CAIE A-Level Chemistry 23 Chemical Energetics

Practise lattice energies, Born–Haber cycles, electron affinities and enthalpy changes of solution and hydration.

Covered syllabus points

23.1 Lattice energy and Born-Haber cycles 23.2 Enthalpies of solution and hydration 23.3 Entropy change, ΔS 23.4 Gibbs free energy change, ΔG

[Maximum number: 11]

Potassium chloride, KCl , and magnesium chloride, $\mathrm{MgCl}_{2}$ , are both ionic solids.

Table 1.1

(a)

Complete the energy cycle involving the enthalpy change of solution and the lattice energy of potassium chloride, KCl, and the relevant enthalpy changes of hydration. Label your diagram.

State symbols should be used.

Figure for Question (a) — CAIE A-Level Chemistry A2

[ 2 ]

Figure for Answer to Question (a) — CAIE A-Level Chemistry A2

M1 $\mathrm{K}^{+}(\mathrm{g})$ and $\mathrm{Cl}^{-}(\mathrm{g})$

AND
$\mathrm{KCl}(\mathrm{aq}) \text { OR } \mathrm{K}^{+}(\mathrm{aq})+\mathrm{Cl}^{-}(\mathrm{aq})$

M2 three correct directional arrows COND M1

(b)

Use the data in Table 1.1 to calculate the enthalpy change of hydration of magnesium ions, $\mathrm{Mg}^{2+}$ . Show your working.

\Delta H_{\text {hyd }}^{\ominus} \text { of magnesium ions, } \mathrm{Mg}^{2+}=\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . \mathrm{kJ} \mathrm{~mol}^{-1}

[ 2 ]

use of data -155,-2493 AND $2 \times-364$ [1]

$\Delta H_{\text {hyd }} \mathrm{Mg}^{2+}=-\mathbf{1 9 2 0}\left(\mathrm{kJ} \mathrm{mol}^{-1}\right)[\mathbf{1}] \mathrm{min} 3 \mathrm{sf}$

(c)

Explain the reasons why the lattice energy of $\mathrm{MgCl}_{2}$ is more exothermic than the lattice energy of KCl.

[ 2 ]

$\quad \mathrm{Mg}^{2+}$ is smaller (than $\mathrm{K}^{+}$ )

- $\mathrm{Mg}^{2+}$ is greater charge (than $\mathrm{K}^{+}$ )

- greater attraction

between $\mathrm{Mg}^{2+}$ and $\mathrm{Cl}^{-} /$ between the ions (in $\mathrm{MgCl}_{2}$ )

OR stronger ionic bonds (in $\mathrm{MgCl}_{2}$ )

(d)

Define the following terms.

[ 2 ]

(i)

enthalpy change of atomisation

[ 1 ]

(ii)

first electron affinity

[ 1 ]

(e)

Explain what is meant by entropy, S.

[ 1 ]

(f)

Potassium chloride is very soluble in water at $20^{\circ} \mathrm{C}$ .

Explain the solubility of potassium chloride by reference to change in entropy, $\Delta S$ .

[ 1 ]

$\Delta \mathrm{S}$ is positive
$\text { AND } \mathrm{KCl}(\mathrm{~s}) \rightarrow \mathrm{K}^{+}(\mathrm{aq})+\mathrm{Cl}^{-}(\mathrm{aq}) /$

ionic lattice solid forms aqueous ions OWTTE [1]

OR

$\Delta \mathrm{S}$ is positive

AND $\Delta \mathrm{G}$ is (therefore becomes) negative /

$\mathrm{T} \Delta \mathrm{S}$ is greater than $\Delta H_{\mathrm{sol}}$ OWTTE [1]

(g)

Use the Gibbs equation and your answer to (e)(ii) to predict whether potassium chloride is more soluble in water at $20^{\circ} \mathrm{C}$ or at $80^{\circ} \mathrm{C}$ . Explain your answer.

[ 1 ]

more soluble

AND $\Delta \mathrm{G}$ is more negative at higher T /

$\mathrm{T} \Delta \mathrm{S}$ is more positive at higher T /

$-\mathrm{T} \Delta \mathrm{S}$ is more negative at higher ecf from (e)(ii) [sign $\Delta \mathrm{S}$ ]

[Maximum number: 13]

Potassium iodide, KI, is used as a reagent in both inorganic and organic chemistry.

