Enthalpy

 

Thermochemistry

Thermodynamics  is the study of energy and its transformations. Thermochemistry  is the branch of thermodynamics which is concerned with the  study of energy changes which accompany chemical reactions. According to the First Law of Thermodynamics,  energy can neither be created nor destroyed, but it can be converted from one form to another.  In a chemical reaction, the energy stored in chemical bonds, or chemical energy,  may be converted into other forms of energy such as  heat and light. In a chemical reaction  bonds in the reactant  molecules are broken and new bonds in the product molecules are formed.  Bond breakage requires an  input of energy, whereas bond formation results  in a release of energy.  If the energy  released in bond formation exceeds the energy absorbed in bond breakage then the reaction occurs with a net release of energy.   In many reactions this energy appears in the surroundings as heat, symbolized by q.   For example, the combustion of natural gas produces heat energy.  The reaction is:

CH4 (g) + 2O2 (g) CO2(g) + 2H2O(l)

               (1)

A chemical reaction can also occur with the absorption of heat from the surroundings.  In this case the energy required for bond breakage exceeds the energy released in bond formation.  The heat released or absorbed by a chemical reaction can be related to a thermodynamic function called the enthalpy, H. If the reaction is carried out under constant pressure conditions the heat released or absorbed by the reaction, qP,  is equal to the enthalpy change for the reaction, DH. Where

DH = Enthalpy of Products - Enthalpy of Reactants  (2)

Thus,  for the combustion of methane at constant pressure, as would occur if methane were burned in a furnace open to the atmosphere,

qP = DH.

The enthalpy of a substance is a measure of its stored chemical energy.  By convention, if the reaction releases heat DH is negative , and the reaction is said to be exothermic.  On the other hand, if the reaction occurs with the absorption of heat  it is said to be endothermic, and qP and DH are positive . These relationships are shown in the diagram below.

Figure 1

The enthalpy change for a chemical reaction depends on the temperature and pressure of the reactants and products.  The standard enthalpy of reaction, DHo  is the enthalpy change for a reaction in which the reactants and products are all in their standard states.  The standard state  of a substance is taken to be the pure substance at 1 atm pressure, and at some specified temperature, usually 25oC.  

For example, the combustion of methane is an exothermic process.  For the combustion of 1 mole of methane, DHo = -890 kJ/mole.  This can be summarized in terms of a thermochemical equation:

CH4 (g) + 2O2 (g) CO2(g) + 2H2O(l)  DHo  = -890 kJ/mole  (3) 

This equation shows both the amount of material reacting, and the enthalpy change. Each molecular formula represents 1 mole of substance.

 The standard enthalpy of formation of a substance, DfHo  is the enthaply change for the formation of 1 mole of the substance in its standard state from the elements in their standard states.   By convention, the enthalpies of formation of the pure elements are zero.  Equation (2), can be rewritten in terms enthalpies of formation:

DH = S DfHo Products - S DfHoReactants  (4)

In the case of reaction (3), we have:

DH = 2DfHo(H2O) + DfHo(CO2) - 2DfHo(O2) - DfHo(CH4)  (5)

Numerical values of DfHoare available in tables of thermodynamic data (see your textbook).  Substituion into equation (5) yields:

DH = 2(-285.83 kJ/mol) + 1(-393.51 kJ/mol) -2(0 kJ/mol) -1(-74.81 kJ/mol)  
      = -890.31 kJ/mol (6)

Hess's Law:  According to Hess's Law of hear summation, The enthalpy change of a chemical reaction is independent of whether the reaction is carried out in one step, or in a series of steps.  the enthalpy change depends only on the inititial and final states of the reaction.  For example, reaction (3) could be carried out in a two-step process:

CH4(g) + O2(g) CO2(g) + 2H2O(g)  DHo1 =-802.29 kJ/mol (7)
2[H2O(g) H2O(l)] DHo2= 2[-44.01 kJ/mol] (8)
____________________________ ___________________________  
CH4 (g) + 2O2 (g) CO2(g) + 2H2O(l) DHoRXN = DHo1 + DHo2 = -890.31 kJ/mol (3)

In this process 1 mol of methane is burned to produce 1 mol of gaseous CO2 and  2 mols of gaseous water.  The gaseous water is then condensed to the liquid.  Note that DHo2 is equal to twice the enthalpy of freezing of water. The overall change is the same as in reaction (3).  This can be shown by summing reaction (7) and  reaction (8).  According to Hess's Law, DH for the overall process is the sum of the DH's of the individual steps.

