About Bomb Calorimeter

BOMB CALORIMETRY

1.  Purpose of Bomb Calorimetry Experiments

Bomb calorimetry is used to determine the enthalpy of combustion, D_combH, for hydrocarbons:

C_xH_YO_{z (s)}  +  (2X+Y/2-Z)/2 O_{2 (g)}  ®  X CO_{2 (g)} + Y H₂O _(l)

Since combustion reactions are usually exothermic (give off heat), D_combH is typically negative.  (However, be aware that older literature defines the "heat of combustion" as -D_combH, so as to avoid compiling tables of negative numbers!)

2.  Construction of a Bomb Calorimeter

The bomb calorimeter consist primarily of the sample, oxygen, the stainless steel bomb, and water.

The dewar prevents heat flow from the calorimeter to the rest of the universe, i.e.,

q_calorimeter = 0

Since the bomb is made from stainless steel, the combustion reaction occurs at constant volume and there is no work, i.e.,

w_calorimeter = -ò p dV = 0

Thus, the change in internal energy, DU, for the calorimeter is zero

DU_calorimeter = q_calorimeter + w_calorimeter = 0

The thermodynamic interpretation of this equation is that the calorimeter is isolated from the rest of the universe.

3.  DU and DH in a Bomb Calorimeter

3.  A.  Internal energy change DU

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

Since the process if constant volume, dV=0.  Thus, recognizing the definition of heat capacity C_v yields

Assuming C_v to be independent of T over small temperature ranges, this expression can be integrated to give

where C_v is the heat capacity of the surroundings, i.e., the water and the bomb.

3.  B.  Enthalphy change DH

By definition of enthalpy

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

3.  C.  Intuitive difference between DU and DH

Recall that DU=q_v is the heat flow under constant volume conditions, whereas DH=q_pis the heat flow under constant pressure conditions.  The difference between these two situations is that pV work can be done under constant pressure conditions, whereas no pV work is done under constant volume conditions.

Consider the case where Dn_gas > 0. i.e., the system expands during the reaction.  The same amount of energy is released by the reaction under both sets of conditions.  However, some of the energy is released in the form of work at constant pressure; thus, the heat released will be less than at constant volume.  Mathematically,

In the case where Dn_gas < 0. i.e., the system contracts during the reaction, the surroundings does work on the system.  Thus, this work is available for energy release from the system back to the surroundings in the form of heat.  Mathematically,

These cases can be depicted pictorially as follows:

	Dngas > 0 work done by system -DH < -DU or DH > DU
	Dngas < 0 work done on system -DH > -DU or DH < DU

4.  Calibration of the Calorimeter

4.  A.  Estimating C_v

The heat capacity of the bomb calorimeter can be estimated by considering the calorimeter to be composed of 450 g water and 750 g stainless steel.  Knowing the specific heat capacity of water to be 1 cal/g·K and estimating the specific heat capacity of steel to be 0.1 cal/g·K yields

4.  B.  Measuring C_v

For accurate work, the heat capacity of the calorimeter must be measured.  This is done by depositing a known amount of energy into the calorimeter and observing the temperature increase.  The two most common methods for measuring C_v are

1.  Burning a standard with known DU, e.g., benzoic acid.

mbenzoic acid DUbenzoic acid = mbenzoic acid -6318 cal/g·K = -Cv DT

2.  Doing electrical work by passing current though a resistor.

DU = w + q = V·I·t + 0 = Cv DT

5.  Corrections in Bomb Calorimetry

5.  A.  Combustion of fuse

Nickel and iron fuses can burn according to

Ni + O₂ ® NiO

or

2Fe + O₂ ® Fe₂O₃

The heat released by combustion of the fuse is accounted for by recognizing that

DU = DUsample·msample + DUburned fuse·mburned fuse = -Cv DT

where the mass of the burned fuse is determined by weighing the fuse before and after firing the bomb.

