IB Chemistry HL 1.2 Energy Cycles Questions

Practise IB Chemistry HL energy cycles by calculating reaction enthalpy from bond energies and Hess pathways, then applying standard data and Born–Haber cycles.

Exam points

Calculate reaction ΔH as Σ bond energies broken − Σ bond energies formed, using equation coefficients.
Explain why mean bond enthalpies give estimates rather than compound-specific reaction values.
Calculate percentage uncertainty in ΔH from the stated uncertainties in bond enthalpy values.
Reverse or scale Hess-cycle steps, track signs and state symbols, and combine them to find target ΔH.
Write formation and combustion equations for one mole, using standard states and complete combustion.
Calculate ΔH° from formation data: ΣΔHf°(products) − ΣΔHf°(reactants), with coefficients.
Calculate ΔH° from combustion data: ΣΔHc°(reactants) − ΣΔHc°(products), with coefficients.
Label Born–Haber steps and calculate lattice enthalpy from signed terms, including electron affinity.
Compare lattice enthalpies by ionic charge and radius, explaining stronger attraction for smaller ions.

Covered syllabus points

1.2.1—Bond energies 1.2.2—Hess's law 1.2.3 (HL)—Standard enthalpy changes 1.2.4 (HL)—Hess's law applications 1.2.5 (HL)—Born-Haber cycle

[Maximum number: 6]

Organic compounds have many industrial applications.

(a)

Ethene reacts with steam to produce ethanol.

\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{~g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{~g}) \rightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\mathrm{~g})

[ 6 ]

(i)

Calculate the enthalpy, in kJ , of the reaction using section 12 of the data booklet.

[ 3 ]

ALTERNATIVE 1:

Bonds broken:

$1 \mathrm{C}=\mathrm{C}+4 \mathrm{C}-\mathrm{H}+2 \mathrm{O}-\mathrm{H} / 614+4(414)+2(463) / 3196$ «kJ»

Bonds formed:

1 C-C+1 C-O+5 C-H+1 O-H /

346+358+5(414)+463 /

3237 «kJ»
$\Delta H=\text { «3196-3237 }=\text { » }-41 \text { «kJ» » }$

ALTERNATIVE 2:

Bonds broken:
$1 \mathrm{C}=\mathrm{C}+1 \mathrm{O}-\mathrm{H} / 614+463 /$

1077 «kJ»

Bonds formed:
$\begin{aligned} & 1 \mathrm{C}-\mathrm{C}+1 \mathrm{C}-\mathrm{O}+1 \mathrm{C}-\mathrm{H} / 346+358+414 / & 1118\langle\mathrm{~kJ}\rangle{ }^{2} & \Delta H=\langle 1077-1118=\rangle-41\left\langle\mathrm{~kJ} \|{ }^{2} \right. \end{aligned}$

Award [3] for correct final answer.

Award [2 max] for +41 «kJ».

(ii)

Calculate the enthalpy of the reaction, in kJ . Use section 13 of the data booklet and $\Delta H_{f}^{\ominus}$ of $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(\mathrm{g})=-235 \mathrm{~kJ} \mathrm{~mol}^{-1}$ .

[ 2 ]

$\begin{aligned} \text { 《 } \Delta H^{\ominus}=\Sigma\left(\Delta H_{\mathrm{f}}^{\ominus} \text { products }\right)-\Sigma\left(\Delta H_{\mathrm{f}}^{\ominus} \text { reactants }\right) =-235-(+52+(-242)) =-45 \text { «kJ» } \end{aligned}$

Award [2] for correct final answer.

Award [1 max] for +45 «kJ»

(iii)

Outline why the enthalpies calculated in (i) and (ii) are different.

[ 1 ]

[Maximum number: 5]

Solid ionic compounds form crystal lattices.

(a)

Enthalpy of solution, enthalpy of hydration and lattice enthalpy are related in an energy cycle.

[ 3 ]

(i)

Annotate the energy cycle for the enthalpy of solution of solid magnesium chloride, $\mathrm{MgCl}_{2}$ (s), by naming the processes A, B and C and completing the boxes. Include state symbols.

Figure for Question (i) — IB Chemistry HL

A:
B:
C:

[ 2 ]

Figure for Answer to Question (i) — IB Chemistry HL

A: enthalpy of solution / $\Delta H$ solution / $\Delta H_{\text{sol}}$ .
B: lattice enthalpy / $\Delta H_{\text{lattice}}$ .
C: enthalpy of hydration / $\Delta H_{\text{hydration}}$ .

(ii)

Calculate the enthalpy of solution for magnesium chloride, $\mathrm{MgCl}_{2}$ . Use sections 18 and 20 of the data booklet.

[ 1 ]

$\Delta H_{\text{solution}}=\Delta H_{\text{lattice}}+\Delta H_{\text{hydration}}$ $\Delta H_{\text{solution}}=2540+(-1963)+2(-359) =-141\ \mathrm{kJ\ mol^{-1}}$

(b)

Explain why the lattice enthalpy of barium chloride, $\mathrm{BaCl}_{2}$ , is lower than that of magnesium chloride.

[ 2 ]

ionic radius $\mathrm{Ba}^{2+}$ is greater than that of $\mathrm{Mg}^{2+}$ weaker attraction between « $\mathrm{Ba}^{2+}$ and $\mathrm{Cl}^{-}$ » ions

[Maximum number: 2]

Phosphoryl chloride, $\mathrm{POCl}_{3}$ , is a dehydrating agent.