Purpose: The purpose of this experiment is to measure the enthalpy change of each of the three reactions below, and to analyze the results in terms of Hess's Law.

HCl(aq) + NaOH(aq) H2O(l) +NaCl(aq) (9)
HCl(aq) +NaOH(s) H2O(l) + NaCl(aq) (10)
NaOH(s)  NaOH(aq) (11)

Reactions (9)  and (10) are acid-base neutralization reactions.  They involve the reaction of an acid,HCl, and a strong base, NaOH, to produce water and a salt,NaCl.  Reaction (11) represents the dissolution of solid NaOH in water.

Stockroom: Things for each group to borrow and return on the same day.

  • Nothing

Method  

 The measurement of the enthalpy change of a reaction involves measuring the heat of the reaction at constant pressure.  This is accomplished by using a device known as a calorimeter.  There are many different kinds of calorimeters. The one used in this experiment is a "Coffee Cup Calorimeter"consisting of  two nested coffee cups, a cardboard lid and a temperature measuring device called a thermistor. The thermistor is connected to a computer which collects and records temperature versus time. See below. 

Figure 2

 

In making a measurement, a known amount of acid is poured into the calorimeter and the temperature   measured.  This is the initial temperature, Ti . A measured amount of base is  added, and, since the reaction is exothermic, the temperaure of the calorimeter and its contents rises. The final temperature after the reactants are mixed,  Tf ,is then measured .  The temperature change of the calorimeter and its contents, in oC is:

 DT =Tf -T (12)

The hear absorbed by the calorimeter  and its contents is CCAL*DT + Cp*m*DT, 

where  

CCAL = the heat capacity of the calorimeter, in J/oC
Cp = the specific heat of the calorimeter contents, in J/(g-oC )
m = the mass of the calorimeter contents in g

It is assumed that all of the heat produced by the reaction, qRXN  is absorbed by the calorimeter and its contents:

qRXN = -[CCAL*DT + Cp*m*DT]

    (13)

From equation (12) we see that the determination of qRXN requires, in addition to DT, the values of m, Cp and CCAL. The value of m will calculated, and that of Cp will be given.  The value of CCAL will be determined experimentally as described in the "Procedure".

PROCEDURE 

 Part 1. Calibration of the thermistor 

Turn on the computer at your work station.  Connect the thermistor to port "A" on the interface box next to the computer.  Place a stir bar  and 50 mL of tap water into  the calorimeter.  Wrap a rubber band around the shaft of the thermistor, and insert the thermistor through the cardboard lid. Use the rubber band to adjust the height of the thermistor so that it is immersed as far as possible in the water without contacting the stir bar. Pour out the water.

Click on the Labworks icon on the computer's desktop.  Click on Calibrate.  Click on Temp A.

Fill the calorimeters with water and ice, and place the thermistor in the ice water.  Wait for the thermistor current reading on the computer screen to stabilize, the enter a zero in the space for the COLD water temperature.

  Fill the calorimeter  with hot tap water to pre-heat it.  Pour out the water and refill it with water heated to 50-55oC.  Place both the thermistor and a thermometer in the cup. Click in the space for the HOT temperature on the computer screen. When the thermistor current reading has stabilized, but not cooled, enter  the reading from the thermometer into the space for HOT temperature.  Click OK.  The thermistor is now calibrated.

Part 2. The heat capacity of the calorimeter 

Click on Design, then on EZ Program.  Under 3 choose Time, and under 4 choose Temp A.  Click on Aquire.   

