Search results
Results from the WOW.Com Content Network
The Van 't Hoff equation relates the change in the equilibrium constant, K eq, of a chemical reaction to the change in temperature, T, given the standard enthalpy change, Δ r H ⊖, for the process. The subscript r {\displaystyle r} means "reaction" and the superscript ⊖ {\displaystyle \ominus } means "standard".
Boltzmann's equation—carved on his gravestone. [1]In statistical mechanics, Boltzmann's equation (also known as the Boltzmann–Planck equation) is a probability equation relating the entropy, also written as , of an ideal gas to the multiplicity (commonly denoted as or ), the number of real microstates corresponding to the gas's macrostate:
Since an entropy is a state function, the entropy change of the system for an irreversible path is the same as for a reversible path between the same two states. [22] However, the heat transferred to or from the surroundings is different as well as its entropy change. We can calculate the change of entropy only by integrating the above formula.
In 1884, Jacobus van 't Hoff proposed the Van 't Hoff equation describing the temperature dependence of the equilibrium constant for a reversible reaction: = where ΔU is the change in internal energy, K is the equilibrium constant of the reaction, R is the universal gas constant, and T is thermodynamic temperature.
In the case of an ideal gas, the heat capacity is constant and the ideal gas law PV = nRT gives that α V V = V/T = nR/p, with n the number of moles and R the molar ideal-gas constant. So, the molar entropy of an ideal gas is given by (,) = (,) + . In this expression C P now is the molar heat capacity. The entropy of inhomogeneous ...
The Sackur–Tetrode equation is an expression for the entropy of a monatomic ideal gas. [ 1 ] It is named for Hugo Martin Tetrode [ 2 ] (1895–1931) and Otto Sackur [ 3 ] (1880–1914), who developed it independently as a solution of Boltzmann's gas statistics and entropy equations, at about the same time in 1912.
This is the most useful form of the second law of thermodynamics in chemistry, where free-energy changes can be calculated from tabulated enthalpies of formation and standard molar entropies of reactants and products. [19] [15] The chemical equilibrium condition at constant T and p without electrical work is dG = 0.
Entropy of activation determines the preexponential factor A of the Arrhenius equation for temperature dependence of reaction rates. The relationship depends on the molecularity of the reaction: for reactions in solution and unimolecular gas reactions A = (ek B T/h) exp(ΔS ‡ /R), while for bimolecular gas reactions A = (e 2 k B T/h) (RT/p ...