4.5: Enthalpy Changes by Calorimetry

Objectives

The aims of the experiment are:

1. to determine the enthalpy change which accompanies the melting of a solid, and
2. to determine the enthalpy change for the formation of a chemical compound by using calorimetric data and applying Hess' Law.

Introduction

The heat evolved or absorbed when a process occurs at constant pressure is equal to the change in enthalpy. Since H is defined by the equation:

\[\mathrm{H}=\mathrm{U}+\mathrm{pV} \nonumber \]

then \(\Delta \mathrm{H}=\Delta \mathrm{U}+\mathrm{p} \Delta \mathrm{V}\) at constant pressure; where \(\Delta \mathrm{H}\) represents the change in enthalpy.

Reactions which occur in unsealed containers in the laboratory, occur essentially at constant pressure (= atmospheric pressure). Chemical processes which occur in plants and animals also occur at constant pressure. This is why enthalpy is such an important thermochemical parameter for physical and chemical processes. It can be related directly to the heat evolved or absorbed when the processes occur under "natural" conditions.

When processes occur in a pressure-tight, sealed container, such as a bomb calorimeter, the heat evolved or absorbed is equal to the change in internal energy, \(\Delta \mathrm{U}\), since the process occurs at constant volume.

Enthalpy is a state function, and so if one wants to define uniquely the enthalpy change in a physical or chemical process, one needs to define only the initial and final states of the system when the process occurs. For a physical process such as the melting of ice, once the pure substance is identified and the pressure is specified, the enthalpy change is uniquely defined.

The value which is now most often quoted for the enthalpy change in this process, is the molar enthalpy of melting (or "latent heat" of melting) when the process occurs at a pressure of 1 bar. (1 bar = \(10^{\times 5}\) Pa)
For chemical reactions, one can define a "standard" enthalpy of reaction by specifying "standard" initial and final states of the reacting system. The standard enthalpy of formation of a chemical compound, \(\Delta \mathrm{Hf}\), is the heat evolved or absorbed when the compound is formed in its standard state from its constituent elements in their standard states.

The standard state of a substance is defined as the stable form of that substance at a pressure of 1 bar and a specified temperature. The standard molar enthalpies of formation of elements are zero at all temperatures - by definition.

The standard molar enthalpy of formation of a compound is therefore a uniquely defined quantity, \(\Delta \mathrm{Hf}(\mathrm{T})\), and values given in thermodynamic tables are usually at 298.15 K. These quantities are useful because they can be used to obtain enthalpy of any reactions in which the individual compounds are involved.
The heat, \(\mathrm{Q}\) required to change the temperature of a substance from \(\mathrm{T_i}\) to \(\mathrm{T_f}\) is given by:

\[\mathrm{Q}=\mathrm{m C}\left(\mathrm{T_f-T_i}\right) \nonumber \]

where m is the mass whose temperature is changed from \(\mathrm{T_i}\) to \(\mathrm{T_f}\) and \(\mathrm{C}\) is the heat capacity of the substance. When \(\mathrm{m\) is in kg, \(\mathrm{C}\) is in J K^-1 kg^-1, and \(\mathrm{T}\) is in °C or K, the heat is in Joule.

Note that the heat capacity, \(\mathrm{C}\), quoted here, bears no indication of conditions, that is, whether it is \(\mathrm{C_p}\) or \(\mathrm{C_v}\). This is because only solids and liquids are usually involved in calorimetry at this level, and \(\mathrm{C_p}\) and \(\mathrm{C_v}\) are very nearly the same value for matter in these "condensed" phases.

Enthalpy Change in the Formation of Chemical Compound

Theoretical Considerations

From our definition, the enthalpy of formation of \(\ce{MgO(s)}\) is the heat produced (or absorbed) when one mole of magnesium solid reacts with a half mole of oxygen gas, the reactants and products being in their standard states.

It would be difficult to carry out this process in the laboratory particularly because a gaseous reagent is involved, but the difficulty can be avoided by selecting more convenient reactions for investigation, and combining the results using Hess' Law.

Consider the following reactions:

(a) \(\ce{Mg(s) + 2H+(aq) ---> Mg2+(aq) + H2(g) : ΔHl}\)

(b) \(\ce{MgO(s) + 2H+(aq) ---> Mg2+(aq) + H2O(l) : ΔH2}\)

(c) \(\ce{H2(g) + 1/2 02(g) ---> H2O(l) : ΔH3}\)

Combination of these equations (a - b + c) results in

\[\ce{Mg(s) + 1/2 02(g) ----> MgO(s) : ΔHf (MgO)} \nonumber \]

The enthalpy of formation of magnesium oxide can be obtained from experimental observation of reactions (a) and (b) and by using data for the \(\Delta \mathrm{Hf}\) of water from the literature:

\(\Delta \mathrm{Hf}\)(298) of water = -285.8 kJmol^-1

Procedure

(a) Determination of \(\Delta \mathrm{H} 1\).

Make sure your calorimeter is clean and dry. Weigh it empty and again with about a 10 cm length of clean magnesium ribbon. The mass should be taken to at least +/- 0.001 g.

Measure out 50 cm³ (to +/- 0.5cm³) of 1 M \(\ce{HCl}\) (density (\(\ce{HCl}\)) = 1.018 gcm^-3) into a measuring cylinder and record its temperature at four one minute intervals. On the fifth minute pour the \(\ce{HCl}\) solution into the calorimeter and put the lid on. Insert the thermometer and stirrer quickly through the lid and continue to take the temperature at 30-second intervals for about seven minutes after mixing, stirring the mixture constantly.

Graphically display your data and follow the instructions given to find the initial and final temperatures. Calculate the heat evolved, using the temperature rise determined above.

\(\mathrm{Q} = \mathrm{M}.\ce{HCl} \; \mathrm{C}.\ce{HCl} \left(\mathrm{T_f-T_i}\right) (\mathrm{C}.\ce{HCl}\) = 4.00JK-1g^-1)

Convert this to heat evolved when a mole of magnesium reacts. This is \(\Delta \mathrm{H1}\) (kJ mol^-1). Remember this is heat evolved so \(\Delta \mathrm{H1}\) is negative according to the normal convention.

Combine the three values \(\Delta \mathrm{H1}\), \(\Delta \mathrm{H2}\) and \(\Delta \mathrm{H3}\), (paying attention to the signs), to obtain \(\Delta \mathrm{Hf}\)(\(\ce{MgO}\)), and determine the uncertainty (error) in this final value.

Calculate \(\Delta \mathrm{Uf}\) of magnesium oxide, assuming that \(\Delta \mathrm{Hf}\) is the value you have found in this experiment.

Comment on the accuracy and precision of the procedure as pointedly as you can.