(a)

KI forms an ionic lattice that is soluble in water.

[ 3 ]

(i)

Define enthalpy change of solution, $\Delta H_{\text {sol }}$ .

[ 1 ]

(ii)

KI(s) has a high solubility in water although its enthalpy change of solution is endothermic.

Explain how this high solubility is possible.

[ 2 ]

there is a (large) increase in entropy $\mathbf{OR} \Delta \mathrm{S}$ is positive $\mathbf{OR} \mathrm{T} \Delta \mathrm{S}$ is positive

so $\Delta G$ is negative / $T \Delta S$ outweighs $\Delta H$

(b)

Table 1.1 gives some data about the halide ions, $\mathrm{Cl}^{-}, \mathrm{Br}^{-}$ and $\mathrm{I}^{-}$ , and their potassium salts.

Table 1.1

[ 7 ]

(i)

Explain the trend in the enthalpy change of hydration of the halide ions.

[ 2 ]

anionic charge density decreases (down the group / $\mathrm{Cl}^{-}$ to $\mathrm{I}^{-}$ )

(so hydration enthalpies become less negative / less exothermic because)

less attraction of ion to water / the dipole-ion force weakens

(ii)

The $\Delta H_{\text {sol }}$ values of these potassium halides are almost constant.

Use the $\Delta H_{\text {hyd }}$ and $\Delta H_{\text {latt }}$ data in Table 1.1 to suggest why.

[ 1 ]

the difference between $\Delta H_{\text {latt }}$ and $\Delta H_{\text {hyd }}$ remains roughly constant

OR $\Delta H_{\text {latt }}$ and $\Delta H_{\text {hyd }}$ become less exothermic by a similar amount

(iii)

The enthalpy change of solution of KI(s) is $+21.0 \mathrm{~kJ} \mathrm{~mol}^{-1}$ .

Use this information and the data in Table 1.1 to calculate the enthalpy change of hydration of the potassium ion, $\mathrm{K}^{+}(\mathrm{g})$ .

\Delta H_{\text {hyd }} \text { of } \mathrm{K}^{+}(\mathrm{g})=\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . \mathrm{kJ} \mathrm{~mol}^{-1}

[ 2 ]

$\Delta H_{\mathrm{hyd}}\left(\mathrm{K}^{+}(\mathrm{g})\right)=-629+21.0-(-293)=-315 \mathrm{~kJ} \mathrm{~mol}^{-1}$

(iv)

The ionic radius of $\mathrm{Pb}^{2+}$ is 0.120 nm compared to 0.133 nm for $\mathrm{K}^{+}$ .

Suggest how the $\Delta H_{\text {latt }}^{\ominus}$ of $\mathrm{PbI}_{2}(\mathrm{~s})$ differs from $\Delta H_{\text {latt }}^{\ominus}$ of KI(s).
Explain your answer.

[ 2 ]

$\mathrm{Pb}^{2+}$ has a greater charge

- $\mathrm{Pb}^{2+}$ is smaller (than $\mathrm{K}^{+}$ ) $\mathbf{OR}\left(\mathrm{Pb}^{2+}\right)$ smaller ionic radius

- greater attraction between $\mathrm{Pb}^{2+}$ and $\mathrm{I}^{-}$

OR ionic bond between $\mathrm{Pb}^{2+}$ and $\mathrm{I}^{-}$ is stronger

OR lattice energy is more exothermic / more negative

mark as •

(c)

KI slowly oxidises in air, forming $\mathrm{I}_{2}$ .

$reaction $1 \quad 4 \mathrm{KI}(\mathrm{s})+2 \mathrm{CO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{~K}_{2} \mathrm{CO}_{3}(\mathrm{~s})+2 \mathrm{I}_{2}(\mathrm{~s}) \quad \Delta H^{\ominus}=-203.4 \mathrm{~kJ} \mathrm{~mol}^{-1}$$

Table 1.2 shows some data relevant to this question.

Table 1.2

[ 3 ]

(i)

Calculate the standard entropy change, $\Delta S^{\ominus}$ , of reaction 1 .