(a)

$\quad \mathrm{POCl}_{3}(\mathrm{~g})$ decomposes according to the following equation.

2 \mathrm{POCl}_{3}(\mathrm{~g}) \rightarrow 2 \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g})

[ 2 ]

(i)

Define the term standard enthalpy change of formation, $\Delta H_{\mathrm{f}}{ }^{\ominus}$ .

[ 1 ]

heat/enthalpy change/required/absorbed when 1 mol of a compound is formed from its elements in their standard states/at $100 \mathrm{kPa} / 10^{5} \mathrm{~Pa} / 1 \mathrm{bar}$ ;

(ii)

Calculate the standard enthalpy change for the reaction, $\Delta H^{\ominus}$ , in $\mathrm{kJ} \mathrm{mol}^{-1}$ , using the data below.

Table for Question (ii) — IB Chemistry HL

[ 1 ]

$\left.\left(\Delta H^{\ominus}=[(2)(-288.1)]-[(2)(-542.2)]\right)=\right)(+) 508.2\left(\mathrm{~kJ} \mathrm{~mol}^{-1}\right)$ ;

[Maximum number: 1]

Phosphoryl chloride, $\mathrm{POCl}_{3}$ , is a dehydrating agent.

$\quad \mathrm{POCl}_{3}(\mathrm{~g})$ decomposes according to the following equation.

2 \mathrm{POCl}_{3}(\mathrm{~g}) \rightarrow 2 \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g})

Define the term standard enthalpy change of formation, $\Delta H_{\mathrm{f}}{ }^{\ominus}$ .

heat/enthalpy change/required/absorbed when 1 mol of a compound is formed from its elements in their standard states/at $100 \mathrm{kPa} / 10^{5} \mathrm{~Pa} / 1 \mathrm{bar}$ ;

[Maximum number: 1]

Phosphoryl chloride, $\mathrm{POCl}_{3}$ , is a dehydrating agent.

$\quad \mathrm{POCl}_{3}(\mathrm{~g})$ decomposes according to the following equation.

2 \mathrm{POCl}_{3}(\mathrm{~g}) \rightarrow 2 \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g})

Calculate the standard enthalpy change for the reaction, $\Delta H^{\ominus}$ , in $\mathrm{kJ} \mathrm{mol}^{-1}$ , using the data below.

$\left.\left(\Delta H^{\ominus}=[(2)(-288.1)]-[(2)(-542.2)]\right)=\right)(+) 508.2\left(\mathrm{~kJ} \mathrm{~mol}^{-1}\right)$ ;

[Maximum number: 6]

Magnesium, a reactive metal found in many common minerals, is also an essential nutrient for both plants and animals.

(a)

Although magnesium is usually found as $\mathrm{Mg}^{2+}$ in its compounds, it is possible to use the Born-Haber cycle to investigate the possibility of $\mathrm{Mg}^{+}$ being able to form stable compounds.

Use the ionization energy data from part (b), along with the other data provided below, to determine the enthalpy change of formation of MgCl(s). Assume that, because $\mathrm{Mg}^{+}$ would be similar in size to $\mathrm{Na}^{+}, \mathrm{MgCl}$ would have a similar lattice enthalpy to NaCl .

\begin{array}{ll} \text { Enthalpy of atomization of Mg } & +146 \mathrm{~kJ} \mathrm{~mol}^{-1} \\ \text { Bond enthalpy in } \mathrm{Cl}_{2} & +243 \mathrm{~kJ} \mathrm{~mol}^{-1} \\ \text { Electron affinity of } \mathrm{Cl} & -349 \mathrm{~kJ} \mathrm{~mol}^{-1} \\ \text { Lattice enthalpy of } \mathrm{NaCl} & +790 \mathrm{~kJ} \mathrm{~mol}^{-1} \end{array}

[ 3 ]

$\quad \Delta H_{\mathrm{at}}(\mathrm{Cl})=\frac{1}{2} \times 243\left(\mathrm{~kJ} \mathrm{~mol}^{-1}\right)$ ;
$\Delta H_{\mathrm{f}}=+146+\frac{1}{2} 243+738+(-349)+(-790) ;$ $=-134\left(\mathrm{~kJ} \mathrm{~mol}^{-1}\right)$ ;

(b)

Consider the lattice enthalpies of $\mathrm{MgF}_{2}, \mathrm{MgCl}_{2}$ and $\mathrm{CaCl}_{2}$ . List these from the most endothermic to the least endothermic and explain your order.
Most endothermic
Least endothermic

[ 3 ]

$\quad \mathrm{MgF}_{2}-\mathrm{MgCl}_{2}-\mathrm{CaCl}_{2}$ ;
$\mathrm{F}^{-}$ smaller (ionic radius) than $\mathrm{Cl}^{-}$ / $\mathrm{Cl}^{-}$ larger (ionic radius) than $\mathrm{F}^{-}$ ;
$\mathrm{Mg}^{2+}$ smaller (ionic radius) than $\mathrm{Ca}^{2+}$ / $\mathrm{Ca}^{2+}$ larger (ionic radius) than $\mathrm{Mg}^{2+}$ ;

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Covered syllabus points

Question 1

Question (a)

Question (i)

Question (ii)

Question (iii)

Question 2

Question (a)

Question (i)

Question (ii)

Question (b)

Question 3

Question (a)

Question (i)

Question (ii)

Question 4

Question 5

Question 6

Question (a)

Question (b)