How to Calculate Enthalpy and Internal Energy Changes Easily
Introduction to Measurement of Enthalpy and Internal Energy Change
Normally, the measurement of enthalpy and internal energy change is carried out by an experimental approach called calorimetry. These techniques are established on thermometric procedures which are done in a vessel known as calorimeter that is submerged in a known liquid volume. The heat which is evolved in the procedure is evaluated by using known heat capacities of the calorimeter and liquid by quantifying the difference in temperatures.
Notably, there are two separate conditions under which enthalpy and internal energy can be measured. These include constant pressure called enthalpy and constant volume termed as internal energy.
Before moving on with the measurements, however, you must know what enthalpy is , and difference between enthalpy and internal energy.
What is Enthalpy?
The heat energy, which is evolved or absorbed during a chemical reaction progression, is called enthalpy. It is represented by H, and the letter H indicates the energy amount. Enthalpy change is given by ΔH where delta symbol shows the change and its unit is joules or kilojoules.
It can be said that sum of internal energies of the system is enthalpy. The reason is that a change in internal energy takes place at the time of chemical reaction, and this change is calculated as enthalpy. It can be given by the following expression:
H = U + PV
Where H = enthalpy,
U = sum of internal energy,
P = pressure of system,
V = volume of system.
So, enthalpy is the addition of internal energy and energy needed to conserve a system’s volume at a given pressure. PV represents the work that is required to be done on environment to create space for system.
What is Internal Energy?
A system’s internal energy refers to the addition of potential and kinetic energy of that particular system. The stored energy is potential energy and the energy released due to movement of molecules is kinetic energy. Moreover, internal energy is represented by U and change in internal energy is given by ΔU.
At constant pressure, internal energy and enthalpy are same for a particular system. Internal energy change can take place in two ways. One because of transfer of heat – a system can absorb or release heat, and the second is by doing work. Hence, internal energy change can be expressed by the following equation:
ΔU = q + w
Where ΔU = internal energy change,
q = transfer of heat,
w = work done by or on a system.
Enthalpy Change Measurement
As ΔH is expressed as the flow of heat at constant pressure, calculations done using a calorimeter of constant-pressure (a system utilised to measure changes in enthalpy during chemical reactions at constant pressure) gives out direct value of delta h enthalpy. This apparatus is appropriately suitable for studying reactions which are carried out in solution at fixed atmospheric pressure. In general laboratories of chemistry, a “student” version named coffee-cup calorimeter is frequently encountered. The commercial calorimeters also function on a similar principle. Still, they can be utilised with solutions of smaller volumes, having better thermal insulation and can detect temperature change as little as like 10-6 degree Celsius. As the heat absorbed or released at fixed pressure is equivalent to ΔH, the relation between ΔHrxn and heat is:
ΔHrxn = qrxn = -qcalorimeter = -mCsΔT
Constant pressure calorimeter usage is shown in the following figure.
(Image to be added soon)
This coffee-cup calorimeter is a simplified version of calorimeter of constant pressure consisting of two nested Styrofoam cups and closed with a stopper which is insulated to isolate the system thermally from the surrounding environment. Between the two stopper holes, one is for the stirrer which will blend the reactants, and the second one is for utilisation of a thermometer to calculate the temperature.
Take a look at the following example to understand the calculation of enthalpy change clearly.
Example: In a coffee-cup calorimeter, 5.03 g of solid potassium hydroxide is dissolved in distilled water of 100.0 mL, and the liquid temperature rises from 23.0 degree Celsius to 34.7 degree Celsius. The average density of water in this range of temperature is 0.9969 g / cm3. What will be the delta h enthalpy in kilojoules per mole? Imagine that a negligible amount of heat is absorbed by the calorimeter and due to high volume of water; the solution’s specific heat is equal to pure water’s specific heat.
Substance mass, solvent volume and initial and final temperatures are provided in the question, and ΔHsoln is required to be evaluated.
Strategies:
Calculation of mass of solution from its density and volume, and evaluation of change in temperature of the solution.
Determining the flow of heat that goes along with dissolution reaction by putting the suitable values in equation qcalorimeter = mCsΔT.
Using KOH’s molar mass to evaluate ΔHsoln.
Solution:
To evaluate ΔHsoln, first, you need to determine the heat released amount in the experiment of calorimetry. So, the mass of solution is:
(100.0 mL H2O) (0.9969 g / mL) + 5.03 g KOH = 104.72 g
The change in temperature is = (34.7 – 23.0) degree Celsius = + 11.7 degree Celsius
As the solution is not much concentrated (near about 0.9 M), it can be assumed that specific heat of the solution is similar to that of water. The flow of heat that goes with dissolution is:
qcalorimeter = mCsΔT = (104.72 g) (4.184 J / g ⋅ C) (11.7 C) = 5130 J = 5.13 lJ
The solution’s temperature increased as the solution absorbed heat (q > 0). However, from where did heat come from? It was generated by potassium hydroxide which was dissolved in water.
ΔHrxn = - qcalorimeter = -5.13 kJ
This experiment shows us that when 5.03 g of potassium hydroxide is dissolved in water, 5.13 kJ of energy is also released. As the solution temperature increases, potassium hydroxide dissolution in water has to be exothermic.
The final step is to make use of molar mass of potassium hydroxide to evaluate ΔHsoln – heat generated after dissolving one mole of potassium hydroxide:
ΔHsoln = (5.13 kJ / 5.03 g) (56.11 g / 1 mol) = − 57.2 kJ / mol
Change in Internal Energy Measurement
In chemical reactions, change in internal energy at constant volume is calculated using a bomb calorimeter.
