IB Chemistry R1.2: Energy cycles in reactions worked solutions

An energy measurement is to describe homolytic separation of gaseous hydrogen fluoride into isolated neutral atoms. Which balanced equation belongs in the experimental record?

A   \mathrm{HF(g)}\rightarrow\mathrm{H^{+}(g)}+\mathrm{F^{-}(g)}

B   \mathrm{HF(l)}\rightarrow\mathrm{H(g)}+\mathrm{F(g)}

C   \mathrm{HF(g)}\rightarrow\mathrm{H(g)}+\mathrm{F(g)}

D   2\,\mathrm{HF(g)}\rightarrow\mathrm{H_{2}(g)}+\mathrm{F_{2}(g)}

At common conditions \mathrm{A(g)}\rightarrow\mathrm{B(g)} has enthalpy p and \mathrm{C(g)}\rightarrow\mathrm{B(g)} has enthalpy q. A, B and C have the same elemental composition. Which expression gives the enthalpy for 2\,\mathrm{C(g)}\rightarrow2\,\mathrm{A(g)}?

A   2(p+q) B   p-q C   2(q-p) D   2(p-q)

A reference table at 298.15\,\mathrm{K} lists \mathrm{Br_2(l)}, \mathrm{Br_2(g)}, \mathrm{Br(g)} and \mathrm{Br^-(g)}. Which entry has \Delta H_{\mathrm f}^{\ominus}=0 by convention?

A   \mathrm{Br(g)}

B   \mathrm{Br^-(g)}

C   \mathrm{Br_2(g)}

D   \mathrm{Br_2(l)}

A gas-phase sulfur ion accepts a second electron. Which pairing gives the required initial species and the expected sign of this isolated electron-addition step?

A   \mathrm{S(g)}; negative

B   \mathrm{S^{2-}(g)}; positive

C   \mathrm{S^-(g)}; positive

D   \mathrm{S^-(g)}; negative

A gas reaction releases energy overall. Which account of its covalent bonds is consistent with that observation?A Break: input; form: larger release. B Break: release; form: smaller input. C Both release energy. D Both require energy.

Write the one-mole formation equation for liquid hydrogen peroxide at 298.15\,\mathrm K and 100\,\mathrm{kPa}. Include states.

For two gas isomers, 2\mathrm{P(g)}\rightarrow2\mathrm{Q(g)} has \Delta H=-164\,\mathrm{kJ\,mol^{-1}} of the displayed equation. Find the energy released when 0.150\,\mathrm{mol} of Q forms.

A supplied ionic route contains \mathrm{M(s)\xrightarrow{a}M(g)\xrightarrow{b}M^+(g)+e^-}. Name processes a and b and state the sign of each enthalpy.

The symmetrical alkene \mathrm{(CH_3)_2C=C(CH_3)_2} reacts with bromine to form \mathrm{(CH_3)_2C(Br)C(Br)(CH_3)_2}. Use mean bond enthalpies: C=C 614, C–C 346, Br–Br 193 and C–Br 285, all in \mathrm{kJ\,mol^{-1}}.

(a) List the bonds broken and formed in the bond-accounting model, excluding unchanged bonds.   [2]

(b) Calculate the estimated molar reaction enthalpy.   [2]

(c) Explain one reason this estimate may differ from a measured value.   [1]

At identical conditions the following records are supplied: 2\,\mathrm{Cu(s)}+\mathrm{Cl}_{2}\mathrm{(g)}\rightarrow2\,\mathrm{CuCl(s)},\qquad\Delta H_1=-274\,\text{kJ mol}^{-1}. \mathrm{CuCl(s)}+\frac{1}{2}\,\mathrm{Cl}_{2}\mathrm{(g)}\rightarrow\mathrm{CuCl}_{2}\mathrm{(s)},\qquad\Delta H_2=-82.0\,\text{kJ mol}^{-1}.

(a) Determine the net equation obtained by adding the first equation to twice the second.   [2]

(b) Calculate the enthalpy for that net equation.   [2]

\mathrm{LiI} and \mathrm{CsI} have the same crystal structure and the same anion. A student predicts that \mathrm{LiI} requires more energy to separate into gas ions. Which argument supports the prediction?

