Chemistry Measurement of `Delta U` and `Delta H` : Calorimetry

Topics Covered :

● Measurement of `Delta U` and `Delta H` : Calorimetry
● `Delta U` Measurements
● `Delta H` Measurements

Measurement of `ΔU` and `ΔH` : Calorimetry

`=>` We can measure energy changes associated with chemical or physical processes by an experimental technique called `color{red}("calorimetry")`.

● In calorimetry, the process is carried out in a vessel called calorimeter, which is immersed in a known volume of a liquid.

● Knowing the heat capacity of the liquid in which calorimeter is immersed and the heat capacity of calorimeter, it is possible to determine the heat evolved in the process by measuring temperature changes.

● Measurements are made under two different conditions:

(i) at constant volume, `color{purple}(q_V)`

(ii) at constant pressure, `color{purple}(q_p)`

`ΔU` measurements :

`=>` For chemical reactions, heat absorbed at constant volume, is measured in a `color{red}("bomb calorimeter")` (Fig. 6.7).

● Here, a steel vessel (the bomb) is immersed in a water bath. The whole device is called calorimeter.

● The steel vessel is immersed in water bath to ensure that no heat is lost to the surroundings.

● A combustible substance is burnt in pure dioxygen supplied in the steel bomb. Heat evolved during the reaction is transferred to the water around the bomb and its temperature is monitored.

● Since the bomb calorimeter is sealed, its volume does not change i.e., the energy changes associated with reactions are measured at constant volume.

● Under these conditions, no work is done as the reaction is carried out at constant volume in the bomb calorimeter. Even for reactions involving gases, there is no work done as `color{purple}(ΔV = 0)`.

● Temperature change of the calorimeter produced by the completed reaction is then converted to `q_V`, by using the known heat capacity of the calorimeter with the help of equation 6.11(`color{purple}(q = c ×m × DeltaT =C DeltaT)`).

ΔH measurements :

`=>` Measurement of heat change at constant pressure (generally under atmospheric pressure) can be done in a calorimeter shown in Fig.6.8.

`=>` We know that `color{pu(rple}ΔH = q_p)` (at constant p) and, therefore, heat absorbed or evolved, `q_p` at constant pressure is also called the heat of reaction or enthalpy of reaction, `color{purple}(Δ_r H)`.

● In an exothermic reaction, heat is evolved, and system loses heat to the surroundings. Therefore, `color{purple}(q_p)` will be negative and `color{purple}(Δ_r H)` will also be negative.

● Similarly in an endothermic reaction, heat is absorbed, `color{purple}(q_p)` is positive and `color{purple}(Δ_r H)` will be positive.
Q 3057723684

`1g` of graphite is burnt in a bomb calorimeter in excess of oxygen at `298 K` and `1` atmospheric pressure according to
the equation.

`C text{(graphite)} + O_2 (g) → CO_2 (g)`

During the reaction, temperature rises from 298 K to 299 K. If the heat capacity of the bomb calorimeter is 20.7kJ/K, what is the enthalpy change for the above reaction at 298 K and 1 atm?


Suppose `q` is the quantity of heat from the reaction mixture and `C_V` is the heat capacity of the calorimeter, then the quantity of heat absorbed by the calorimeter.

`q = C_V xxDelta T`

Quantity of heat from the reaction will have the same magnitude but opposite sign because the heat lost by the system (reaction mixture) is equal to the heat gained by the calorimeter.

`q = - C_V xx Delta T = -20.7 kJ //K xx (299-298) K`

` = -20.7 kJ`

(Here, negative sign indicates the exothermic nature of the reaction)

Thus, `DeltaU` for the combustion of the 1g of graphite `= – 20.7 kJK^(–1)`

For combustion of 1 mol of graphite,

` = (12.0 g mol^(-1) xx (-20.7 kJ ))/(1 g)`

`= – 2.48 ×10^2 kJ mol^(–1) ,` since `Deltan_g = 0`.

`DeltaH = DeltaU = -2.48xx10^2 kJ mol^(-1)`