [2 marks]

(b)

The actual mass of

\text{CO}_2

emitted is measured as

14.5\,\text{kg}

. Determine the percentage yield of

\text{CO}_2

. [1 mark]

(c)

Explain why the percentage yield of

\text{CO}_2

is less than

100\%

in a real car engine, referring to two distinct chemical reasons. [2 marks]

Solutions

21ChallengeSAQ-LRate law and order of reactions9 marksPaper 2~14 min

Data

t\,/\,\text{s}

—

0

—

120

—

240

—

360

—

480

—

600

[\text{OH}^-]\,/\,\text{mol}\,\text{dm}^{-3}

—

0.100

—

0.075

—

0.056

—

0.042

—

0.032

—

0.024

Ethyl methanoate (

\text{HCOOC}_2\text{H}_5

) undergoes hydrolysis in alkaline solution:

\text{HCOOC}_2\text{H}_5\text{(aq)} + \text{OH}^-\text{(aq)} \rightarrow \text{HCOO}^-\text{(aq)} + \text{C}_2\text{H}_5\text{OH(aq)}

A student investigates the kinetics at

25\,^\circ\text{C}

with initial concentrations

[\text{ester}]_0 = [\text{OH}^-]_0 = 0.100\,\text{mol}\,\text{dm}^{-3}

. Samples are withdrawn and titrated with standard acid to give the following

(a)

Using the data above, show that the reaction is second order with respect to

\text{OH}^-

. [2 marks]

(b)

Calculate the rate constant

k

, including its units. [2 marks]

(c)

Explain why the order with respect to the ester cannot be determined from this data alone. [2 marks]

(d)

A student proposes repeating the experiment using

[\text{ester}]_0 = 0.100\,\text{mol}\,\text{dm}^{-3}

and

[\text{OH}^-]_0 = 1.00\,\text{mol}\,\text{dm}^{-3}

. Deduce how this modification allows the order with respect to the ester to be determined, and identify what quantity should be plotted to confirm a first-order dependence on the ester. [3 marks]

Solutions

22MasterySAQ-SCollision theory and activation energy5 marksPaper 2~8 min

A Maxwell–Boltzmann distribution curve for a gas at temperature

T_1

shows the distribution of molecular kinetic energies. The shaded area under the curve to the right of the activation energy

E_a

represents the proportion of molecules with sufficient energy to react.

(a)

Describe how the Maxwell–Boltzmann distribution curve changes when the temperature is increased from

T_1

to

T_2

, and explain why this leads to a large increase in reaction rate even for a small temperature rise. [2 marks]

(b)

For a particular reaction, only molecules with energy greater than

52\,\text{kJ mol}^{-1}

can react. At

300\,\text{K}

, the proportion of molecules with

E > 52\,\text{kJ mol}^{-1}

is

2.0\%

of the total. When the temperature is raised to

310\,\text{K}

, this proportion increases to

3.5\%

. Calculate the factor by which the rate of reaction increases. [1 mark]

(c)

A catalyst provides an alternative reaction pathway with a lower activation energy

E_a'

, where

E_a' < E_a

. Using the Maxwell–Boltzmann distribution at constant temperature, explain why the catalysed reaction has a significantly greater rate than the uncatalysed reaction, and deduce what happens to the rate if the catalyst is removed and the temperature is simultaneously lowered. [2 marks]

Solutions

23ChallengeSAQ-LRate law and order of reactions7 marksPaper 2~11 min

The reaction between iodine and propanone in acidic solution is:

\text{CH}_3\text{COCH}_3\text{(aq)} + \text{I}_2\text{(aq)} \rightarrow \text{CH}_3\text{COCH}_2\text{I(aq)} + \text{H}^+\text{(aq)} + \text{I}^-\text{(aq)}

A student investigates the rate by measuring the time for the iodine colour to disappear. The following initial rate data were obtained at

298\,\text{K}

: Experiment —

[\text{CH}_3\text{COCH}_3] / \text{mol dm}^{-3}

—

[\text{H}^+] / \text{mol dm}^{-3}

—

[\text{I}_2] / \text{mol dm}^{-3}

— Initial rate /

\text{mol dm}^{-3}\text{s}^{-1}

1 —

0.50

—

0.10

—

0.050

—

2.5 \times 10^{-5}

2 —

1.00

—

0.10

—

0.050

—

5.0 \times 10^{-5}

3 —

0.50

—

0.20

—

0.050

—

5.0 \times 10^{-5}

4 —

0.50

—

0.100

—

2.5 \times 10^{-5}

The rate constant

k

at

298\,\text{K}

is

5.0 \times 10^{-4}\,\text{dm}^6\,\text{mol}^{-2}\,\text{s}^{-1}

.

