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Just for fun!
More than you ever wanted to know about magnesium!  From BMWs and Volkswagons to spinach, almonds, and Milk of Magnesia.  It's in almost EVERYTHING!  Check it out.

Should we do this experiment at the North Pole or while skiing in Switzerland?  Vernier LoggerPro is portable!  Check it out.

Joke
A florence flask was getting dressed for the opera. All of a sudden she screamed: "Erlenmeyer, my joules! Somebody has stolen my joules!"
The husband replied: "Take it easy honey, don't overreact. We'll find a solution."

Laughing face image taken from Microsoft Office Clip Art.

Is Enthalpy a State Function?

Goals

• Use Hess's Law to determine the enthalpy of combustion of a reaction that can not be measured easily.
• Confirm Hess's Law by comparing our result to published measured values.

Background

I. The Reactions

The reaction that you will be studying is the oxidation of magnesium metal, Mg, to form magnesium oxide, MgO.

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 simple thermos jar calorimeter, as shown in Figure 1.

Figure 1: Thermos Calorimeter

A digital thermometer will be lowered through the right-hand stopper 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 plus that absorbed by the calorimeter.

q_rxn = - (q_solution + q_calorimeter)

Since the thermos is constructed from a good insulator, there should be a negligible amount of heat lost from the calorimeter. The amount of heat absorbed by the calorimeter, q_cal for short, may be determined from

q_cal = CΔT

where C is the heat capacity of the calorimeter in J/deg C (the amount of heat required to raise its temperature by 1 degree Celsius) and ΔT is the temperature change (final minus initial temperature). The heat capacity of the calorimeter (C) was previously determined to be 54 ± 7 J/°C.

The magnitude of heat flow into solution may be calculated by using the relation

q_solution = m SΔT

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:

ΔH α q_rxn = -(q_cal + q_solution)

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|.
   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: AU = sum of AU's
  
  

  When calculating uncertainty for the sum or difference of measured values, AU of the calculated value is the sum of the absolute uncertainties of the numbers being added and subtracted. 
  

• Multiplication and Division: RU = sum of RU's
  

  When calculating uncertainty for the product or ratio of measured values, RU of the calculated value is the sum of the relative uncertainties of the individual terms. 
  

Refer to Notes on 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. Click here for an uncertainty practice worksheet: pdf or Word format

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 (Zumdahl, Appendix Four). 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.

Preparation

Reading Assignment:

• Description of experiment.
• Hess’s Law—Zumdahl, Section 9.5
• Uncertainty Analysis—see "Notes on Uncertainty Analysis" in the Lab Manual Appendix.
• Precision and Accuracy Tutorial

Questions:

Fill out the prelab worksheet that can be found at the end of the Experiment section.

Experiment

To print instructions, select the portion that you with to print, choose File/Print, and choose "selection" to prevent printing the entire document.

Safety

• Wear safety glasses
• Pour all waste solutions into the appropriate waste container.

Equipment and Materials:

• Computer
• Vernier SS temperature probe
• LabPro computer interface
• Thermos jar calorimeter
• Analytical balance
• Magnetic stirrer
• Small stir bar
• Magnesium oxide (MgO)
• Magnesium ribbon (Mg)
• 1.0 M HCl

Table of Physical Constants:

• Heat Capacity of Calorimeter:
  C = 54 ± 7 J/°C
• Specific Heat of MgCl₂ Solutions:
  S = 3.8 ± 0.2 J/°Cg

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 and find and open the data file named, "18 Hess's Law.xmbl" which is buried in the last folder of this folder sequence:

[C:/Program Files/Vernier Software/Logger Pro 3/Experiments/_Chemistry with Computers.]
If you run into problems or questions regarding the software, refer to “Directions for using LoggerPro Data Analysis Software” in the Appendix. 

B. Determination of  ΔH for Reaction (2):

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

Record all measured values with appropriate uncertainties.

Weigh a calorimeter (with its cover and stirring bar) on a top-loading balance to the nearest 0.01 g. If the balance is not fluctuating, assume that the uncertainty in your mass measurement is 0.01 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).

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

Transfer approximately 0.4 g of MgO into a small test tube using the top-loading balances.  Take the full test tube and weigh it on the analytical balances to the nearest 0.0001g.  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.

Set the data collection mode (found under "Experiment" and "Data Collection…") to Time Based, the Length of the experiment to 6 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).

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.)

At approximately one minute remove the stopper without the hole and carefully add the MgO from the test tube into the calorimeter. Replace the stopper. Note the time of addition from your data table.  This is initial time, t_o. 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.

Reweigh the calorimeter with solution to determine the mass of the solution involved in the reaction.  Reweigh the 'empty' test tube on the same analytical balance used earlier to obtain the actual mass of MgO transferred. 

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.

To determine the initial temperature, T₁, highlight the flat, "pre-reaction" portion of your curve (leave out the first few and last few points of the flat region).  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 T₁. 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 T₁ is the sum of these two factors.

To determine the final temperature T₂, 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 (T₂) at the value of x (time) at which the reaction was initiated, t_o. You can assume that the uncertainty in T₂ is the same as that for T₁.

Give your graph an appropriate title by double clicking on the existing title and then print a copy of your graph for each person in your lab group.  These graphs are your data, and should be permanently attached to your lab notebook 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…'.

C. Determination of ΔH for Reaction (3):

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

Transfer approximately 0.15 g of Mg ribbon cut into small pieces (< 5mm in length) into a small test tube.  Obtain the mass of the test tube before and after the reaction using the analytical balance and recording the mass to the nearest 0.0001 g.

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.

Workshop 6: Calculations in Excel

Click here to download the Workshop 06 Excel template that you will use to practice performing calculations in Excel. You may use "Excel tips for chem lab" as a reference.

Prelab & Results

Click here for Prelab worksheet: pdf or Word format

Click here for Results spreadsheet

All of your results calcualtions will be performed using Excel and submitted electronically. All calculations should include a propagation of error (uncertainties) so that all final values are reported with uncertainties and the correct number of significant figures.  For the molar masses and the ΔH for reaction 4, use as many digits as are available, and assume that the uncertainty is zero. Clarifications on how to determine T_initial and T_final follow:

Determination of T_initial and T_final:

1. Determine T_initial by averaging the data points before you added 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.
2. To determine T_final, first fit a line to the upper part of the curve so that the line is a good fit to a good portion of the data (see figure below). T_final is the temperature that corresponds to the y-value of the linear fit at t_o, the time when you added your MgO or Mg. Simply plug in your t_o value as t in the equation for the line and solve for y (temperature).
   
   
   
   
   
   

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