Prepare about 200 mL of chilled water in a beaker by adding ice to it. Use a graduated cylinder to measure 50.0 mL of chilled  water into the  calorimeter. Make sure that no ice is transferred to the graduated cylinder. Turn on the stirrer, and adjust for a slow stirring rate. Place the lid with the thermistor on the calorimeter.      

Click on Start, and measure the temperature of the chilled water for about 1 min. A graph of temperature versus time will appear on the right-hand side of the screen. While the computer is collecting the temperature data for the cold water, place 50.0 mL of water which has been heated to 50-55oC into a graduated cylinder. Using the same thermometer used for the thermistor calibration, measure and record the temperature of the hot water, and immediately add it to the cold water in the calorimeter. In adding the hot water  do not lift the thermistor out of the water. This can be done by sliding the calorimeter lid aside, pouring the water, and repositioning the lid. The temperature will initially rise, reach a maximum, and the start to decrease.  Continue collecting data until your graph is similar to the one in Figure2, below.    

Repeat this measurement once and average your results.

Part 3. Calculation of the heat capacity of the calorimeter

  When the hot water is added to the cold water in the calorimeter, the hot water loses heat to the cold water and the calorimeter.  The temperature of the hot water decreases from some initial temperature T to a final temperature T , and its temperature change is 

DT H = T - TM

.The temperature of the cold water and the calorimeter increases from and initial temperature, TC ,to a final temperature, TM , and its temperature change is 

DT C = T - TC

The temperature TM is the temperature of the water in the calorimeter at the time of mixing, and can be obtained graphically as shown in Figure 2.

Figure 3 

The heat lost by the hot water is     ;  qH = Cp*mH*DT H

 The heat gained by the cold water  is 

qc = Cp*mC*DT

 and the heat gained by the calorimeter is 

qCAL = CCAL*DT C

where Cp is the specific heat of water (4.184 J/(K-g)),  and mC and mH are the masses in grams of the cold and hot water respectively. The heat lost by the hot water is equal to the heat gained by the cold water and the calorimeter. That is,

qH = qC + qCAL

 Example: In an experiment to calibrate her coffee-cup calorimeter, a student obtained the  data in Figure 2.  In addition, she found that the initial temperature of the hot water, TH, was 51.0oC.  What is the heat capacity of the calorimeter? 

Solution:   From the graph in Figure 2, TM = 27.0 oC, and TC = 5.0 oC.  Therefore, 

heat lost by hot water =  4.184 J/(oC-g)*50.0 mL*1.00g/mL*(51.0 - 27.0)oC = 5.02*103 J
heat gained by cold water = 4.184 J/(oC-g)*50.0 mL*1.00g/mL*(27.0 - 5.0)oC = 4.60*103J  
heat gained by calorimeter = CCAL*DT C = 5.02*103 J - 4.60*103 J = 418. J
 CCAL =  418. J/(27.0 - 5.0)oC = 19.0 J/oC     

                        

Part 4. The heat of neutralization of HCl(aq) and NaOH(aq)

 Place 50.0 mL of 1.00 M HCl(aq) and the stir bar in  the  calorimeter, and 50.0 mL of 1.00 M NaOH(aq) in a graduated cylinder. Measure the temperature of the HCl with the thermistor, and that of the NaOH with the thermometer.  The two solutions should be at the same temperature (within + 0.2oC)  If the temperatures are not the same adjust the temperature of the NaOH by running  warm or cold tap water over the cylinder. Place the calorimeter on the stirrer.  Start the stirrer,  click Start  on the computer screen, and measure the temperature of the HCl solution for  about 1 min.  Measure and record the temperature of the NaOH solution, and quickly add it to the HCl solution.  Again, add the NaOH solution by sliding the lid aside and then quickly replacing it. The temperature will quickly rise and then level off. Continue collecting data for about 1min after the initial temperature rise. 