A   \mathrm{Li} has a larger atomic mass than \mathrm{Cs}.

B   Iodide changes from charge -1 in \mathrm{CsI} to charge -2 in \mathrm{LiI}.

C   The smaller lithium ion allows a shorter separation between opposite charges.

D   The larger caesium ion attracts iodide more strongly because it contains more electrons.

The booklet gives standard combustion enthalpy -1086\,\mathrm{kJ\,mol^{-1}} for gaseous methylamine, \mathrm{CH_3NH_2}. Assume complete oxidation produces carbon dioxide gas, nitrogen gas and liquid water. Use formation values \mathrm{CO_{2}(g)} -394 and \mathrm{H_{2}O(l)} -286\,\mathrm{kJ\,mol^{-1}}.

(a) Write the balanced oxidation equation for one mole of methylamine.   [1]

(b) Use the data to derive the standard formation enthalpy of gaseous methylamine.   [3]

(c) Write the equation corresponding to that formation enthalpy.   [1]

A supplied rubidium iodide cycle has \Delta H_{\mathrm f}^{\ominus}=-331.3\,\mathrm{kJ\,mol^{-1}}. Other values, in \mathrm{kJ\,mol^{-1}}, are: first \mathrm{Rb} ionization +403; iodine sublimation \mathrm{I_2(s)\rightarrow I_2(g)} +62.4; I–I dissociation +151; first iodine affinity -295; \mathrm{RbI} lattice dissociation +632.

(a) Calculate the energy needed to produce one mole of \mathrm{I(g)} from the elemental standard state.   [2]

(b) Use the cycle to infer the rubidium atomization enthalpy.   [3]

(c) Explain why using the full iodine sublimation and bond-dissociation values would be incorrect for one mole of \mathrm{RbI}.   [1]

Two liquid isomers X and Y have supplied combustion enthalpies -2020 and -2005\,\mathrm{kJ\,mol^{-1}}, respectively. Both burn to the same amounts and states of carbon dioxide and water. (a) Calculate \Delta H for \mathrm{X(l)\rightarrow Y(l)}. [2] (b) Explain the subtraction direction by comparing the two complete routes. [2]

The supplied triangular route joins three gas isomers at matching conditions. Its arrows are J to K, +42.0; K to L, -71.0; and J to L, h, all in \mathrm{kJ\,mol^{-1}}. (a) Find h and the enthalpy for L to J. [2] (b) Evaluate the sum around J to K to L to J, and explain its value. [2]

For a fictional MX solid, the supplied route to its gaseous ions has successive changes +88, +106, +496 and -305\,\mathrm{kJ\,mol^{-1}}: metal atomisation, halogen atomisation, metal ionisation and electron attachment. Formation of MX from the same elements is -402\,\mathrm{kJ\,mol^{-1}}. (a) Determine the lattice dissociation enthalpy. [3] (b) Which named gas-ion preparation step releases energy? [1]

A calorimeter tests this gas route: \mathrm{Cl_{2}(g)}+2\,\mathrm{HBr(g)}\rightarrow2\,\mathrm{HCl(g)}+\mathrm{Br_{2}(g)} The enthalpy for that equation is -81.0\,\mathrm{kJ\,mol^{-1}}. The produced bromine is then condensed, releasing another 31.0\,\mathrm{kJ} per mole of bromine. A run consumes 0.0200\,\mathrm{mol} \mathrm{HBr}. The gas route and condensation both transfer energy to 50.0\,\mathrm{g} of water. Use c=4.18\,\mathrm{J\,g^{-1}\,K^{-1}}.

(a) Find the total ideal heat released by the run, including condensation.   [2]

(b) Find the ideal water temperature rise.   [2]

(c) The measured rise is 75.0\% of the ideal rise. State a plausible cause and calculate the measured rise.   [2]

A molecular-beam measurement gives +294\,\mathrm{kJ\,mol^{-1}} for \mathrm{CH_{3}Br(g)}\rightarrow\mathrm{CH_{3}(g)}+\mathrm{Br(g)} The booklet formation value for \mathrm{CH_3Br(g)} is -36\,\mathrm{kJ\,mol^{-1}}. A supplied formation value for \mathrm{Br(g)} is +112\,\mathrm{kJ\,mol^{-1}}.

