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For a reversible reaction, the equilibrium constant can be measured at a variety of temperatures. This data can be plotted on a graph with ln K eq on the y-axis and 1 / T on the x axis. The data should have a linear relationship, the equation for which can be found by fitting the data using the linear form of the Van 't Hoff equation
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.
This equation can be used to calculate the value of log K at a temperature, T 2, knowing the value at temperature T 1. The van 't Hoff equation also shows that, for an exothermic reaction ( Δ H < 0 {\displaystyle \Delta H<0} ), when temperature increases K decreases and when temperature decreases K increases, in accordance with Le Chatelier's ...
As the value of ρ is related to the charge during the rate determining step, mechanisms can be devised based on this information. If the mechanism for the reaction of an aromatic compound is thought to occur through one of two mechanisms, the compound can be modified with substituents with different σ values and kinetic measurements taken.
In mathematics, and specifically differential geometry, a density is a spatially varying quantity on a differentiable manifold that can be integrated in an intrinsic manner. Abstractly, a density is a section of a certain line bundle , called the density bundle .
the golden ratio 1.618... in mathematics, art, and architecture [43] Euler's totient function in number theory [44] the argument of a complex number in mathematics; the value of a plane angle in physics and mathematics; the angle to the z axis in spherical coordinates (mathematics) epoch or phase difference between two waves or vectors
Using the number density as a function of spatial coordinates, the total number of objects N in the entire volume V can be calculated as = (,,), where dV = dx dy dz is a volume element. If each object possesses the same mass m 0 , the total mass m of all the objects in the volume V can be expressed as m = ∭ V m 0 n ( x , y , z ) d V ...
The relative density of a liquid can be measured using a hydrometer. This consists of a bulb attached to a stalk of constant cross-sectional area, as shown in the adjacent diagram. First the hydrometer is floated in the reference liquid (shown in light blue), and the displacement (the level of the liquid on the stalk) is marked (blue line). The ...