(a)

Determine the order of reaction with respect to each reactant. [3 marks]

(b)

State the overall rate law for this reaction. [1 mark]

(c)

Explain why the rate-determining step must involve

\text{CH}_3\text{COCH}_3

and

\text{H}^+

but not

\text{I}_2

. [2 marks]

(d)

The Arrhenius equation is

k = Ae^{-E_a/RT}

. Using this equation, deduce and explain how adding a catalyst affects the value of

k

at

298\,\text{K}

. [1 mark]

Solutions

24ChallengeSAQ-LRate law and order of reactions9 marksPaper 2~14 min

Nitrosyl bromide (NOBr) decomposes according to:

2\text{NOBr}(\text{g}) \rightarrow 2\text{NO}(\text{g}) + \text{Br}_2(\text{g})

Initial rate data obtained at

300\,\text{K}

: Experiment —

[\text{NOBr}] / \text{mol\,dm}^{-3}

— Initial rate

/ \text{mol\,dm}^{-3}\text{s}^{-1}

1 —

0.10

—

1.6 \times 10^{-4}

2 —

0.20

—

6.4 \times 10^{-4}

3 —

0.30

—

1.44 \times 10^{-3}

The activation energy for this reaction is

\,E_a = 58.0\,\text{kJ\,mol}^{-1}

.

(a)

State the order of reaction with respect to NOBr. [1 mark]

(b)

Calculate the rate constant

k

at

300\,\text{K}

using data from Experiment 1. Include units. [2 marks]

(c)

A two-step mechanism is proposed: - Step 1:

2\text{NOBr}(\text{g}) \rightarrow 2\text{NO}(\text{g}) + \text{Br}_2(\text{g})

(slow) - Step 2:

\text{Br}_2(\text{g}) \rightarrow 2\text{Br}(\text{g})

(fast) Explain whether this mechanism is consistent with the experimentally determined rate law. [2 marks]

(d)

Using the Arrhenius equation, calculate the rate constant

k

at

350\,\text{K}

. [2] (e) Evaluate the effect of increasing temperature from

300\,\text{K}

to

350\,\text{K}

on the rate of reaction, with reference to the Maxwell–Boltzmann distribution. [2 marks]

Solutions

25ChallengeLAQShifting equilibrium: Concentration, pressure, and temperature effects17 marksPaper 3~26 min

The industrial synthesis of methanol from synthesis gas is an exothermic equilibrium process:

\text{CO}(g) + 2\text{H}_2(g) \rightleftharpoons \text{CH}_3\text{OH}(g) \qquad \Delta H = -91\,\text{kJ mol}^{-1}

A chemical engineer is designing a methanol plant. Pilot-plant data at equilibrium are given below. Experiment — Temperature / K — Pressure / atm — Mole fraction of

\text{CH}_3\text{OH}

1 — 500 — 50 — 0.42 2 — 600 — 50 — 0.18 3 — 600 — 100 — 0.32

(a)

State and explain, using Le Chatelier's Principle, the change in equilibrium mole fraction of methanol when temperature is increased from

500\,\text{K}

to

600\,\text{K}

at constant pressure. [3 marks]

(b)

State and explain, using Le Chatelier's Principle, the change in equilibrium mole fraction of methanol when pressure is increased from

50\,\text{atm}

to

100\,\text{atm}

at constant temperature. [3 marks]

(c)

The engineer proposes operating the plant at

650\,\text{K}

and

200\,\text{atm}

. (i) Explain, with reference to collision theory and activation energy, why a higher operating temperature may be chosen despite the lower equilibrium yield. [3]
(ii) A colleague argues that

200\,\text{atm}

is a poor choice. Identify and evaluate TWO practical limitations of operating at

200\,\text{atm}

, and justify which limitation presents the greater obstacle to plant operation. [4 marks]

(d)

The engineer adds helium gas to the reactor. (i) Helium is added at constant volume. Using the expression for

K_c

shown below, explain why the equilibrium position does not shift.