(a) Determine the formation enthalpy of the gaseous methyl radical.   [3]

(b) Explain why the bromine gas-atom formation enthalpy is not zero.   [2]

(c) Compare the species-specific cleavage with the average C–Br value 285\,\mathrm{kJ\,mol^{-1}}, and explain why these values may differ.   [2]

Two invented salts, \mathrm{X_2Y} and \mathrm{Z_2Y}, contain monovalent cations and the same divalent anion. The table supplies model cycle data in \mathrm{kJ\,mol^{-1}} per mole of solid. The preparation cost includes all atomization and cation-ionization steps but no electron additions to \mathrm{Y}.\begin{array}{lrrr}\text{Solid} & \text{Preparation cost} & \Delta H_{\mathrm f}^{\ominus} & \text{Lattice dissociation}\\\hline \mathrm{X_2Y} & 1350 & -410 & 2350\\ \mathrm{Z_2Y} & 1200 & -370 & 2150\end{array}The first affinity of \mathrm{Y} is -180\,\mathrm{kJ\,mol^{-1}}. Treat the other terms as exact.

(a) Use each independent cycle to infer the second electron affinity of \mathrm{Y}.   [3]

(b) Explain why the two inferred values should agree, and identify the size of the inconsistency.   [2]

(c) The measured formation value for \mathrm{Z_2Y} is corrected to -380\,\mathrm{kJ\,mol^{-1}}. Recalculate its inferred second affinity and state whether this resolves the inconsistency.   [2]

A 0.0250\,\mathrm{mol} mixture of liquid isomers X and Y releases 42.9\,\mathrm{kJ} on complete combustion. Their supplied combustion enthalpies are -1680 and -1740\,\mathrm{kJ\,mol^{-1}}. Assume additive combustion energies and identical oxidation endpoints. (a) Find the mole fraction of Y. [2] (b) Infer the enthalpy for \mathrm{X(l)\rightarrow Y(l)}. [2] (c) The isomers have identical counts of each bond category in a mean-bond table. Explain the prediction of that table and its limitation here. [2]

A gas reaction \mathrm{A+2B\rightarrow C} has supplied \Delta H=-146\,\mathrm{kJ\,mol^{-1}} of reaction. Mix 0.0300\,\mathrm{mol} A with 0.0400\,\mathrm{mol} B and let it reach completion. An 80.0\,\mathrm g water bath receives heat; use c=4.18\,\mathrm{J\,g^{-1}\,K^{-1}}. (a) Identify the limiting reagent and calculate the energy released. [2] (b) Calculate the ideal temperature rise of the bath. [2] (c) The measured rise is 7.20\,\mathrm K. Find the fraction of the reaction energy transferred to the bath and suggest a cause of the deficit. [2]

A model oxygenated fuel F has formula \mathrm{C_2H_6O} and molar mass 46.1\,\mathrm{g\,mol^{-1}}. Complete gas-phase combustion of one mole of F releases 1250\,\mathrm{kJ} and produces 3.00\,\mathrm{mol} of water vapour. Fuel vaporisation requires +38.0 and water condensation releases 43.0\,\mathrm{kJ\,mol^{-1}} at the same temperature. (a) Calculate the combustion enthalpy for liquid fuel giving liquid water. [3] (b) Find its energy release per gram. [2] (c) Fuel G releases 30.0\,\mathrm{kJ\,g^{-1}}. Which fuel requires less mass for the same heat output? [1]

Two fictional 1:1 salts contain the same monovalent anion. Supplied sums for preparing the gaseous ions from the elements are +315 for MX and +360\,\mathrm{kJ\,mol^{-1}} for NX. Their formation enthalpies are -425 and -290\,\mathrm{kJ\,mol^{-1}}, respectively. The structures are comparable; the cation radii are 72 and 118\,\mathrm{pm}. Take the supplied enthalpies to apply at 500\,\mathrm K. (a) Calculate both lattice dissociation enthalpies. [3] (b) Explain whether their order agrees with the radius model. [2] (c) For NX, supplied \Delta S^\circ=-120\,\mathrm{J\,mol^{-1}\,K^{-1}}. Calculate \Delta G^\circ at 500\,\mathrm K and state its thermodynamic implication under standard conditions. [3]