In this apparatus, the bomb (inner vessel) and its covering are made up of strong steel. The cover is sealed tightly to the bomb with the help of metal screws and lid.
The following is an image of a bomb calorimeter.
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A certain amount of a substance is taken in the cup of platinum linked with electrical wires for creating an arc to ignite combustion. After that, the vessel is tightly closed, and pressure is exerted by putting excess oxygen. The vessel or bomb is submerged in water, in the calorimeter’s inner volume. The stirrer which is placed in the area between the bomb and calorimeter wall is used to uniformly stir the water. Upon striking the substance by electrical heating, the reaction begins.
The amount of substance which is burnt in the vessel by oxygen is known. The calorimeter and water in which the vessel is submerged, absorb the heat released at the time of reaction. Temperature change is evaluated by a Beckman thermometer. As the bomb is sealed, the volume of the same does not alter, and therefore, measurement of heat is equivalent to combustion heat at a fixed volume (ΔU)c.
The amount of heat released in the reaction (ΔU)c is similar to total heat absorbed by water and calorimeter.
So, absorption of heat by calorimeter can be expressed as:
q1 = k . ΔT
Where k = calorimeter constant which is equal to mc Cc (mc is calorimeter’s mass, and Cc is calorimeter’s heat capacity)
Now, absorption of heat by water can be written as:
q2 = mw Cw ΔT
Where, mw is water’s molar mass, and Cw is water’s molar heat capacity (4.184 kJ K-1 mol-1)
Hence, ΔUc = q1 + q2
= k . ΔT + mw Cw ΔT
= (k + mw Cw) ΔT
Following Are Some Uses Of Bomb Calorimeter:
This type of calorimeter is utilised to decide heat release amount in burning reaction.
It can be used to find calorific food value.
Bomb calorimeters are used in several industries like food processing, metabolic study, testing of explosives, etc.
Measurement of enthalpy and internal energy change is an important part of thermodynamics. If you wish to know more related concepts and attend our online interactive sessions, download our Vedantu app for easy access.
FAQs on Measurement of Enthalpy and Internal Energy Change
1. How is the change in a system's internal energy (ΔU) measured experimentally?
The change in internal energy (ΔU) is measured using a device called a bomb calorimeter. This instrument is designed to measure the heat evolved or absorbed during a reaction at a constant volume (ΔV = 0). Since no work is done (w = -PΔV = 0), the first law of thermodynamics (ΔU = q + w) simplifies to ΔU = qv, where qv is the heat change at constant volume. The heat absorbed by the calorimeter (CΔT) allows for the direct calculation of the internal energy change of the reaction.
2. What is the method for measuring the enthalpy change (ΔH) of a reaction?
Enthalpy change (ΔH) is measured under conditions of constant pressure, which is typical for most chemical reactions in a lab. This is often done using a simple coffee-cup calorimeter. At constant pressure, the heat evolved or absorbed (qp) is equal to the enthalpy change. The temperature change (ΔT) of the solution is measured, and using the specific heat capacity and mass of the solution, the heat of the reaction (ΔH) can be determined.
3. What is the fundamental relationship between enthalpy change (ΔH) and internal energy change (ΔU)?
The relationship between enthalpy (H) and internal energy (U) is defined by the equation H = U + PV. For a change at constant pressure, this becomes ΔH = ΔU + PΔV. For reactions involving gases, this relationship is more conveniently expressed as ΔH = ΔU + ΔngRT, where:
- Δng is the change in the number of moles of gaseous products and reactants.
- R is the universal gas constant.
- T is the absolute temperature in Kelvin.
4. What are some real-world applications where understanding enthalpy change is important?
Understanding enthalpy change is crucial in many everyday applications. For example:
- Instant Cold/Hot Packs: Cold packs use an endothermic reaction (absorbs heat, ΔH is positive), while hot packs use an exothermic reaction (releases heat, ΔH is negative).
- Combustion: The energy released from burning fuels in engines or for heating is a direct result of the large negative enthalpy change of combustion.
- Refrigeration: The cycle of vaporisation and condensation of a refrigerant fluid relies on its specific enthalpy of vaporisation to absorb heat from the inside of the fridge and release it outside.
5. Why is enthalpy change (ΔH) used more frequently in chemistry than internal energy change (ΔU)?
Enthalpy change (ΔH) is more commonly used because most chemical and biological processes occur in open systems at constant atmospheric pressure, not at constant volume. Since ΔH represents the heat flow under these constant-pressure conditions, it is a more direct and practical measure of energy transfer in typical laboratory and real-world scenarios. Measuring ΔU requires a specialised, sealed bomb calorimeter, which is less common for general reactions.
6. What makes internal energy (U) and enthalpy (H) state functions, and why is this concept significant?
Internal energy and enthalpy are called state functions because their values depend only on the current state of the system (defined by variables like temperature, pressure, and volume), not on the path taken to reach that state. This is significant because it simplifies thermodynamic calculations. We only need to know the initial and final states to calculate ΔU or ΔH, regardless of the intermediate steps. In contrast, quantities like heat (q) and work (w) are path functions, as their values depend on the specific process followed.
7. What is the main difference between how a bomb calorimeter and a coffee-cup calorimeter measure energy?
The primary difference lies in the conditions under which they operate and what they measure:
- A bomb calorimeter operates at constant volume. It is a sealed, robust steel container, ideal for combustion reactions. The heat measured (qv) directly gives the internal energy change (ΔU).
- A coffee-cup calorimeter operates at constant pressure (open to the atmosphere). It is a simpler, insulated container used for reactions in solution. The heat measured (qp) directly gives the enthalpy change (ΔH).
