The student is expected to perform calculations involving heat, mass, temperature change, and specific heat AND use calorimetry to calculate the heat of a chemical process.
The ΔH (change in enthalpy) of a system is equivalent to the heat of the system (q). The heat gained or lost by a system may be calculated using the mass, specific heat and temperature change of the system.
The equation used to calculate these variables is
q = m (mass in grams) x cp (specific heat) x ΔT (change in temperature). The specific heat (cp) of a substance is defined as the amount of heat required to raise the temperature of 1 gram of the substance by 1 degree Celsius.
Calorimetry includes the complete set of equations and experimental procedures used to measure the heat flow of physical and chemical processes. A calorimeter is the device used to measure the heat absorbed or released during a chemical process.
THE FOUNDATIONS FOR CALORIMETRY
A Scottish scientist named Joseph Black performed extensive studies of the heating of water. He found that, during phase changes (ice changing to liquid water or liquid water changing to steam), the temperature of the water did not increase. This led to him coining the term latent heat in 1762. He used this term in relation to the heat transfer that occurred during a change of state that caused a change in the volume of the water when the temperature of the system remained the same. Further experiments led to him finding that each substance has its own specific heat. Joseph Black’s findings were the beginnings of the study of thermodynamics.
In 1782, two other scientists named Antoine Lavoisier and Pierre-Simon Laplace used Black’s findings on latent heat to create the first ice-calorimeter. These men used this primitive calorimeter to calculate the heat released during chemical reactions, and so the study of calorimetry was born.
Heat is the thermal energy in transit, and a calorimetry is the method used to measure it. The amount of heat energy that is absorbed or released is called the enthalpy (H) of reaction and it is measured in joules (J). You can calculate the change of enthalpy (H) of a system (the change in the heat content of the system) by calculating the heat flow of the system. The heat flow is represented by the letter q.
The enthalpy change during a chemical reaction is the following:
It can be written as:
If the heat flow experiment occurs under constant pressure, then the heat flow (q) will equal the enthalpy change (H). Assume that the pressure remains constant for reactions that take place in solution. As no heat is lost to the surroundings with a calorimeter, the following relationship is true:
q = ΔH
Calorimetry includes the complete set of equations and experimental procedures used to measure the heat flow of physical and chemical processes. A calorimeter is the device used to measure the heat absorbed or released during a chemical process.
HEAT FLOW
Calorimetry is the measurement of the amount of heat gained or lost (q) in physical and chemical processes. These calculations are dependent on the mass of the matter (m), the specific heat of matter (cp), and the change in temperature of the system (ΔT). Any of these variables may be found if the other three variables are known.
The following is the equation used to calculate these variables:
The specific heat of a substance (cp) is defined as the amount of heat required to raise the temperature of 1 gram of a substance by 1o Celsius. Water has a vital role in global and local temperature regulation. This can be explained by water’s specific heat, which is 4.186 joules per gram•1 degree Celsius, or 4.186 J/g°C. The specific heat of water is higher than other common matter.
SAMPLE HEAT CALCULATION
To calculate the heat flow during a chemical process:
As stated before, m is the mass, cp is the specific heat, and ΔT is the change in temperature.
For example, we can use burning charcoal to boil water. The mass of water is 2000 grams. If the temperature of the water increases from room temperature, 25°C, to 100°C under standard atmospheric pressure, what is the amount of heat transferred? Does the water absorb or release heat?
The heat transfer direction is from the burning charcoal and causes a chemical reaction to occur in the water. Hence, the water absorbs heat while the charcoal releases heat. The chemical reaction of the charcoal is not an endothermic reaction, but an exothermic reaction.
Let’s calculate the transfer of heat quantitatively. The specific heat of water is 4.186 J/g°C, so:
q = m • cp • ΔT = (2000 g)(4.186 J/g°C)(100°C - 25°C) = 6.279 x 105 J
Please note that the temperature we used here is the change of temperature, not the initial state (25°C) or the final state (100°C). As heat is absorbed or released, a dynamic process from beginning to the end, the corresponding heat transferred should also reflect this phenomenon. Thus, it is the change of temperature during the process, not a single temperature state, that is used in the formula.
Many calorimetry experiments need to calculate the amount of heat transferred during phase changes. For example, in order to find out how much heat is transferred in a system with 125 g of water that starts at -5.0°C and is heated to 110°C, one must use the correct equations that take into account the two phase changes that occur during this process. q = m • cp • ΔT can be used for equations with temperature changes, as this equation includes a value (ΔT) for the change in temperature of the system. There is no phase change during these processes. q = m • ΔHfus or q = m • ΔHvap must be used during phase changes, as the temperature does not change.
Therefore, you would use q = m • cp • ΔT to calculate the heat flow where there was a temperature change, and q = m • ΔHfus or q = m • ΔHvap to calculate the heat flow during phase changes. Using the diagram above, let us look at which calculations would be used during each portion of the graph.
q = m • cp • ΔT would be used as there is a change in temperature. The ice is warming from -5.0°C to 0°C.
q = (125 g) (2.1 J/g°C) (-5.0°C - 0°C) = -1.3 x 103 J = -1.3 kJ
q = m • ΔHfus would be used during the phase change from solid water (ice) to liquid water, as there is no change in temperature. The ice is melting at 0°C.
(125 g) (335 J/g) = 4.18 x 104 J = 41.8 kJ
q = m • cp • ΔT would be used as there is a change in temperature. The liquid water is warming from 0°C to 100°C.
q = (125 g) (4.184 J/g°:C) (100°C - 0°C) = 5.2 x 104 J = 52 kJ
q = m • ΔHvap would be used during the phase change from liquid water to steam (gas), as there is no change in temperature. The liquid water is turning to steam at 100°C
(125 g) (2.26 kJ/g) = 283 kJ
q = m • cp • ΔT would be used as there is a change in temperature. The steam is heating from 100° to 115°C
q = (125 g) (2.0 J/g°:C) (115°C - 100°C) = 3.75 x 103 J = 3.75 kJ
Then you would add all of the values together to find the total heat flow of the system.
-1.3 kJ + 41.8 kJ + 52 kJ + 283 kJ + 3.75 kJ = 379.42 kJ