Measurement of ΔU and ΔH: Calorimetry
Quick Notes
- ΔU = Change in internal energy (at constant volume)
- ΔH = Change in enthalpy (at constant pressure)
- Calorimetry is used to measure heat transfer
- Bomb calorimeter = a constant volume and measures ΔU
- Coffee cup calorimeter = constant pressure and measures ΔH
- Relationship:
ΔH = ΔU + Δngas × R × T
Full Notes
Recap
- ΔU (internal energy change): Represents the total energy change within the system, including both heat and work. It is typically measured under constant volume conditions.
- ΔH (enthalpy change): Refers to the heat exchange that occurs at constant pressure, which is the most common condition for reactions occurring in open containers like test tubes or beakers.
To measure these energy changes experimentally, we use a technique called calorimetry, which involves finding heat changes via measuring temperature changes in an insulated system.
The tools used vary based on whether pressure or volume is kept constant.
ΔU Measurements
To measure change in internal energy (ΔU), a bomb calorimeter is used. It operates at constant volume, meaning no work is done by expansion or compression.
Bomb Calorimeter Setup
A bomb calorimeter includes:
- A strong steel container (“the bomb”) sealed with the reactants
- Oxygen under pressure to enable combustion
- A surrounding water bath with a thermometer and stirrer
- Insulation to prevent heat loss
Since no volume change occurs:
qv = ΔU
The heat evolved is used to heat the surrounding water and is calculated as:
q = −Ccal × ΔT
- Ccal is the total heat capacity of the calorimeter
- ΔT is the observed temperature change
- The negative sign reflects that heat is released in exothermic reactions
ΔH Measurements
To measure enthalpy change (ΔH), a coffee cup calorimeter is used, which operates at constant pressure (typically atmospheric).
- Commonly used in reactions such as acid–base neutralisation, dissolution, etc.
- The system is open to the atmosphere, so pressure remains constant.
- The heat measured is directly equal to enthalpy change:
qp = ΔH
This method is simpler and widely used in chemistry labs.
Relationship between ΔU and ΔH
For gaseous reactions where there is a change in the number of moles of gas:
This formula accounts for the expansion work done when gas volume changes at constant pressure.
Summary
- Bomb calorimetry at constant volume measures ΔU directly via qv.
- Coffee cup calorimetry at constant pressure measures ΔH via qp.
- Calorimetry tracks temperature change to determine heat transfer.
- For gases, ΔH relates to ΔU through Δngas × R × T.