Lecture 5 Chemical and Phase Equilibrium (2). VARIATION OF KP WITH TEMPERATURE. The equilibrium constant KP of an ideal gas depends on temperature only, and it is related to the standard-state Gibbs function change ∆ G *( T ) through the relation. Substituting.
Chemical and Phase Equilibrium (2)
The equilibrium constant KP of an ideal gas depends on temperature only, and it is related to the standard-state Gibbs function change ∆G*(T) through the relation
∆G*(T) = ∆H*(T) - T ∆S*(T)
into the above relation and differentiating with respect to temperature, we get
T ds = dh -v dP,
T ds =dh.
T d(∆S*) = d(∆H*)
where hR is the enthalpy of reaction at temperature T.
First, it provides a means of calculating the of a reaction from a knowledge of KP, which is easier to determine. Second, it shows that exothermic reactions such as combustion processes are less complete at higher temperatures since KP decreases with temperature for such reactions (Fig. 16–16).
Estimate the enthalpy of reaction hR for the combustion process of hydrogen
H2 + 0.5O2 → H2O at 2000 K, using (a) enthalpy data and (b) KP data.
The hR at a specified temperature is to be determined using the enthalpy and Kp data.
Both the reactants and the products are ideal gases.
Analysis (a) The of the combustion process of H2 at 2000 K is the amount of energy released as 1 kmol of H2 is burned in a steady-flow combustion chamber at a temperature of 2000 K. It can be determined from
The magnitude of this force depends, among other things, on the relative concentrations of the two phases. A wet T-shirt dries much quicker in dry air than it does in humid air. In fact, it does not dry at all if the relative humidity of the environment is 100 percent. In this case, there is no transformation from the liquid phase to the vapor phase, and the two phases are in phase equilibrium.
The total Gibbs function of this mixture is:
The change in the total Gibbs function during this disturbance is
since gfand ggremain constant at constant temperature and pressure.
dmg = - dmf.
Therefore, the two phases of a pure substance are in equilibrium when each phase has the same value of specific Gibbs function.
IV the number of independent variables,
C the number of components,
PH the number of phases present in equilibrium.