08. Is Enthalpy a State Function?

This is a highly exothermic reaction that occurs violently with a bright flame. Its enthalpy of combustion, ΔH₁ is difficult to measure directly. However, using Hess's Law, which states that in going from a particular set of reactants to a particular set of products, the change in enthalpy is the same whether the reaction takes place in one step or in a series of steps, ΔH₁ can be obtained by combining the enthalpies of the following reactions:

How would you combine equations (2)-(4) to obtain equation (1)? Similarly, ΔH₁ can be obtained by combining ΔH₂, ΔH₃, and ΔH₄.

II. The Thermochemistry

The amount of heat evolved (q < 0 because heat is given off by the reaction) or absorbed (q > 0 because heat is gained) in a chemical reaction may be determined from experiments performed in a device called a calorimeter. Although heat flow cannot be measured directly, heat flow can be calculated from the temperature change of the surroundings (calorimeter and the solution it contains) accompanying a reaction (see below).

In this experiment, you will use a calorimeter with a clear plastic top. See Figure 1 below.

A digital thermometer will be lowered through the right-hand stopper (with a hole in it) of the calorimeter to allow you to measure temperature changes resulting from heat flow.

When an exothermic chemical reaction in solution occurs in a calorimeter, some heat is used to warm the calorimeter and some raises the temperature of the solution. The amount of heat evolved in the reaction is numerically equal to that absorbed by the solution.

q_rxn = −q_solution

Since the thermos contains styrofoam, a good insulator, there should be a negligible amount of heat transferred to the calorimeter itself or lost to the outside world. The magnitude of heat flow into solution may be calculated by using the relation

q_solution = m S ΔT

where m is the mass of the solution in grams, S is the specific heat of the solution (the amount of heat required to raise the temperature of 1 gram of the solution by 1 degree Celsius), and ΔT is as above. For the reactions that you will be running, S refers to the specific heat of a solution of MgCl₂. This value has been determined experimentally to be 3.8 ± 0.2 J/°C.g.

If a reaction is carried out directly at a constant pressure (as it will be in our case), then the heat flow, q, is proportional to the enthalpy change for the reaction:

q_rxn = nΔH

Here, ∆H is the enthalpy of the reaction (in kJ/mol or J/mol), and n is a number of moles related to the moles of limiting reagent that react. The only difference between ΔH and q_rxn is that ΔH is usually expressed in energy per mole, whereas q_rxn is expressed for the specific system that was measured (i.e. q_rxn would be different depending on whether 1 mole or 20 moles were reacted). The reactions you will be following are all exothermic. The reactions give off heat to the solution and calorimeter and the temperature rises. What does this indicate about the sign of ΔH?

III. Uncertainty Review

There is uncertainty (a.k.a. "error") in any measurement that you make. There are two contributions to uncertainty: precision (reproducibility error) and accuracy (systematic error). The total uncertainty for a measurement is the sum of the precision and accuracy components of uncertainty.

Example: In today's lab, the thermometers have a systematic error of up to ±0.03. In addition, there is a reproducibility error associated with the fluctuation in temperature readings. You will determine the reproducibility error by taking the standard deviation of temperature readings. The total uncertainty in your temperature readings is the sum of these contributions.

Example: In today's lab, you will use analytical balances whose accuracy is ±0.0001g. In addition, you may see fluctuations in the reading on the scale (precision error). If the reading fluctuates by ±0.0002g (it typically does not fluctuate this much), then the total uncertainty for the scale is the sum of these two contributions, namely 0.0003g.

There are two ways to represent uncertainty:

• 1. Absolute uncertainty (AU) is the uncertainty in a quantity, with the same units as the reported value. For example, the grape's width is 12.3 ± 0.2 mm, where 0.2 mm is the AU.

  2. Relative uncertainty (RU) represents AU as a fraction or percentage. RU = AU/|value|.

  3. For example, 0.2mm/12.3mm = 0.02 = 2%. The grape's width is 12.3 mm ± 2%, where 2% is the RU.

Uncertainty always has only one significant figure.

IV. Uncertainty Propagation Review

Uncertainty propagation refers to the fact that if you perform calculations with values that each have an uncertainty associated with them, you can follow a simple set of rules to determine the uncertainty in your final calculated value.