Evaluate DT in equation (12)  from a graph of temperature versus time as shown in Figure 3. Calculate the heat of the reaction, qRXN, using equation (13).  The density of the 0.5 M NaCl(aq) solution produced is 1.02 g/mL and its  specific heat is 4.02 J/(g-oC). Finally calculate DH.  Here, DH, is the enthalpy change of reaction (9), and represents the heat produced when 1 mol of HCl reacts with 1 mol of NaOH. It is the heat per mol of HCl or NaOH reacted.  Hence,

DH = qRXN/(moles of HCl reacted)

Repeat this measurement once.

Figure 4

Part 5. The Heat of Solution of NaOH(s).  

Carefully weigh about 2.00 g (to + 0.01g) of NaOH(s).  Since NaOH(s) is very hygroscopic, weigh it by difference in a stoppered 50 mL Erlenmeyer flask.  This will require about 19 pellets.  Measure 50.0 mL of deionized water into your calorimeter.  

Due to the time required for all of the NaOH(s) to dissolve it will be necessary to modify the data gathering program so that readings are taken less frequently than in the previous experiments.  Click on Design, then on EZ Program.  Under 6, "Delay"  choose 1 second.  The computer will now collect data once every second, rather than instantaneously as in previous experiments.  Turn on the stirrer. Proceed as before and measure the temperature for about 1 min.  Carefully add the NaOH(s) to the calorimeter by sliding the lid aside, and quickly replacing it once all of the solid has been added. Continue taking readings for about 4 minutes after mixing.  Measure DT at the time of addition by extrapolation, as shown in Figure 4. 

Figure 5

Calculate the heat of solution per mole of NaOH(s) dissolved.  The final concentration of NaOH is 1 M.  The mass of solution is about 52 g and its specific heat is 3.93 J/(g-oC).

Perform this measurement in duplicate.

Part 6. The Heat of Reaction of HCl(aq) and NaOH(s).

Again weigh out about 2.00g of NaOH(s), using the procedure of Part 4.  Carefully Measure 55 mL of 1 M HCl in a 100 mL graduated cylinder, and dilute it to 100 mL with deionized water.  This ensures that an excess amount of HCl is present and that all of the NaOH will react.  Transfer the entire 100 mL of HCl(aq) to the calorimeter.  Replace the lid and thermistor. Turn on the stirrer.  Again using a 1 second delay time,  measure the temperature for about 1 min.  Carefully add the NaOH(s) to the calorimeter, and continue taking readings for 3-4 min.  Prepare a graph of temperature versus time, and, as in Part 4, determine DT at the time of mixing by extrapolation.  

Assume that the density and specific heat of the NaCl solution is the same as that in part 2.  In this case,  the NaOH(s) is the limiting reactant, and DH is given by

DH = qRXN/(moles of NaOH reacted)

Repeat this measurement once and average your results.

CALCULATIONS and GRAPHS

Use Excel to prepare graphs of temperature versus time for Parts 1 through 4.  Include these in your notebook.  Clearly show your calculations of: 

  1.  The average heat capacity of the calorimeter

  2.  The average enthalpy change for reaction (9), DH9.

  3.  The average enthalpy change for reaction (10), DH10.

  4.  The average enthalpy change for reaction (11),DH11.

CONCLUSION

  1.  Report the average enthalpy change for each of the reactions 9, 10 and11.  

  2.  Explain how your results can be used to check the validity of Hess's Law.      Are your results consistent with Hess's Law? Please explain.

  3.  Given the enthalpies of formation at 25oC, in Table 1, below, calculate the enthalpy change  for reaction  9.

    Table 1

    Compound DfHo, kJ/mol, at 25 oC
    HCl(aq) -167.16
    NaOH(aq) -470.11
    NaCl(aq) -407.27
    H2O(l) -285.83

  4. Compare your measured value of DH9 with the value calculated in question 3. What is the percent difference between your experimental result, and the calculated value?

  5. Can you think of any reasons, other than experimental error, why your experimental value for DH9    might be different from the calculated value?