\Delta S^{\ominus}=\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . \mathrm{JK}^{-1} \mathrm{~mol}^{-1}

[ 1 ]

$\Delta \mathrm{S}=2(155.5)+2(116.1)-4(106.3)-2(213.6)-205.2$ $\Delta \mathrm{S}=-514.4\left(\mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right) \mathrm{min} 3 \mathrm{sf}$ ECF

(ii)

Use your answer to (c)(i) to show that reaction 1 is spontaneous at 298 K .

[ 2 ]

$\Delta G=\Delta \mathrm{H}-\mathrm{T} \Delta \mathrm{S}$ AND use of 298 K for T OR clear working to represent this

$\Delta G=-203.4-298(-514.4 / 1000)$ $\Delta G=\mathbf{- 5 0 . 1}$ OR $\mathbf{- 5 0 . 2}\left(\mathrm{kJ} \mathrm{mol}^{-1}\right)$ OR $\Delta G=\mathbf{- 5 0 1 0 8 . 8 ~ J ~ m i n} 3 \mathrm{sf}$ ECF from (c)(i)

(negative so spontaneous)

[Maximum number: 8]

(a)

Define, in words, the term enthalpy change of solution.

[ 1 ]

(b)

The following enthalpy changes are given.

Table for Question (b) — CAIE A-Level Chemistry A2

Determine the standard enthalpy change of solution of potassium phosphate, $\mathrm{K}_{3} \mathrm{PO}_{4}(\mathrm{~s})$ . It may be helpful to draw a labelled energy cycle.

\Delta H_{\mathrm{sol}}^{\ominus}=\ldots \ldots \ldots \ldots . . . . . . . . . . . . . . . . . . . . . k J ~ m o l-1

[ 3 ]

calculation of $\Delta H^{\circ}$ sol with -251,-1284 and -2035 only and two correct signs [1]

calculation of $\Delta H^{\ominus}$ sol with -251,-1284 and -2035 only and correct signs

OR calculation of $\Delta H^{\circ}$ sol with ( $-251 \times 3$ ), -1284 and -2035 only and two correct signs [2]
$\Delta H^{\ominus}{ }_{\mathrm{sol}}=(3 \times-251)+(-1284)-(-2035)=-2\left(\mathrm{~kJ} \mathrm{~mol}^{-1}\right)[3]$

(c)

Some lattice energy values are shown in the table.

Table for Question (c) — CAIE A-Level Chemistry A2

Suggest an explanation for why $\Delta H_{\text {latt }}^{\ominus} \mathrm{CaBr}_{2}$ is more exothermic than $\Delta H_{\text {latt }}^{\ominus} \mathrm{KBr}$ .

[ 2 ]

$\mathrm{Ca}^{2+}$ have a higher charge / greater charge density [1] ora

stronger electrostatic forces between $\mathrm{Br}^{-}$ and $\mathrm{Ca}^{2+}$ [1]

(d)

For a particular gas phase reaction the variation in standard Gibbs free energy change, $\Delta G^{\ominus}$ , with temperature is shown.

Assume standard enthalpy change, $\Delta H^{\ominus}$ , and standard entropy change, $\Delta S^{\ominus}$ , remain constant with temperature.

Figure for Question (d) — CAIE A-Level Chemistry A2

[ 2 ]

(i)

Write the equation that relates $\Delta G^{\ominus}$ to $\Delta H^{\ominus}$ and $\Delta S^{\ominus}$ .

[ 1 ]

$\Delta G^{\ominus} = \Delta H^{\ominus} - \mathrm{T}\Delta S^{\ominus}$

(ii)

Use this equation to explain why $\Delta G^{\ominus}$ becomes less positive as temperature increases in this reaction.

[ 1 ]

$\mathrm{T} \Delta S$ is more positive

OR -T $\Delta \mathrm{S}$ becomes more negative [1]

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Covered syllabus points

23. Chemical energetics question 1

Question (a)

Question (b)

Question (c)

Question (d)

Question (i)

Question (ii)

Question (e)

Question (f)

Question (g)

23. Chemical energetics question 2

Question (a)

Question (i)

Question (ii)

Question (b)

Question (i)

Question (ii)

Question (iii)

Question (iv)

Question (c)

Question (i)

Question (ii)

23. Chemical energetics question 3

Question (a)

Question (b)

Question (c)

Question (d)

Question (i)

Question (ii)