K_c = \frac{[\text{CH}_3\text{OH}]}{[\text{CO}][\text{H}_2]^2}

[2]
(ii) The same amount of helium is instead added at constant total pressure, allowing the volume to increase. Predict the direction of the shift in equilibrium position and explain your prediction using Le Chatelier's Principle. [2 marks]

Solutions

26ChallengeLAQCalculating equilibrium constants (Kc)15 marksPaper 3~23 min

The esterification of ethanoic acid with ethanol is an equilibrium reaction:

\text{CH}_3\text{COOH}(l) + \text{C}_2\text{H}_5\text{OH}(l) \rightleftharpoons \text{CH}_3\text{COOC}_2\text{H}_5(l) + \text{H}_2\text{O}(l)

A student mixes

0.500\,\text{mol}

of ethanoic acid with

0.500\,\text{mol}

of ethanol in a

1.00\,\text{dm}^3

flask. After adding a few drops of concentrated sulfuric acid as catalyst, the mixture is allowed to reach equilibrium at

298\,\text{K}

. The total volume remains

1.00\,\text{dm}^3

. At equilibrium, the student titrates a

25.0\,\text{cm}^3

sample of the mixture against

0.200\,\text{mol}\,\text{dm}^{-3}

sodium hydroxide solution. The titration requires

18.6\,\text{cm}^3

of NaOH solution to reach the end point.

(a)

Calculate the equilibrium concentration, in

\text{mol}\,\text{dm}^{-3}

, of ethanoic acid in the mixture. [3 marks]

(b)

Determine the value of

K_c

for this reaction at

298\,\text{K}

, and state its units. [4 marks]

(c)

Explain why the student added a catalyst to the mixture, and state whether the catalyst affects the value of

K_c

. [3 marks]

(d)

The student repeats the experiment at

323\,\text{K}

and obtains

K_c = 2.8

. Using both values of

K_c

and the Van't Hoff principle, evaluate whether the forward reaction is exothermic or endothermic, and justify your answer with reference to Le Chatelier's principle and the relationship between

K_c

and temperature. [5 marks]

Solutions

27ChallengeLAQLimiting reagents and theoretical yield15 marksPaper 3~23 min

Data

- Molar masses /

\text{g mol}^{-1}

:

\text{NH}_3 = 17.03

;

\text{CO}_2 = 44.01

;

(\text{NH}_2)_2\text{CO} = 60.06

;

\text{H}_2\text{O} = 18.02

-

R = 8.31\,\text{J K}^{-1}\text{mol}^{-1}

- At

150\,°\text{C}

, water exists entirely in the gaseous state; urea is solid.

A student investigates the industrial synthesis of urea,

(\text{NH}_2)_2\text{CO}

, a key nitrogen fertiliser. Urea is produced by reacting ammonia with carbon dioxide according to the following equilibrium:

2\text{NH}_3(g) + \text{CO}_2(g) \rightleftharpoons (\text{NH}_2)_2\text{CO}(s) + \text{H}_2\text{O}(g)

In a laboratory-scale experiment, a student places

17.0\,\text{g}

of

\text{NH}_3

and

44.0\,\text{g}

of

\text{CO}_2

in a sealed

5.00\,\text{dm}^3

reactor at

150\,°\text{C}

. The reaction proceeds to completion.