5.  B.  Nonadiabaticity of calorimeter

A bomb calorimeter is only approximately adiabatic.  In reality, there is a small heat leak through the dewar (q_calorimeter ¹ 0) and the stirrer does work on the calorimeter (w_calorimeter ¹ 0).  Nonadiabaticity is corrected for with an empirical radiative correction, RC.

The time at which the bomb is considered to be fired is the time that makes the areas indicated in the above figure equal.  For the Parr calorimeter, this is estimated to be at t = 7 minutes.  Thus, the temperature at t = 6 minutes must be extrapolated forward 1 minute by the pre-firing slope, and the temperature at t = 12 minutes must be extrapolated backward 5 minutes by the post-firing slope.  Mathematically, this is done as follows

5.  C.  Nitric acid formation

At high temperatures, nitrogen can form nitric acid in the presence of oxygen and water.  (This reaction also occurs in automobile engines and is partially responsible for smog production.)

N₂ + O₂ + H₂O ® 2HNO₃

Flushing the bomb with oxygen prior to firing, thereby displacing all nitrogen, eliminates nitric acid formation.

6.  Application of D_combH

In addition to measuring the energy release of one particular reaction, calorimetry is an important tool for determining the enthalpy of formation for the compound under study.  This information can then be applied to any reaction involving the compound.

The enthalpy of combustion for the reaction

can be written as

DcombH(CxHyOz) =

v(CxHyOz)DfH°(CxHyOz) + v(O2)DfH°(O2) + v(CO2)DfH°(CO2) + v(H2O)DfH°(H2O)

D_combH(C_xH_yO_z) = v(C_xH_yO_z)D_fH°(C_xH_yO_z) + v(O₂)D_fH°(O₂) + v(CO₂)D_fH°(CO₂) + v(H₂O)D_fH°(H₂O)

where v(i) is the stoichiometric coefficient of i.  Since D_fH°(C_xH_yO_z) and D_fH°(H₂O) are known (and D_fH°(O₂) equals zero), measurement of D_combH(C_xH_yO_z) allows calcualtion of D_fH°(C_xH_yO_z).

7.  Other Types of Calorimeters

There are many kinds of calorimeters, each designed for measuring the heat released by a particular chemical process.  Some examples include:

	Flame Calorimeter The combustible gas is metered into the calorimeter.  Temperatures of all reactants must be controlled.  Since the reaction occurs at constant pressure, DcombH is measured directly.
	Solution Calorimeter Reactants are initially separated.  The temperature change is measured when they are allowed to mix.  Quantities that can be determined include DmixH, DdilutionH, and DsolvationH.

Calorimeter design is very tricky, especially for processes involving very small energy changes, e.g., protein folding, or energy changes on top of a large background, e.g., excess heat from "cold fusion".  Heat leaks must be minimized, and all other heat generating processes must be accounted for.

What is a calorie?

What the heck is a calorie anyway?

A calorie is a way to measure energy. It’s a unit of measurement, just like a centimetre is a unit of measurement.

Now, it’s easy to understand what a centimetre is, since I can draw a line 1 cm long and show it to you, but a calorie is a little harder to grasp.

A food calorie (technically, a kilocalorie, or kcal) is simply how much energy you need to increase the temperature of 1 kilogram (about 1 L*) of water by 1˚C.

(*Note: depending on temperature and pressure 1 kg of water can be a little more or less than 1 litre.)

There are other ways of measuring energy, just like there are other ways of measuring length (inches, centimetres, furlongs). The official scientific (SI) unit for energy is kilojoules (kJ). 4.2 kJ = 1 kCal = 1 food calorie. But because I’m talking about food, any time I refer to a calorie, it’s a food calorie.

Since I can’t draw you a picture of what a calorie looks like, I’m going to give you an example of what you can do with calories.

Fun with calories

Let’s say you want to have a nice warm bath, but your hot water heater is broken, so the water in your tub is cold (only 21˚C – room temperature).

