# 1. Heat of Combustion using Bomb Calorimetry

## ULTIMATE GOAL IS

To determine the heat of combustion of naphthalene or phenanthrene using bomb calorimetry. Time permitting, also to determine the number of calories in a suitable piece of candy.

## REPORT RESULTS

1. Calculate and report the calorimeter constant for your Calculate for each trial and then report the average (with 95% CI).
2. Calculate the enthalpy of combustion for naphthalene or Calculate for each trial and then report the average (with 95% CI).
3. Compare your enthalpy of combustion with the literature
4. If there was time, report the number of calories from your Is this consistent with the information on the package?

## USEFUL INFORMATION Of

This experiment is a little different from the Thermodynamic Investigations. In scientific work, frequently you will be using instruments based on their manuals. These manuals will often use different terminology, variables, and equations than the ones with which you are familiar. Part of the point of this lab is for you to develop your plan and procedure based on the provided operating manual for the bomb calorimeter.

The initial calculations you will perform are described in detail in the operator’s manual, but you will need to understand exactly what those calculations mean. We will NOT do the acid correction or the sulfur correction due to time constraints and you do not have the data to make the thermometer correction.

GQ 1.1 Do the calculations in the operating manual give the enthalpy?

## Theory

Since the calorimeter is isolated from the rest of the universe, we can define the reactants (sample and oxygen) to be the system and the rest of the calorimeter (bomb and water) to be the surroundings.

The change in internal energy of the reactants upon combustion can be calculated from:

`dUtot = dUsys + dUsurr = 0                                                                                               1.1`

were dU is the change in internal energy and the subscripts indicate total, system, and surroundings. Since the total change in internal energy is zero, we have:

`dUsys = -dUsurr                                                                                                                                                      1.2`

Recalling the definition of the differential dU with respect to the two variables T and V gives us:

`dUsys = -`
```[()

+ (

)

]```

1.3

Where

```(6U)

6T  v```

is the change in interval energy per change in temperature at constant volume, and

```(6U)

6V   T```

is the

change in internal energy per change in volume at constant temperature.

Since we have constant volume calorimetry, dV = 0. Thus, using the definition of heat capacity Cv yields:

`dUsys = -Cv dT                                                                                                                1.4`

where Cv is the heat capacity of the surroundings, i.e., the water and the bomb. Assuming the heat capacity (Cv) to be independent of T over small temperature ranges, this expression can be integrated to give:

`∆U = -Cv ∆T                                                                                                                   1.5`

By definition of enthalpy (∆H):

`∆H = ∆U + ∆ (pV)                                                                                                          1.6`

Where pV is the work done by pressure and volume changes. Since there is very little expansion work done by condensed phases, D(pV) » 0 for solids and liquids. Assuming the gas to be ideal yields:

`∆H = ∆U + RT ∆ngas                                                                                                                                        1.7`

where ∆ngas is the change in the number of moles of compound (number of moles of gas in the products – number of moles of gas in the reactants). The P-V work must be taken into consideration for the calculation as it depends on the extra amount (dn moles) of dH, if the calorimetry is performed at constant volume as in a bomb calorimeter.

## Experimental Apparatus Calorimeter:

The bomb calorimeter is a device for measuring heats of combustion. It consists of a metal bomb (in which the combustion takes place), a water bath in which the bomb rests, and an insulating jacket. The material for combustion is connected to an ignition switch and then placed in the bomb. The bomb is then charged (pressurized) with oxygen (your instructor will show you how to do this safely) and placed in the water bath to begin the experiment. Further instructions are in the operating manual. We will NOT do the acid correction or the sulfur correction due to time constraints.

A minimum of two steps must be completed:

1.) Determine the heat capacity of the calorimeter using benzoic acid as a standard (three trials; ‘Standardizing the Calorimeter’; week 1-2)

2.) Determine the heat of combustion of your chosen organic sample (three trials; ‘Operating the Calorimeter’, ‘Calculating the Heat of Combustion’; week 2-3)

3.) If time permits, you may also determine the number of calories present in an appropriate candy As you read through the operating manual, ponder the following questions:

GQ 1.2 How can you best accurately measure the required 2 L of water? Do you have to worry about the temperature of the water?

GQ 1.3 Does the stirrer create heat while it is stirring the water? If so, how do you take that into account?

GQ 1.4 Why is time “b” taken at 60%?

## Pellet Press:

For step 2, the organic sample must be made into a pellet.

GQ 1.5 Why must you make your sample into a pellet rather than use powder?

This requires the use of the pellet press. Your instructor will show you the details of how to use this apparatus. Generally, you will want to measure out approximately the desired mass of powder initially, but make sure to weigh the pellet AFTER. It might even be a good idea to weigh it after the ignition wire has been attached (but you will need to weigh the ignition wire separately beforehand). The cored metal cylinder should initially be on the press with the counter-sunk side up; this will make it easier to remove the pellet once it has been made.

## 9V Battery:

One of the options for attaching your pellets to the ignition wire is to use a 9V battery to heat the wire just enough that it sinks into the pellet. Your instructor will show you how to do this; it will require some patience. This process works, but requires that the battery be charged. If you are having difficulty, it may be worth trying a fresh battery.

## Safety Concerns:

Do not use more than 0.5 g of naphthalene or phenanthrene. Do not use more than 1.0 g of benzoic acid.

Check for defects or imperfections in all equipment prior to setting up a new run. Do not overfill the bomb with oxygen (30.0 atm MAX)

If you submerge the bomb and see gas bubbles, DO NOT fire! Before igniting your reaction:

1.) Loudly let the rest of the class know (aka “FIRE IN THE HOLE!”) 2.) Ensure no one is standing or walking near your bomb calorimeter 3.) Send non-firing classmates behind the safety blast shield!

4.) Lean away from the top of the calorimeter

Stay away from the bomb calorimeter for at least 30 seconds after firing. Please, please, be very careful with the thermometers so you do not break them!

Discussion ideas:

Further ideas to ponder when writing your report:

GQ 1.6 Why and how do the chemical structures of the compounds affect the heat of combustion?

GQ 1.7 How do your experimental heat of combustions relate to literature values?

GQ 1.8 Why do we need to make a correction for the fuse wire?

GQ 1.9 Why do we standardize with benzoic acid?

Hints to avoid common errors

Read through the ‘Operating the Calorimeter’ section in the operating manual repeatedly. Discuss with your lab mates the plan for the times at which you will take data (and how you will time them) BEFORE setting up the experiment.

Determine what things you need to measure BEFORE you run an experiment.

When you have completed your first good run with the benzoic acid, run through the calculations BEFORE starting another trial.

Make up a list of the variables in the operating manual and relate them to variables that are more familiar. Taking multiple trials will serve as your replication; do not try to have every member of your group make independent measurements of each point.

## ULTIMATE GOAL IS

To determine the enthalpy, entropy, and Gibbs energy for the mechanical stretching of 1) a metal spring and 2) a rubber band.

## REPORT RESULTS

1. Plot your data and extract the desired parameters for each trial. Report average values for the entropy, enthalpy, and Gibbs free energy of stretching for the elastomer (with 95% CI). Gibbs free energy should be found for room temperature (25°C).
2. Repeat for the metal
3. Explain the results!!

## USEFUL INFORMATION

Background

The linear expansion coefficient β is given by the change in length (L) for rubber (an elastomer) as it is stretched with respect to an increase of applied force f at a constant temperature T:

 `)`

