Exercises: Enthalpy and calorimetry

Calcium carbonate decomposes thermally according to the following thermochemical equation at $298\,\text{K}$ and $1\,\text{bar}$:

$$\mathrm{CaCO_3(s)} \rightarrow \mathrm{CaO(s)} + \mathrm{CO_2(g)} \quad \Delta H^\circ = +178.0\,\text{kJ}\times\text{mol}^{-1}$$

1. a) Justify whether the process is exothermic or endothermic and which physical quantity this enthalpy change represents if the reaction is carried out in an open container at constant pressure.
2. b) Calculate the heat exchanged, expressed in kilojoules, when $25.0\,\text{g}$ of pure calcium carbonate decompose completely.

Data: Atomic molar masses: $M(\mathrm{Ca}) = 40.1\,\text{g}\times\text{mol}^{-1}$, $M(\mathrm{C}) = 12.0\,\text{g}\times\text{mol}^{-1}$, $M(\mathrm{O}) = 16.0\,\text{g}\times\text{mol}^{-1}$.

$A 298\,\text{K}$, the combustion of carbon monoxide gas to give carbon dioxide proceeds with release of energy according to:

$$2\,\mathrm{CO(g)} + \mathrm{O_2(g)} \rightarrow 2\,\mathrm{CO_2(g)} \quad \Delta H_1^\circ = -566.0\,\text{kJ}$$

1. a) Determine the value of the standard enthalpy of the oxidation reaction of carbon monoxide, expressed per mole of $\mathrm{CO_2(g)}$ formed.
2. b) Calculate the standard enthalpy change, $\Delta H_2^\circ$, for the decomposition reaction:

$$\mathrm{CO_2(g)} \rightarrow \mathrm{CO(g)} + \frac{1}{2}\,\mathrm{O_2(g)}$$

Two fuels are available for domestic heating: methane, $\mathrm{CH_4(g)}$, and propane, $\mathrm{C_3H_8(g)}$. The standard thermochemical equations for complete combustion at $298\,\text{K}$ are:

$$\mathrm{CH_4(g)} + 2\,\mathrm{O_2(g)} \rightarrow \mathrm{CO_2(g)} + 2\,\mathrm{H_2O(l)} \quad \Delta H^\circ = -890.4\,\text{kJ}\times\text{mol}^{-1}$$ $$\mathrm{C_3H_8(g)} + 5\,\mathrm{O_2(g)} \rightarrow 3\,\mathrm{CO_2(g)} + 4\,\mathrm{H_2O(l)} \quad \Delta H^\circ = -2220.0\,\text{kJ}\times\text{mol}^{-1}$$

1. a) Calculate the energy released per gram of fuel consumed in each case.
2. b) State, justifying your answer with the results obtained, which of the two hydrocarbons provides the greater energy yield per unit mass.

Data: Atomic molar masses: $M(\mathrm{C}) = 12.0\,\text{g}\times\text{mol}^{-1}$, $M(\mathrm{H}) = 1.0\,\text{g}\times\text{mol}^{-1}$.

The industrial synthesis of ammonia is described by the Haber-Bosch process. The following enthalpy diagram shows the energy associated with this thermochemical transformation at $298\,\text{K}$:

The figure outlines the enthalpy balance of the reaction:

The gaseous reactants are at a relative enthalpy of $0\,\text{kJ}$ and the products at $-92.0\,\text{kJ}$ per mole of $\mathrm{N_2(g)}$ that reacts.

1. a) Write the balanced thermochemical equation with the smallest integer stoichiometric coefficients and deduce, with justification, the sign and numerical value indicated by the arrow with the question mark.
2. b) Calculate the amount of heat exchanged at constant pressure when $0.50\,\text{mol}$ of $\mathrm{N_2(g)}$ react completely with excess hydrogen, and determine the heat required to decompose $68.0\,\text{g}$ of gaseous ammonia into its elements at the same temperature.

Data: Molar mass: $M(\mathrm{NH_3}) = 17.0\,\text{g}\times\text{mol}^{-1}$.

In a constant-pressure calorimeter of $1\,\text{bar}$ (whose heat capacity is considered negligible), $100.0\,\text{mL}$ of an aqueous solution of $\mathrm{HCl} 0.50\,\text{M}$ are mixed with $100.0\,\text{mL}$ of an aqueous solution of $\mathrm{NaOH} 0.50\,\text{M}$, both initially at $21.0\,^\circ\text{C}$. After neutralisation is complete, the final temperature of the homogeneous mixture stabilises at $24.4\,^\circ\text{C}$.

1. a) Write the net ionic equation of the process and determine the amount of substance, in moles, of water formed.
2. b) Calculate the experimental molar enthalpy of neutralisation, expressed in $\text{kJ}\times\text{mol}^{-1}$ of water produced.

Data: Assume that the density of all aqueous solutions is $1.00\,\text{g}\times\text{mL}^{-1}$ and that their mean specific heat capacity is equal to that of pure water, c_e $= 4.18\,\text{J}\times\text{g}^{-1}\times\text{K}^{-1}$. Assume there are no heat losses to the surroundings.

$A 298\,\text{K}$ and $1\,\text{bar}$, the complete combustion of liquid ethanol experimentally released heat at constant pressure of $1366.8\,\text{kJ}\times\text{mol}^{-1}$ according to:

$$\mathrm{C_2H_5OH(l)} + 3\,\mathrm{O_2(g)} \rightarrow 2\,\mathrm{CO_2(g)} + 3\,\mathrm{H_2O(l)}$$

1. a) Deduce the general formal relationship between the enthalpy change $(\Delta H)$ and the change in internal energy $(\Delta U)$ for an ideal gas-phase reaction and calculate the value of $\Delta n_g$ for this reaction.
2. b) Calculate the standard molar change in internal energy, $\Delta U^\circ$, in $\text{kJ}\times\text{mol}^{-1}$, for the combustion of ethanol at that temperature.