A completely full bathtub holds about 140 litres, so 100 litres of water should be more than enough for you to have a nice satisfying bath. A warm bath is about 35˚C. To heat your tub of water (100 L) by 14˚C (from 21 to 35˚C), you would need 1400 calories.

What to do? Luckily you just came back from McDonald’s, where you bought a large Coke (310 cals), an Angus bacon & cheese burger (790 cal) and a large container of fries (500 cal) for a grand total of 1600 calories. You could warm your tub water by burning your McDonald’s meal!

That would take a bit of work, but it’s possible, and then you and your rubber ducky could have a nice warm bath with 200 calories to spare.

Put that Supersize meal to work

Calorie counting

For years the experts said a calorie is a calorie is a calorie, and as long as you eat fewer calories than you expend (through your basal metabolism and activity), then you will lose weight.

Yet despite this, people got fatter. Why?

Because of one big flaw: there is no consideration for the calories’ source or quality. The calories could be from a pound of broccoli, a Pop Tart, or a ¼ teaspoon of bacon grease. They were all treated the same.

Calorie counting distorted what people thought they could eat. They ended up (over)eating low-calorie cookies, low-fat ice cream, and diet cola, and avoiding high calorie healthy food, like avocados and nuts.

If they were rigid and careful with their intake, they might end up with a calorie deficit, thus reducing the quantity of calories, but the quality of what they ate was pretty bad.

For example, you could be on a diet that allows for 1600 calories a day. You could go to the drive thru, get the bathtub-warming special at McDonald’s, actually eat it instead of heating up your bathwater, and have consumed the day’s allotment of energy.

That’s a whopping quantity of trans fat, sugar, sodium, food additives, and other garbage. A slice of tomato, some lettuce, a pickle and fries are your fruits and vegetables for the day. Can you say scurvy?

Another problem with calorie counting is that you have to rely on the companies making the food to tell you how many calories are in their food. For years you couldn’t get the calorie counts for most restaurants. Eventually, companies provided them (often rather grudgingly).

Now, as it turns out, those calorie counts may not even be correct.

This weeks’ review looks at the accuracy of calorie information presented on food labels and restaurant websites.

Urban LE, Dallal GE, Robinson, LM, Ausman, LM, Saltzman E, Roberts SB. The accuracy of stated energy contents of reduced-energy, commercially prepared foods. J Am Diet Assoc. 2010. 110(1):116-123.

Methods

If you live in the Boston area and saw somebody in a lab coat wondering around your local grocery store sometime last year, chances are it was a researcher from this study. In this week’s study researchers went out and bought meals that you or I would get from a grocery store or restaurant.

Frozen foods were from:

• Lean Cuisine
• Weight Watchers
• Healthy Choice
• South Beach Living
• Bell & Evans

Restaurants surveyed were:

• Denny’s
• Ruby Tuesday
• Taco Bell
• PF Chang
• The Olive Garden
• McDonald’s
• Applebee’s
• Domino’s
• Dunkin Donuts
• Wendy’s

There were 39 meals in total, all with nutritional information available (either on the package or on the web) and labelled as low calorie (<500 kcal).

The researchers picked the lowest calorie meals on the menu at the restaurants and matched those meals when picking the frozen dinners at the grocery store.

This is an important point: The researchers deliberately set out to find the low-calorie options. They didn’t look for obvious offenders, such as the Domino’s Mac ‘n’ Cheese Breadbowl or the Ruby Tuesday Double Chocolate Cake. They purposely sought foods that calorie-conscious eaters might select.

Calorie recipe

We’ve all picked up a package of food of the shelf and looked at how many calories it contained. Have you ever wondered how they came up with the calorie count?

Do they feed people the food and see how much weight they gain in a week? Nope. Do they use mice? Nope.

You don’t need any people or animals to figure out how many calories are in food. You just need a scale, a blender, a dryer and a way to measure heat.

Calorie recipe – how to figure out how many calories in your favourite food in five easy steps!