(a)

Calculate theoretical yield of urea, in grams, when the limiting reagent is completely consumed. [3 marks]

(b)

The student repeats the experiment using

34.0\,\text{g}

of

\text{NH}_3

and

44.0\,\text{g}

of

\text{CO}_2

. The student claims that the mass of urea produced will be exactly double that from part (a). Evaluate this claim. [4 marks]

(c)

(i) In industrial practice, ammonia is used in excess relative to carbon dioxide. Explain, using Le Chatelier's principle and one economic reason, why this done. [3]
(ii) Using excess ammonia lowers the atom economy of a single pass through the reactor. Evaluate whether this represents a significant disadvantage for the industrial process. [2 marks]

(d)

Predict whether the total pressure in the reactor after the reaction in part (a) will be greater than, less than, or equal to the initial total pressure. Justify your answer with a calculation. [3 marks]

Solutions

28ChallengeLAQLimiting reagents and theoretical yield15 marksPaper 3~23 min

A pharmaceutical company is developing a new synthesis of paracetamol (

\text{C}_8\text{H}_9\text{NO}_2

) via the reaction of 4-aminophenol (

\text{C}_6\text{H}_7\text{NO}

) with ethanoic anhydride (

(\text{CH}_3\text{CO})_2\text{O}

):

\text{C}_6\text{H}_7\text{NO} + (\text{CH}_3\text{CO})_2\text{O} \rightarrow \text{C}_8\text{H}_9\text{NO}_2 + \text{CH}_3\text{COOH}

A process chemist mixes

5.00\,\text{g}

of 4-aminophenol with

8.00\,\text{g}

of ethanoic anhydride in a solvent. After purification,

6.12\,\text{g}

of paracetamol isolated. Molar masses /

\text{g mol}^{-1}

:

\text{C}_6\text{H}_7\text{NO} = 109.13

;

(\text{CH}_3\text{CO})_2\text{O} = 102.09

;

\text{C}_8\text{H}_9\text{NO}_2 = 151.16

;

\text{CH}_3\text{COOH} = 60.05

(a)

Determine the limiting reagent and calculate theoretical yield of paracetamol in grams. [4 marks]

(b)

Calculate the percentage yield of the reaction. [2 marks]

(c)

(i) The chemist scales up the reaction using

50.0\,\text{g}

of 4-aminophenol and

80.0\,\text{g}

of ethanoic anhydride. Calculate the mass of paracetamol predicted if the percentage yield from (b) is unchanged. [2]
(ii) Explain one reason why the actual percentage yield at this larger scale might differ from that obtained in the small-scale reaction. [2 marks]

(d)

The atom economy of this synthesis defined as:

\text{atom economy} = \frac{M_r(\text{desired product})}{\sum M_r(\text{all products})} \times 100\%

(i) Calculate the atom economy of the reaction as written. [2]
(ii) An alternative route replaces ethanoic anhydride with ethanoyl chloride (

\text{CH}_3\text{COCl}

,

M_r = 78.50

), producing HCl (

M_r = 36.46

) as the only by-product. Evaluate whether this substitution improves atom economy, and suggest one additional consideration that would affect the choice of reagent in an industrial pharmaceutical context. [3 marks]

Solutions

29ChallengeLAQFactors affecting reaction rates: Concentration, temperature, surface area, catalysts15 marksPaper 3~23 min

The catalytic decomposition of hydrogen peroxide,

2\text{H}_2\text{O}_2\text{(aq)} \rightarrow 2\text{H}_2\text{O(l)} + \text{O}_2\text{(g)}

is studied using manganese(IV) oxide as a heterogeneous catalyst. A student measures the volume of oxygen gas collected over time in three separate experiments, all performed at

298\,\text{K}

and

1.01 \times 10^5\,\text{Pa}

. - Experiment 1:

25.0\,\text{cm}^3

of

0.50\,\text{mol dm}^{-3}

\text{H}_2\text{O}_2

+

0.50\,\text{g}

of powdered

\text{MnO}_2

(surface area:

2.5\,\text{m}^2\,\text{g}^{-1}

) - Experiment 2:

25.0\,\text{cm}^3

of

1.0\,\text{mol dm}^{-3}

\text{H}_2\text{O}_2

+

0.50\,\text{g}

of the same powdered

\text{MnO}_2

- Experiment 3:

25.0\,\text{cm}^3

of

0.50\,\text{mol dm}^{-3}

\text{H}_2\text{O}_2

+

0.50\,\text{g}

of

\text{MnO}_2

pellets (surface area:

0.10\,\text{m}^2\,\text{g}^{-1}

) The initial rate for Experiment 1 is

2.4 \times 10^{-4}\,\text{mol dm}^{-3}\,\text{s}^{-1}

and the maximum volume of

\text{O}_2

collected in Experiment 1 is

152\,\text{cm}^3

.