``` = (        (

)

```

2.1

That is, an increase in force is needed to expand an elastomer in length. You already knew that.

In this lab, you will measure the tension of a rubber band and a metal spring as a function of their length. By making this measurement at several different temperatures, you will be able to use some fun mathematics to determine the change in enthalpy H and entropy S for the rubber band and metal that would result from it being stretched at constant temperature.

GQ 2.1 If you are asked to report the change in entropy for a given change in length, what would that parameter look like mathematically?

You will indirectly measure the force f exerted on a rubber band and a spring at various temperatures and constant length, L. You will calculate f with the use of a balance. You should make at least 3 sets of T vs. f measurements for each material. Note that f, is really ½ measured f for the rubber calculations since there are 2 lengths in the loop of the rubber band.

## Theory

Internal energy (U) is defined as:

`U = q + w                                                                           2.2`

where q is the heat energy which flows into or out of the system and w is the work done by or on the system. The change in entropy (ΔS) of a system can be defined as the change in heat of the system divided by the absolute temperature of the system (T in Kelvin):

`DS = `

2.3

Equation 2.3 can be re-arranged so that the absolute temperature of the system times the change in entropy can be used to define the change in heat of the system.

`TΔS = q                                                                             2.4`

With that, we can re-write the change in internal energy (ΔU) of the system by:

`DU = TDS + w                                                                   2.5`

For the stretching of a rubber band, the work has two components. That is, the work done by system on the surroundings, given by D(pV)—where p is the pressure on the system, this has a negative sign as the system is doing work; and the change in length (ΔL) of the rubber band under constant force (ƒ)—where the sign is positive since the work is done on the system. Substitution of this in for work in equation 2.5 yields:

`DU = TDS + fDL -D(pV)                                                   2.6`

We are interested in a system that is at constant temperature and pressure, so the equation for Gibbs free energy is a good one:

`DG = DH - TDS                                                                 2.7`

where ΔH is the change in enthalpy of the system. The change in enthalpy (at constant pressure) is defined as:

`DH = DU+ pΔV                                                                 2.8`

Therefore, with substitution of this definition of the change in enthalpy into the change in Gibb’s free energy (Equation 2.7), we have:

`DG = DU+ pΔV- TDS                                                       2.9`

The change in internal energy (Equation 2.6) can then be substituted into the new equation for Gibbs free energy change (7), yielding:

`DG = TDS – pDV+ fDL- VDp + pDV -TDS                                             2.10`

Since in our system both temperature (T) and pressure (p) are constant (at a given data point):

`DG = TDS – pDV+ fDL- VDp + pDV -TDS                                             2.11`

we are left with:

`DG =ƒDL                                                                                2.12`

Solving for the force in the above equation (at constant temperature (T) and pressure (p)), we see that the force (ƒ) has an enthalpy (H) and entropy (S) component:

