Constant-Volume Calorimetry - Online Tutor, Practice Problems & Exam Prep

The heat of combustion is the energy released when a mole of a substance undergoes combustion, typically involving carbon and hydrogen or oxygen. This exothermic process is quantified by the enthalpy of combustion (ΔH°_comb). A bomb calorimeter, a device used for constant volume calorimetry, measures the heat released during combustion reactions. Within the sealed environment of the calorimeter, the volume remains constant, ensuring that the explosion from combustion does not expand the container. The enthalpy of standard combustion is calculated as the negative of the heat lost by the reaction:

${\mathrm{\Delta S}}_{\mathrm{rxn}}°=-Q_{\mathrm{lost}}$

The calorimeter's heat capacity (C) and the temperature change (ΔT) are used to determine the heat gained by the calorimeter and water, with the formula:

${\mathrm{\Delta S}}_{\mathrm{rxn}}°=C\mathrm{\Delta T}$

reflecting the relationship between heat lost and gained during the reaction.

Constant-Volume Calorimetry

Here we're going to say that the heat of combustion is the amount of heat released when a mole of a substance is burned or combusted. Now recall, a combustion reaction normally involves a compound with carbon and hydrogen or carbon, hydrogen and oxygen reacting with O₂.

Of course there are other elements that could be involved, such as sulfur or nitrogen, but the most common types of combustion reactions are just carbon and hydrogen or carbon, hydrogen and oxygen. Now we're going to say associated with any combustion reaction is a heat of combustion value, which we represent as ΔH⁰ so that little circle combustion.

So we'll abbreviate it as comb. So just remember when discussing constant volume calorimetry, we associated with a combustion reaction.

Constant-Volume Calorimetry Example 1

Here it says which of the following statements is true about the combustion of propane. So propane is C₃H₈ gas. It reacts with five moles of oxygen gas to produce 3 moles of carbon dioxide gas, +4 moles of water vapor. It has an enthalpy of combustion that's equal to -2222 kilojoules.

Here it says it is endothermic, it is exothermic. It absorbs heat from the surroundings or none of the above. So remember, a combustion reaction is accompanied with a negative delta H value, which signifies that it is an exothermic process. It releases heat to the surroundings.

So it is exothermic, not endothermic, and here it's releasing heat to the surroundings. If you're absorbing heat from the surroundings, you are not exothermic, you are endothermic. So out of all the choices, only option B is correct.

Constant-Volume Calorimetry

Here we're going to talk about a bomb calorimeter. Now, a bomb calorimeter is a steel container with a combustible sample submerged in a known quantity of water. And we're going to say with a bomb calorimeter we have the concept of constant volume calorimetry, and this is used to determine the heat released during a combustion reaction. Now here with this whole idea, we also have constant volume itself. This just means that the calorimeter has a fixed volume that doesn't expand after the sample is combusted.

So just think about combustion reaction as kind of a controlled explosion. So there's an explosion that goes on within the bomb calorimeter itself, but the volume stays fixed, it does not expand outward. And we're going to say, since it's a combustion reaction, that would mean that it's exothermic. This would mean that our enthalpy of standard combustion for this reaction would be equal to -Q_lost. So -Q, the amount of heat that's lost by the reaction.

Now if we take a look here, we're going to first look at the bomb calorimeter itself, its components. So with the bomb calorimeter, we're going to have a top, these two wires here. These are actually the fuses that help to ignite the combustion reaction. We're going to say here that they go down here and inside of this orange box, this represents our combustible sample. So we'll just say that this is our sample. This reaction occurs at some designated temperature, and we know that through the use of a thermometer. So here our thermometers saying it's happening at 50�C.

Here we're going to say that this blue outline here is actually our water and the heat that's combusted that's released by our sample. We want to make sure that heat is evenly distributed throughout the water sample, so we use this stirrer and then finally itself. We have our bomb calorimeter. So our bomb calorimeter, remember the sample is combusted, gives off heat. The heat exits the bomb calorimeter, and it goes into the water. The water there, its temperature is read by the thermometer. The heat is dissipated evenly throughout the use of the stirrer.

Now here with the bomb calorimeter, remember we also have our constant volume formula. Here we're going to say this is when both the liquid and calorimeter absorb heat from the hot object. Here we're going to say that it's equal to -Q_lost. So the amount of heat loss equals the amount of heat gained. So gaining heat means Q is positive plus the calorimeter itself. And remember we said that standard enthalpy of combustion is equal to -Q_lost. So here these are the same. So -Q_lost equals our standard enthalpy of combustion.

We're going to say that this amount of heat gained is related to this portion since the heat gain is positive that this MCAT is also positive. And then we're going to finally say that our calorimeter itself, it uses our heat capacity which is capital C times the change in temperature. We would say that this portion when we look at it is the constant volume formula where our standard enthalpy of combustion equals positive MCAT plus our heat capacity times change in temperature.

Constant-Volume Calorimetry Example 2

Here it says the heat capacity of a bomb calorimeter was determined by burning 12.13 grams of ethane. We're told the heat of combustion equals 1560 kilojoules per mole in the bomb. If the temperature changed by 15.2�C, we have to determine the heat capacity of the bomb calorimeter.

