6.03 Calorimetry

The combustion of isooctane fuel (C8H18) has an enthalpy change of −5,460 kJ/mol. How many kilojoules of energy will be released when 2.0 liters of isooctane is burned, if the density of the fuel is 0.692 g/mL?

2.0 L C8H18 x 1000 mL C8H18 / 1 L C8H18 x 0.692 C8H18 x 1 mL C8H18 x 1 mol C8H18 / 114.3 C8H18 x 5460 kJ / 1 mol C8H18 = 66,112 kJ released

Part One—Calorimeters

Chemists use a device called a calorimeter to measure the heat absorbed or released by a chemical or physical change, and the process of measuring this change is called calorimetry. There are several different forms of calorimetry; the simplest form measures the change in temperature as the heat involved in a given process flows into or out of a known amount of water. By measuring the temperature change experienced by the sample of water, you can determine the amount of heat involved in the reaction or process. It is important that a calorimeter is insulated to make the system as close to an isolated system as possible. Using insulation helps prevent any energy from flowing into or out of the water from outside the calorimeter. This demonstration was used to show you the inner workings of a calorimeter. Be sure that when using a calorimeter to replace the lid after adding the substance you are measuring to avoid incorrect measurements. Because polystyrene is a good insulator, sometimes a simple calorimeter can be constructed using polystyrene coffee cups. These simple "coffee cup calorimeters" are often used in general chemistry laboratories at the high school and college level. The lid of the coffee cup calorimeter can be made of cork or polystyrene, and it should have holes for thermometers and a stirring rod to fit through without leaving any space for heat to enter or escape. Other basic calorimeters work in a similar way, but are constructed from metal with layers of cork or polystyrene for insulation. If a reaction, such as combustion, is being investigated that cannot be exposed to water, the reaction takes place in a chamber within the calorimeter. The heat released from the reaction flows into the water that surrounds the reaction chamber, where the temperature change is measured.

Specific Heat Capacity

Different substances have different capacities for storing thermal energy. This means that different types of matter require different amounts of energy to reach the same temperature, and they also cool down at different rates. Each substance has its own specific heat capacity, which is defined as the quantity of heat required to raise the temperature of a one gram of the substance by one degree Celsius. Specific heat values have a unit of joules per degree Celsius per gram: ( J / (°C × g) ) Water has a higher specific heat capacity than most other substances: 4.18 J / (°C × g) In contrast, most metals have a specific heat capacity of less than 1.0. It requires a lot of energy to increase the temperature of water, and water takes longer to cool than many other substances. This property of water makes it a useful coolant for hot engines and helps keep climates near large bodies of water more constant.

Part Two—Energy Gain/Loss

If we assume that the calorimeter, thermometer, and stirrer have no heat capacity, meaning they do not absorb any thermal energy during the process, the amount of heat gained or lost by the water will be equal to the amount of heat lost or gained by the process being examined. Because a known amount of water is used in the calorimeter, and we know the specific heat capacity of water, we can use the equation q = m × c × ∆t to determine the energy gained or lost by the water. The amount of energy gained or lost by the water is equal to the amount of energy lost or gained by the reaction or process being examined in the calorimeter. This means that the quantity of energy values is the same, but the sign on the values will be opposite because heat is flowing into one and out of the other. If the value of q for water is positive (energy was gained), that means that the value of q for the reaction is negative (energy was lost). If the calculated value of q for water is negative (energy was lost by the water), that means that the value of q for the reaction is positive (energy was absorbed, or gained, by the reaction). Scientists use various forms of chemistry to examine the direction of the energy flow, as well as the amount of energy flowing into and out of various systems. Besides examining the amount of energy, in calories or joules, contained in different food items, calorimetry can also be used to compare the usefulness of various possible fuel sources by comparing the amount of energy given off when each fuel is combusted. Anytime scientists want to examine the amount of energy involved in a process, their investigation will probably involve some type of calorimetry.