• Weigh the food or meal
• Blend the food or meal until smooth with an even consistency and very unappetizing.
• Freeze dry the pureed mush.
• Grind the dried pureed mush into a fine powder.
• Cook the powder until it bursts into flames and all that’s left is a pile of ash.

Sounds tasty, no?

As the flaming, pureed, freeze-dried powder burns, it produces heat that you can measure.

Scientists call this direct calorimetry, because you directly measure how many calories come from a food. To do this, they usually use a special type of equipment called a bomb calorimeter.

Bomb calorimeter

Results

On average the 10 frozen meals had 8% more calories than the amount given on the labels. This doesn’t seem too bad, unless you eat these meals regularly.

If you thought you were eating 2000 calories/day, but were actually eating 8% more (160 calories) because all your meals were frozen or prepared foods, then by the end of the week you would have an extra 1120 calories.

Hmmm…now you have a problem, because by the end of the year you will have an extra 58,240 calories, or over 7.55kg (16 pounds) of fat!

Okay, chances are you aren’t eating that much frozen food, but what about restaurants? You eat at restaurants, right? Well, that’s even worse.

In this study restaurants underestimated the calories of their meals by an average of 18%!

The worst estimates were from Denny’s for their toast and grits. Dry white toast was 283 calories per slice instead of the 97 calories listed. Grits served with butter were also much higher in calories than reported by Denny’s (258 calories instead of the reported 86 calories).

Thus, if we do the same calculation as for the frozen food — i.e. if you think you’re eating 2000 calories a day, but are eating all your meals at these kinds of restaurants — you’ll be taking in 18% more than you realize, or 360 calories a day — 2520 a week, or 131,040 a year, for 37.44 additional pounds of fat.

That’s over a pound every two weeks. Ouch.

Conclusion

Restaurant and frozen food meals marketed as low calorie listed fewer calories on the package than the food actually contained.

On average the frozen foods had 8% more calories than the package listed, and the restaurants had 18% more calories.

This is the typical good news, bad news scenario. The good news is that there is some regulation by the US Food and Drug Administration (FDA). The bad news is that it only applies to packaged food. And there’s more bad news: for the FDA, an “acceptable underestimation” of calories is 20%.

Restaurants don’t have to follow any regulations, but frozen food manufacturers have to be within 20%. Really, 20%! That 250 calorie meal could be 300 calories and still be within regulations.

Bottom line

Besides driving yourself crazy, calorie counting is not the best way to lose weight and you’re likely setting yourself up for failure.

Yes, it’s good to have an idea of how many calories you’re eating, but if you’re consistently calculating how many calories left for today, then your mathematical ability isn’t the only thing that may mislead you.

Eat unprocessed, whole foods — for many reasons.

They’re better for you in general. They have more of the good stuff (vitamins, minerals, fibre, phytonutrients, etc.) and less of the bad stuff (additives, sugar, etc.). They fill you up better. They nourish you better.

And you know exactly what you’re eating.

Bomb Calorimetry

Here is a schematic drawing of a bomb calorimeter:

The "Bomb" inside is a steel vessel capable of withstanding the large pressure of gas inside as well as the explosive force of the burning reagents inside.
This is a Constant Volume calorimeter since the reaction occurs within a rigid vessel (the bomb) whose volume cannot change.
The heat capacity of the calorimeter is equal to the sum of the heat capacity of the water + the heat capacity of the dry calorimeter (bomb, stirrer, insulated container, etc):

C_calorimeter = C_{dry parts} + C_H2O

If we know C_calorimeter and measure T, we can obtain the heat change in the calorimeter.
q_calorimeter = C_calorimeter x T
but
E_rxn = q_rxn = - q_calorimeter= - C_calorimeter x T

Example: if a reaction performed in a bomb calorimeter is exothermic then the
heat absorbed by the calorimeter assembly, q_calorimeter is positive (temperature of calorimeter rises)
But this is an exothermic reaction (E_rxn<0) in which no work is done so q_rxn = - q_calorimeter.