All right, so remember that is enthalpy of combustion equals positive Q of object, the one that absorb the heat plus Q of the calorimeter. Here we're going to convert the heat of combustion from kilojoules to Joules, which is customary with these types of questions. So remember one KJ is 10 to the three joules, so that is joules uh mole. Remember, enthalpy of combustion is exothermic, so this is a negative sign here.

Now we have one 2.3 grams of ethane. Ethane's formula is C₂H₆, and here if we convert it into moles, all right, so we have two carbons, which is two 4.02g for the two carbons. And then we have 6 hydrogens each one is 1.008, so their combined mass is 6.048. So this comes from the two carbons and the six hydrogens of ethane. When we add that up together, the mass is 30.068g per one mole.

Take that mole. We're going to plug it in here for the cue of the object, so the map. The moles are 0.4034 moles times its specific heat capacity, which when you look it up is approximately 52.63 joules. Over moles times degrees Celsius, the temperature changed by one 5.2�C, so that's our Delta T. We're looking for the heat capacity of the calorimeter times the change in temperature again, which is still one 5.2�C.

Moles cancel out, Degrees Celsius cancel out. When I multiply those together, I'm going to get 322.710 Joules plus my heat capacity again times the change in temperature. Subtract out what we have here. When we do that, we're going to get 1559677.29 equals heat capacity times the change in temperature. Divide out one 5.2�C and when we do that we're going to get the heat capacity equal to 1.03 * 10⁵ joules over degrees Celsius. So that would represent the heat capacity of the bomb Cal. Remember within this given question.

Here’s what students ask on this topic:

What is bomb calorimetry?

Bomb calorimetry is a method used to measure the heat of combustion of a particular reaction. It involves a device called a bomb calorimeter, which is essentially a strong, sealed container called a bomb. This bomb is submerged in water and filled with oxygen at high pressure. A sample of the substance whose energy content is to be measured is placed inside the bomb, and then the substance is ignited by an electric spark.

As the sample combusts, it releases heat, which is absorbed by the surrounding water. The temperature change in the water is carefully measured, as it is directly related to the amount of heat produced by the reaction. Since the bomb is sealed, the system is isolated, ensuring that no matter can enter or leave during the reaction. This allows for precise calculation of the energy content of the substance by applying principles of thermodynamics, specifically the first law of thermodynamics, which relates heat transfer to work done and internal energy changes.

How does bomb calorimetry work?

Bomb calorimetry is a method used to measure the heat of combustion of a substance. It involves a device called a bomb calorimeter, which is essentially a strong, sealed container known as a bomb. Here's how it works:

1. A small sample of the substance whose energy content you want to measure is placed in the bomb, which is then sealed.
2. The bomb is filled with oxygen at high pressure, providing an environment for complete combustion of the sample.
3. The bomb is submerged in a known volume of water within the calorimeter, and the initial temperature of the water is recorded.
4. The substance is ignited by an electric ignition system. As it burns, the energy from the combustion heats up the water surrounding the bomb.
5. The temperature change in the water is measured. Since the specific heat capacity of water is well-known, you can calculate the amount of heat absorbed by the water.
6. Corrections are made for the heat absorbed by the bomb and the calorimeter itself.
7. The heat of combustion is then calculated, usually in units of energy per mass, such as joules per gram.

The key principle behind bomb calorimetry is the law of conservation of energy: the heat released from the combustion of the sample is equal to the heat absorbed by the water and the calorimeter components.

What is the difference between a bomb calorimeter and coffee cup calorimetry?

A bomb calorimeter and a coffee cup calorimeter are both devices used to measure the heat of chemical reactions, but they differ in design and the types of reactions they are best suited for.

A bomb calorimeter is a high-precision instrument designed for measuring the heat of combustion of a sample. It consists of a strong, sealed container called a bomb, which is filled with oxygen and placed in an insulated water bath. The sample is ignited electrically, and the heat released by the combustion is transferred to the surrounding water, with the temperature change being measured. This setup allows for the measurement of reactions under constant volume and is ideal for determining the energy content of foods, fuels, and other materials.

Coffee cup calorimetry, on the other hand, is a simpler and less precise method that is often used in educational settings. It typically involves a Styrofoam cup, which serves as an insulating container, filled with a known amount of water. A chemical reaction takes place directly in the water, and the temperature change is measured. This type of calorimetry is conducted at constant pressure, making it suitable for reactions that occur in solutions, such as acid-base neutralizations.

How do you calculate the heat of combustion?

The heat of combustion is calculated using a calorimeter, which measures the heat produced when a substance is burned. Here's a basic outline of the steps involved:

1. Prepare the Sample: Weigh the substance (fuel) that you're going to burn.
2. Set Up the Calorimeter: This device has an insulated chamber where the combustion reaction takes place. It's filled with a known amount of water.
3. Measure Initial Temperature: Before starting the combustion, record the initial temperature of the water in the calorimeter.
4. Ignite the Sample: Burn the substance completely in the presence of excess oxygen to ensure full combustion.
5. Measure Final Temperature: After the combustion process is complete, record the final temperature of the water.
6. Calculate the Heat Absorbed: Use the temperature change of the water, the mass of the water, and the specific heat capacity of water (usually 4.184 J/g°C) to calculate the heat absorbed by the water using the formula:

q = m × c × ∆T

1. Adjust for the Mass of the Substance: Finally, divide the heat absorbed by the mass of the substance burned to get the heat of combustion per gram or mole of the substance.