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The dominant technology for abiological nitrogen fixation is the Haber process, which uses iron-based heterogeneous catalysts and H 2 to convert N 2 to NH 3. This article focuses on homogeneous (soluble) catalysts for the same or similar conversions.
Haber's rule states that, for a given poisonous gas, =, where is the concentration of the gas (mass per unit volume), is the amount of time necessary to breathe the gas to produce a given toxic effect, and is a constant, depending on both the gas and the effect. Thus, the rule states that doubling the concentration will halve the time, for example.
For example, if equilibrium is specified by a single chemical equation:, [24] ∑ j = 0 m ν j R j = 0 {\displaystyle \sum _{j=0}^{m}\nu _{j}R_{j}=0} where ν j is the stoichiometric coefficient for the j th molecule (negative for reactants, positive for products) and R j is the symbol for the j th molecule, a properly balanced equation will obey:
The Haber process, [1] also called the Haber–Bosch process, is the main industrial procedure for the production of ammonia. [ 2 ] [ 3 ] It converts atmospheric nitrogen (N 2 ) to ammonia (NH 3 ) by a reaction with hydrogen (H 2 ) using finely divided iron metal as a catalyst:
The Henderson–Hasselbalch equation relates the pH of a solution containing a mixture of the two components to the acid dissociation constant, K a of the acid, and the concentrations of the species in solution. [6] Simulated titration of an acidified solution of a weak acid (pK a = 4.7) with alkali
The Hammett equation predicts the equilibrium constant or reaction rate of a reaction from a substituent constant and a reaction type constant. The Edwards equation relates the nucleophilic power to polarisability and basicity. The Marcus equation is an example of a quadratic free-energy relationship (QFER). [citation needed]
A phase portrait is a qualitative sketch of the differential equation's behavior that shows equilibrium solutions or fixed points and the vector field on the real line. Bifurcations describe changes in the stability or existence of fixed points as a control parameter in the system changes.
Punctuated equilibrium, theory in evolutionary biology; Sedimentation equilibrium, analytical ultracentrifugation method for measuring protein molecular masses in solution; Equilibrium Theory (Island biogeography), MacArthur-Wilson theory explaining biodiversity character of ecological islands