Data: Universal ideal gas constant: $R = 8,314\,\text{J}\times\text{mol}^{-1}\times\text{K}^{-1}$. Assume ideal behaviour for gaseous substances and negligible volume of liquids.

A sample of $1,150\,\text{g}$ of solid benzoic acid, $\mathrm{C_6H_5COOH(s)}$, is completely burned inside a constant-volume bomb calorimeter surrounded by $1200\,\text{g}$ of pure water. The heat capacity of the bomb itself (dry) is $C_b = 850.0\,\text{J}\times\text{K}^{-1}$. During complete combustion, the temperature of the assembly rises from $22.15\,^\circ\text{C}$ to $27.35\,^\circ\text{C}$.

1. a) Write the thermochemical equation for the complete combustion of benzoic acid producing gaseous carbon dioxide and liquid water, and calculate the molar change in internal energy per mole of acid burned $(\Delta U^\circ)$.
2. b) Calculate the standard enthalpy change of combustion, $\Delta H^\circ$, in $\text{kJ}\times\text{mol}^{-1}$, at $298\,\text{K}$.

Data: Atomic molar masses: $M(\mathrm{C}) = 12.0\,\text{g}\times\text{mol}^{-1}$, $M(\mathrm{H}) = 1.0\,\text{g}\times\text{mol}^{-1}$, $M(\mathrm{O}) = 16.0\,\text{g}\times\text{mol}^{-1}$. c_e$(\mathrm{agua}) = 4.18\,\text{J}\times\text{g}^{-1}\times\text{K}^{-1}$. $R = 8,314\,\text{J}\times\text{mol}^{-1}\times\text{K}^{-1}$. Assume the correction for the small temperature change relative to 298 K and the effect of pressure on the properties of the solid are negligible.

Gaseous hydrogen, $\mathrm{H_2(g)}$, and liquid hydrazine, $\mathrm{N_2H_4(l)}$, are compared as aerospace fuels. Under standard conditions at $298\,\text{K}$, the molar enthalpies of formation are $\Delta H_f^\circ[\mathrm{H_2O(l)}] = -285.8\,\text{kJ}\times\text{mol}^{-1}$ and $\Delta H_f^\circ[\mathrm{N_2H_4(l)}] = +50.6\,\text{kJ}\times\text{mol}^{-1}$.

The complete combustion reactions with oxygen gas form, respectively, liquid water in the case of hydrogen, and nitrogen gas together with liquid water in the case of hydrazine.

1. a) Write both balanced thermochemical equations per mole of fuel consumed and determine the standard enthalpy of combustion of each in $\text{kJ}\times\text{mol}^{-1}$.
2. b) If a rocket has a tank with a payload limit of $500\,\text{kg}$ of fuel, work out, with justification, which substance will supply the greater total energy and determine the volume of dry gaseous product that would remain after cooling and completely condensing the water (at $1\,\text{bar}$ and $298\,\text{K}$) for each fuel. Consider only the stoichiometric products: just enough oxygen, with no air or inert gas. This cold volume does not represent the hot exhaust of an engine.

Data: $M(\mathrm{H}) = 1.0\,\text{g}\times\text{mol}^{-1}$, $M(\mathrm{N}) = 14.0\,\text{g}\times\text{mol}^{-1}$, $R = 0.0831\,\text{bar}\times\text{L}\times\text{mol}^{-1}\times\text{K}^{-1}$.

In a laboratory practical to determine the enthalpy of hydration and subsequent neutralisation of calcium oxide, a student carries out two experiments in a constant-pressure calorimeter with negligible heat capacity:

1. $2.80\,\text{g}$ of $\mathrm{CaO(s)}$ are reacted in $200.0\,\text{g}$ of liquid water, producing the reaction $\mathrm{CaO(s)} + \mathrm{H_2O(l)} \rightarrow \mathrm{Ca(OH)_2(s)}$, and the water is observed to heat up, absorbing $3.26\,\text{kJ}$.

2. $3.70\,\text{g}$ of $\mathrm{Ca(OH)_2(s)}$ are reacted with an excess of aqueous solution of $\mathrm{HCl}$, releasing $5.84\,\text{kJ}$ according to: $\mathrm{Ca(OH)_2(s)} + 2\,\mathrm{HCl(aq)} \rightarrow \mathrm{CaCl_2(aq)} + 2\,\mathrm{H_2O(l)}$.

1. a) Calculate the standard molar enthalpy change for each of the two reactions above.
2. b) Applying Hess's law, determine the standard enthalpy for the direct reaction:

$$\mathrm{CaO(s)} + 2\,\mathrm{HCl(aq)} \rightarrow \mathrm{CaCl_2(aq)} + \mathrm{H_2O(l)}$$

Data: Atomic molar masses: $M(\mathrm{Ca}) = 40.1\,\text{g}\times\text{mol}^{-1}$, $M(\mathrm{O}) = 16.0\,\text{g}\times\text{mol}^{-1}$, $M(\mathrm{H}) = 1.0\,\text{g}\times\text{mol}^{-1}$. Consider the heats corrected to 298 K and standard pressure; neglect dilution effects and heat losses.