Search results
Results from the WOW.Com Content Network
A Markov process is called a reversible Markov process or reversible Markov chain if there exists a positive stationary distribution π that satisfies the detailed balance equations [12] =, where P ij is the Markov transition probability from state i to state j, i.e. P ij = P(X t = j | X t − 1 = i), and π i and π j are the equilibrium probabilities of being in states i and j, respectively ...
The expression of the rate equations was rediscovered independently by Jacobus Henricus van 't Hoff. The law is a statement about equilibrium and gives an expression for the equilibrium constant, a quantity characterizing chemical equilibrium. In modern chemistry this is derived using equilibrium thermodynamics.
The extent of reaction is a useful quantity in computations with equilibrium reactions. [citation needed] Consider the reaction 2 A ⇌ B + 3 C. where the initial amounts are = , = , = , and the equilibrium amount of A is 0.5 mol. We can calculate the extent of reaction in equilibrium from its definition
log 10 β values between about 2 and 11 can be measured directly by potentiometric titration using a glass electrode. This enormous range of stability constant values (ca. 100 to 10 11) is possible because of the logarithmic response of the electrode. The limitations arise because the Nernst equation breaks down at very low or very high pH.
The appropriate mathematical expression for the canonical partition function depends on the degrees of freedom of the system, whether the context is classical mechanics or quantum mechanics, and whether the spectrum of states is discrete or continuous. [citation needed]
The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency towards further change.
Combining expressions for the Gibbs–Duhem equation in each phase and assuming systematic equilibrium (i.e. that the temperature and pressure is constant throughout the system), we recover the Gibbs' phase rule. One particularly useful expression arises when considering binary solutions. [9] At constant P and T it becomes:
In this expression m is the particle mass and h is the Planck constant. For a monatomic ideal gas U = 3 / 2 nRT = nC V T, with C V the molar heat capacity at constant volume. A second way to evaluate the entropy change is to choose a route from the initial state to the final state where all the intermediate states are in equilibrium.