```f = (

)```

,

Where:

(

)

,

= (

)

,

– T ()

,

## 2.14

And so, we can see that:

```f = (

)

,```
```- T (

)

,```

## 2.15

This equation should have a familiar structure! If the force on the elastomer (or some parameter that allows you to calculate the force) is measured as a function of temperature, assuming that the partial derivatives in Equation

2.14 do not depend on the temperature, then a LINEAR relationship appears!

GQ 2.2 What is the slope of this line and what thermodynamic parameter can be extracted from it?

GQ 2.3 What is the intercept of this line and what thermodynamic parameter can be extracted from it?

GQ 2.4 Your data will consist of temperature and (eventually) force. What units are these in? What units do they need to be in?

GQ 2.5 Which of these parameters is the independent (x) variable?

## Experimental Apparatus Operation and Measurement:

Spring box:

Turn on and zero the balance (check to make sure mass and hooks are centered with the balance in the hole in the top of the instrument).

Attach the top of the spring to the hook hanging down from the balance on top of the system. Attach the bottom of the spring to other hook and then to the mass that rests on the bottom of the apparatus (this mass should NOT be suspended, it sits on the bottom to hold the spring in tension). Use the lowest level of the spring possible to begin with.

The mass reading on the balance should be within a range of 80 g to 110 g. If it is below 80 grams, adjust the position of the hook to the spring to increase the mass to the desired range.

Once it has been adjusted to the proper mass, remove both of the rubber stoppers from the sides of the box.

Place the hair dryer in right hole on box (opposite from thermometer) and turn it on. Heat system until thermometer reaches 70 °C.

Turn off and remove hair dryer, plug both holes in box with rubber stoppers.

Record the mass indicated on the balance every 5°C from the range of 60°C to 35°C.

Plot temperature vs mass in Excel and find the slope and R2 value to make sure the data is valid.

When the system has cooled to 35 °C remove rubber stoppers, insert hair dryer and redo the procedure. Repeat until 3-4 good runs have been recorded

## Rubber band (elastomer) box:

Turn on and zero the balance (check to make sure mass and hooks are centered with the balance in the hole in the top of the instrument).

Attach the rubber band provided the hook hanging down from the balance on top of the system. Attach the rubber band to other hook and then to the mass that rests on the bottom of the apparatus (this mass should NOT be suspended, it sits on the bottom to hold the spring in tension).

Mass on the balance should range from 120 g to 150 g. If the mass is above or below this range, adjust the length of the hook hanging down from the balance to get the desired mass range (be very careful when doing this, do not move the balance out of position with the hole in the top of the box.

Remove rubber stoppers from the sides of the box. Place hair dryer in right hole on box (opposite from thermometer), heat system until thermometer shows 70°C. Turn off and remove hair dryer, plug holes in box with rubber stoppers.

Record the mass on the balance every 5°C from the range of 60°C to 35°C

Plot temperature vs mass in excel and find the slope and R2 value to make sure the data is good to use When the system has cooled to 35 °C remove rubber stoppers, insert hair dryer and restart the procedure Repeat until 3-4 good runs have been recorded

GQ 2.6 You will be measuring mass, but you need to plot the force. How can you get one from the other?

## Safety concerns:

The thermometers have mercury in them. BE CAREFUL WITH THEM! Do not burn yourselves with the hair dryer.

Discussion ideas:

Further ideas to ponder when writing your report:

GQ 2.7 What material is the spring made of? How does that material respond to tension and temperature change on a macroscopic level? How about on a molecular level?

GQ 2.8 What material is the rubber band made of? How does that material respond to tension and temperature change on a macroscopic level? How about on a molecular level?

Hints to avoid common errors

You should be able to get pretty good R2 values for this data. If you don’t, it might be a good idea to repeat it. The cooling goes faster at higher temperatures; be ready!

Taking multiple trials will serve as your replication; do not try to have every member of your group make independent measurements of each point.

Check the signs in your equations