There are a few rules that govern how uncertainty propagates throughout a calculations:

• • Addition and Subtraction: Always use AUs

    • When calculating uncertainty for the sum or difference of measured values, AU of the calculated value is the square root of the sum of the squares of all the absolute uncertainties involved in the problem.

  • Multiplication and Division: Always use RUs

    • When calculating uncertainty for the multiplication or division of measured values, RU of the calculated value is the square root of the sum of the squares of all the relative uncertainties involved in the problem.

Refer to Uncertainty Analysis in the lab manual appendix for more examples and a more complete discussion of uncertainty propagation. Refer to Summary of Significant Figures and Uncertainty in the lab manual appendix for a summary of the rules of uncertainty propagation. For an uncertainty practice worksheet see attachments of "Uncertainty Analysis" in the appendix.

Synopsis

You will perform reactions (2) and (3) twice each and determine an average value of the enthalpy for each reaction. The enthalpy value of reaction (4) may be found in your textbook. Using Hess's Law, you will use these enthalpies to calculate the enthalpy for reaction 1. You will confirm Hess's Law by comparing your value to the published value for this reaction.

Experiment

Equipment and Materials:

• • Computer

  • Vernier SS temperature probe

  • LabPro computer interface

  • Clear plastic top calorimeter with styrofoam cup inserts

  • Analytical balance

  • Magnetic stirrer

  • Small stir bar

  • Magnesium oxide (MgO)

  • Magnesium ribbon (Mg)

  • 1.0 M HCl

Table of Physical Constants:

• • Specific Heat of MgCl₂ Solutions:

  • S = 0.0038 ± 0.0002 kJ/g °C

Instructions

You will be working in pairs. Each pair will perform each reaction once and share their data with another pair.
Everyone will analyze 2 sets of data for each reaction.

A. Setting up Logger Pro:

You will be using a stainless steel thermometer probe and LoggerPro data acquisition software. Make sure that the temperature probe is plugged into your computer and then launch the LoggerPro 3 program. Before each experiment, open the Logger Pro 3 program, click File, Open, Chemistry with Vernier, and open the file named, "18 Hess's Law.

If you run into problems or questions regarding the software, refer to “Directions for using LoggerPro Data Analysis Software” in the Appendix.

Open the Excel spreadsheet from the Results section and use it to record all measured values (with appropriate uncertainties) for every reaction.

B. Determination of ΔH for Reaction (2):

MgO_(s) + 2 HCl_(aq) → MgCl_2(aq) + H₂O_(l)

1. Weigh a calorimeter (with its cover and stirring bar) on a top-loading balance to the nearest 0.01 g. Record this value on your spreadsheet.

   • If the balance is not fluctuating, assume that the uncertainty in your mass measurement is 0.02 g. If the balance reading fluctuates, add half the range of fluctuation to your uncertainty for each measurement (e.g. if your mass is fluctuating between 0.14 and 0.16, then add 0.01 to your uncertainty).

2. Add 50 ml of 1.0M HCl to your calorimeter and place it on the magnetic stirrer.

3. Insert the digital thermometer probe through the rubber stopper with a hole, turn on the stirrer, and adjust so that the thermometer is in the acid but is not hit by the rotating stirring bar.

4. Transfer approximately 0.4 g of MgO into a weigh boat using the top-loading balances.

5. Take the full weigh boat and weigh it on the analytical balances to the nearest 0.0001g. Record this value on your spreadsheet.

   • If the readout is fluctuating, make sure that all of the doors on the balance are closed, including the top. If the readout is still fluctuating, be sure to record this uncertainty in your reading (see instructions for determining error in top-loading balance, above). The total uncertainty in the mass reading will be this uncertainty added to the uncertainty inherent in the balance itself, which is ± 0.0001g for most analytical balances. As in the top-loading balance masses, your overall uncertainty with the analytical balances will be the sum of the tared balance and the mass of your sample, so ±0.0002g at a minimum.

6. Set the data collection mode (found under "Experiment" and "Data Collection…") to Time Based, the Length of the experiment to 15 minutes, the Sampling Rate to 20 samples/min (and click, done), and the number of decimal points for your data to 2 (double click on the Time AND Temperature headings in the data table, go to Options, and under Displayed Precision select 2 and decimal places).

