Enthalpy Changes by Calorimetry

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Objectives

The aims of the experiment are: (i) to determine the enthalpy change which accompanies the melting of a solid, and (ii) 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:

                           
                              H=U+pV

then DH = DU + pDV at constant pressure; where DH 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, DU, 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 = 10x5 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 enthaly of formation of a chemical compound, DHf, 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 fonnation of a compound is therefore a uniquely defined quantity, DHf(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, Q required to change the temperature of a substance from Ti to Tf is given by:

               
                             Q = mC(Tf - Ti)

where m is the mass whose temperature is changed from Ti to Tf and C is the heat capacity of the substance. When m is in kg, C is in J K-1 kg-1, and T is in C or K, the heat is in Joule.
Note that the heat capacity, C, quoted here, bears no indication of conditions, that is, whether it is Cp or Cv. This is because only solids and liquids are usually involved in calorimetry at this level, and Cp and Cv are very nearly the same value for matter in these "condensed" phases.

I Enthalpy of Melting of Ice

Theoretical Considerations

If ice is mixed with warm water in a calorimeter, the ice will melt and the water so formed will be raised to a final temperature, Tf up from 0 C. If one can assume that no heat enters or leaves the calorimeter, then:

Heat lost by the warm water = Heat gained by the ice and cold
                                water produced by melting.

             mwCw(Ti-Tf) = mice(DHmelt) + miceCw(Tf- 0)

where mw and mice = mass of warm water and ice respectively.

Tf and Ti = final and initial temperatures of the water

      Cw   = heat capacity of water (= 4.18 JK-1g-1).

     DHmelt = enthalpy of melting of ice per unit mass.

Procedure

Heat approximately 200 cm3 of water to about 50C and measure carefully 100 cm3 of this warm water into the calorimeter. Start your clock/watch and record the temperature of the water at 1 minute intervals, stirring constantly, until the temerature is about 40 - 45 C. Temperatures should be read to the nearest 0.1 C, or better if the thermometer allows, and the lid should be on the calorimeter while you are doing this.
Take 4 ice cubes, shake off the excess moisture, and wipe dry as quickly as you can, with paper towels. Add them to the calorimeter exactly on one of the minutes after you have read the water temperature, taking care not to splash water out of the calorimeter. Continue stirring and now read and record the temperature every 30 seconds.
Continue reading the temperature for another ten minutes in order that you have a continuous record of temperature of the water in the calorimeter for at least fifteen minutes.
Measure carefully, using a measuring cylinder, the final volume of water in the calorimeter. The difference between the initial and final volumes, is of course the volume of water obtained as a result of the melting of added ice. Its mass is the mass of ice added. (Assume density = 1.0 gcm-3).
Display your data graphically, and obtain Ti and Tf from your graph following the instructions given by the lab supervisor. Use the equation developed above to obtain DHmelt of ice in kjmol-1.

II. Enthalpy Change in the Formation of Chemical Compound

Theoretical Considerations

From our definition, the enthalpy of formation of 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)   Mg(s)  +  2H+(aq)	--->	Mg++(aq)   +  H2(g)   	: DHl

                                     
(b)   MgO(s) + 2H+(aq)	--->	Mg++(aq)   + H2O(l) 	: DH2

         
(c)   H2(g)  + 1/2 02(g)   --->   	H2O(l)              		: DH3

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

      Mg(s)    + 1/2 02(g)     ---->    MgO(s) 		: DHf (MgO)

The enthalpy of formation of magnesium oxide can be obtained from experimental observation of reactions (a) and (b) and by using data for the DHf of water from the literature:

                                      
     DHf(298) of water = -285.8 kJmol-1

Procedure

(a) Determination of DH1.

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 HCl (density (HCl) = 1.018 gcm-3) into a measuring cylinder and record its temperature at four one minute intervals. On the fifth minute pour the 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.
Display your data graphically and follow the instructions given to find the initial and final temperatures. Calculate the heat evolved, using the temperature rise determined above.

      Q = M.HCl C.HCl(Tf - Ti)      (C.HCl = 4.00JK-1g-1)

Convert this to heat evolved when a mole of magnesium reacts. This is DH1 (kJ mol-1). Remember this is heat evolved so DH1 is negative according to the normal convention.

(b) Determination of DH2

Make sure your calo