(a)

Using collision theory, explain why the initial rate in Experiment 2 is greater than that in Experiment 1. [3 marks]

(b)

Deduce the maximum volume of

\text{O}_2

collected in Experiment 2, and explain why the maximum volume in Experiment 3 equals that in Experiment 1. [3 marks]

(c)

Analyse how the shape of the volume–time curve for Experiment 3 differs from that for Experiment 1, and explain this difference in terms of the mechanism of heterogeneous catalysis. State the ratio of the initial rate of Experiment 1 to that of Experiment 3, assuming rate is proportional to catalyst surface area. [4 marks]

(d)

Calculate the activation energy,

E_a

, for this reaction. The rate constant at

298\,\text{K}

is

k_{298} = 1.2 \times 10^{-3}\,\text{s}^{-1}

and at

318\,\text{K}

is

k_{318} = 4.8 \times 10^{-3}\,\text{s}^{-1}

. State the units of

E_a

.

\ln\!\left(\frac{k_2}{k_1}\right) = \frac{E_a}{R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right), \quad R = 8.31\,\text{J mol}^{-1}\,\text{K}^{-1}, \quad \ln(4.0) = 1.386

[3] (e) Use the maximum volume of

\text{O}_2

from Experiment 1 to calculate the initial moles of

\text{H}_2\text{O}_2

used. Comment on whether this value is consistent with the stated concentration and volume of solution. [2 marks]

Solutions

30ChallengeLAQFactors affecting reaction rates: Concentration, temperature, surface area, catalysts15 marksPaper 3~23 min

The reaction between marble chips (calcium carbonate,

\text{CaCO}_3

) and hydrochloric acid is studied:

\text{CaCO}_3\text{(s)} + 2\text{HCl(aq)} \rightarrow \text{CaCl}_2\text{(aq)} + \text{CO}_2\text{(g)} + \text{H}_2\text{O(l)}

A student performs two experiments at

295\,\text{K}

, measuring mass loss due to escaping

\text{CO}_2

over time. - Experiment A:

5.00\,\text{g}

of large marble chips (total surface area

12\,\text{cm}^2

) added to

50.0\,\text{cm}^3

of

1.00\,\text{mol}\,\text{dm}^{-3}

HCl. - Experiment B:

5.00\,\text{g}

of powdered marble (total surface area

120\,\text{cm}^2

) added to

50.0\,\text{cm}^3

of

1.00\,\text{mol}\,\text{dm}^{-3}

HCl. Molar mass of

\text{CaCO}_3 = 100.1\,\text{g}\,\text{mol}^{-1}

; molar mass of

\text{CO}_2 = 44.0\,\text{g}\,\text{mol}^{-1}

.

(a)

Explain why the initial rate of reaction in Experiment B is greater than in Experiment A, using collision theory. [3 marks]

(b)

(i) Calculate theoretical maximum mass loss of

\text{CO}_2

for these experiments, identifying the limiting reactant. [3]
(ii) The student claims the total mass loss at the end of both reactions will be identical. Evaluate this claim. [2 marks]

(c)

(i) On the same axes, sketch the Maxwell–Boltzmann energy distribution curves for the reactant molecules at

295\,\text{K}

and at

315\,\text{K}

. Label both curves, label the axes, and mark the activation energy

E_a

. [2]
(ii) Using your sketch, explain how increasing the temperature from

295\,\text{K}

to

315\,\text{K}

increases the rate of reaction. [2 marks]

(d)

In industrial production of calcium chloride, manufacturers use powdered limestone and warm hydrochloric acid rather than large limestone blocks and cold acid. Suggest reasons for this choice. [3 marks]

Solutions

Reactivity: How Much, How Fast, and How Far? — Free Chemistry HL Practice Questions