7. When you are ready to begin your experiment, click the Collect button. Record the temperature of the HCl solution for at least one minute. (This will be your “pre-reaction” portion of your experiment.)

8. At approximately one minute, remove the stopper without the hole (or blue cap) and carefully add the MgO from the weigh boat into the calorimeter. Replace the stopper. Note the time of addition from your data table. This is initial time, t_o.

9. Continue stirring and recording the temperature of the solution until the collection period is over. The temperature should have leveled off by then or even begun to fall a bit. If it hasn't, you may want to increase the length of the collection period when you repeat the experiment.

10. Reweigh the calorimeter with solution to determine the mass of the solution involved in the reaction. Record this value on your spreadsheet.

11. Reweigh the 'empty' weigh boat on the same analytical balance used earlier to obtain the actual mass of MgO transferred. Record this value on your spreadsheet.

Before proceeding further and to prevent overwriting your data, save your data by going to File, Save As. Save on the computer’s desktop by using your names, reaction done, and trial number. Then go back to File, Save As and enter the filename for the next data set to be taken, to ensure that you do not accidentally overwrite your previous data set.

Determination of T_initial and T_final:

To determine the initial temperature, Ti, for your reactions, highlight the flat, "pre-reaction" portion of your curve (leave out the first few and last few points of the flat region) BEFORE adding your MgO or Mg. Don't include the very beginning of the line, before things have stabilized, and don't include the end, when it starts to turn upward. See figure below.

Select the STAT button from the toolbar or Statistics from the Analyze menu. Double click on the resulting data box and change Displayed Precision to 2 decimal places. Select the mean value as T_i. All temperature readings with this thermometer have a resolution uncertainty of ± 0.03. In addition, there is an uncertainty in the average value represented by the standard deviation, also given in the data box. The total absolute uncertainty in T_i is the sum of these two factors. (In the figure below, the initial temperature (23.58°C) has an absolute uncertainty = 0.03°C + 0.088°C = 0.118°C (unrounded).

To determine the final temperature T_f, for your reactions, if the final temperature remains constant (aka-plateaus) for a couple minutes, please repeat the exact same procedure as above to determine the final temperature, T_f, as well as the uncertainty for your final temperature.

YET, if the final temperature does NOT remain constant (aka-looks somewhat like the image below):

Please find the equation of the post-reaction portion of the curve by highlighting this part of the curve and performing a regression analysis by either selecting R= from the toolbar or Linear Fit from the Analyze menu. Using the equation of the line, calculate the value of y (T_f) at the value of x (time) at which the reaction was initiated, t_o. For the reaction shown in the graph above, t_o = 1.2 min, and "y = mt + b" becomes "T_final = (-0.3997 °C/min)(1.2 min) + 36.30°C". Therefore, the final temperature for this reaction is 35.82°C. You can assume that the uncertainty in this T_f is the same as that for T_i in this reaction. Overall, the final temperature above would be: 35.82±0.118°C (unrounded).

Give your graph an appropriate title by double clicking on the existing title and then save a copy of your graph for each person in your lab group. These graphs are your data, and should be included in your Experimental section of your lab immediately.

Obtain data from another pair of students so that you have 2 data sets to analyze for each reaction. Be sure to get both mass and temperature data.

Go to 'Experiment,' and 'Clear last run…' before running another reaction.

C. Determination of ΔH for Reaction (3):

Mg_(s) + 2 HCl_(aq) → MgCl_2(aq) + H_2(g)

1. Rinse the calorimeter out well with DI water and dry thoroughly before continuing.

2. Transfer approximately 0.15 g of Mg ribbon cut into small pieces (~ 5mm each in length) into a weigh boat.

3. Obtain the mass of the weigh boat before and after the reaction using the analytical balance and record the masses to the nearest 0.0001 g. Record this value on your spreadsheet.

4. Repeat the procedure as described above with Mg, instead of MgO, with one difference. When the Mg metal is added to the calorimeter, lightly replace the stopper to allow the H₂ gas that is formed to escape.

D. Clean-up

At the end of each experiment, dispose of the reaction mixture in the aqueous waste bottle. Rinse the cup and calorimeter with deionized water and dry thoroughly and discard the water rinse in the waste bottle.

Questions for Thought:

• 1. What significant source of error is not included in the AU values that we record for our data?