Heat Gain or Loss

In chemical reactions, energy can be either gained or lost. This energy is usually in the form of heat and can be measured with a thermometer. The energy gained or lost is called enthalpy, which is represented by the letter q. The enthalpy of an unknown sample can be calculated by using the specific heat capacity of the sample, the temperature change observed during the reaction, and the mass of the sample. Use the interactive below to learn more about calculating the enthalpy of the reaction.

Enthalpy Change

The enthalpy change of a system is equal to the energy flow of heat between the system and its surroundings when the pressure remains constant. The symbol for enthalpy is represented by the symbol ΔH. The sign on the enthalpy change value can be either negative or positive. The sign represents the direction of the heat flow from the perspective of the system, qsystem to the surroundings, qsurroundings. A negative enthalpy change value means that energy was lost by qsystem to the qsurroundings. This is called an exothermic process. A positive enthalpy change value means that the energy is absorbed from qsurroundings by qsystem. This is called an endothermic process. The enthalpy change of a reaction or process is usually expressed in kilojoules per mole (kJ/mol). This means that enthalpy change can be used as a conversion factor to determine the energy gained or lost when a certain amount of reactants are used. Remember to use the periodic table to determine the molar mass, in g/mol, of a compound.

CH4 + O2 → CO2 + 2 H2O ∆H = −890 kJ/mol

The enthalpy change value of this reaction tells us that for every one mole of methane (CH4) burned, 890 kilojoules are given off. If you burned 38.5 grams of methane, how many kilojoules of energy would you expect to be given off? The enthalpy change can be used as a conversion factor between moles of methane and kilojoules of energy. 38.5g CH4 x 1 mol CH4 / 16.05 g CH4 x 890 KJ given off / 1 mol CH4 = 2,135 kJ given off

specific heat capacity:

The quantity of heat required to raise the temperature of one gram of the substance by one degree Celsius.

Enthalpy Problem: A flask containing 855 grams of water was heated over a Bunsen burner. If the temperature of the water was raised from 21.0 degrees Celsius to 85.0 degrees Celsius, how much heat (in joules) did the water absorb? The specific heat capacity of liquid water is 4.18 J / (°C × g).

To set up this calculation, we will use q = m × c × Δt q = 855 g × 4.18 J / (°C × g) × (85.0°C − 21.0°C) q = 228730 J The water absorbed 229,000 joules, or 229 kilojoules, of energy.

Calculate the number of joules released when 72.5 grams of water at 95.0 degrees Celsius cools to a final temperature of 28.0 degrees Celsius.

q = m × c × Δt q = 72.5 g × 4.18 J / (°C × g) × (28.0°C − 95.0°C)) q = −20,300 J (20,300 joules (or 20.3 kilojoules) of energy would be released)

q = m x c x Δt

q: The q represents the heat gained or lost by the system, in joules. m: The m in this equation represents the mass of the sample, measured in grams. c: The c represents the specific heat capacity of the substance being heated or cooled. The unit for specific heat capacity is joules per gram per degree Celsius. Δt: Delta T Δt represents the change in temperature, in degrees Celsius, when a substance gains or loses energy. The change in temperature can be determined by subtracting the initial temperature from the final temperature of the substance (tf - ti).

+ΔH = exothermic (+q)

qsurroundings As heat enters the system, the enthalpy of the system increases. This is why an endothermic process has a positive enthalpy change value.

-ΔH = exothermic (-q)

qsurroundings As heat leaves the system, the enthalpy of the system decreases. This is why an exothermic process has a negative enthalpy change value.

A 120.0 gram sample of metal at 75.0 degrees Celsius is added to 150.0 g of water at 15.0 degrees Celsius. The temperature of the water rises to 18.3 degrees Celsius. What is the specific heat of the metal?

qsurroundings = m × c × Δt qsurroundings = 150.0 g × 4.18 J / (°C × g) × (18.3°C − 15.0°C) qsurroundings = 2,069 J gained qsurroundings = −qsystem −2,069 J = 120.0 g × c × (18.3°C − 75.0°C) c = 0.304 J / (°C × g)