# How to write an equation for constant of proportionality

The law is named after 17th-century British physicist Robert Hooke. He first stated the law in as a Latin anagram. Hooke states in the work that he was aware of the law already in Hooke's equation holds to some extent in many other situations where an elastic body is deformed, such as wind blowing on a tall building, a musician plucking a string of a guitar, and the filling of a party balloon. ## Scientific Notation

The absorbance,is measured at the observation wavelength and infinite time, i. Now a simpler equation, which looks very similar to the rate equation for the first-order thermal reaction can be obtained: Therefore, the time dependence of the reactant concentration cannot be directly used to compare photoreactivity of different molecules, or even the same molecule if it was measured under different irradiation conditions.

We could say that we need to know not only the reactant concentration but also effective 'light concentration',in order to analyze photochemical systems. Even if we use the same light source for two systems we cannot directly compare results unless we know how much light was absorbed by each system.

This plot shows how misleading could be a comparison of relative concentrations plotted against time for photochemical reactions if the system is not completely specified. Time profiles for the normalized concentrations of two compounds undergoing an irreversible first-order photoreaction with a quantum yield of 0.

Solutions containing these compounds at the same initial concentrations were irradiated with the same mercury lamp equipped with a nm narrow-band filter.

Which line, blue or red, corresponds to the molecule with the higher quantum yield more photoreactive? This question can only be answered when the absorbances at the irradiation wavelength are compared see the insert for the absorption spectra. The substance corresponding to the blue curve has 60 times larger absorbance at nm, which is responsible for faster conversion despite the 10 times lower quantum yield for its photoreaction.

As to the question, the correct answer is that the red line corresponds to the molecule with the photoreaction quantum yield of 1.

However, an extremely weak absorption at nm results in a relatively slow phototransformation of this compound. Assuming that light absorption by all transient can also be neglected we can rewrite Eq. To obtain the expression for W we will use the Beer-Lambert law Figure 3and the fact the absorbances of components in a mixture add up together: Here I0 is the intensity of monochromatic light entering the sample expressed in mol L-1s-1, and are molar absorptivities of the reactant and product M-1 cm-1and l is the optical path cm.

The course of a photochemical reaction is often monitored spectrophotometrically at wavelength s different from the irradiation wavelength.

## Measured vs. Exact Numbers

By using the Beer-Lambert law we may write for the absorbance measured at the irradiation and observation wavelength at time t: By using the absorbance,measured at the observation wavelength and infinite time and the three equations shown above we obtain Eq.

In the general case, Eq. In the later case we obtain: Theoretical Models of Photochemical Reactions Within the Born-Oppenheimer approximation, potential energy surfaces govern nuclear motion and, therefore, chemical reactivity.

However, in studying photochemistry it is also good to keep in mind that this is just an approximation, which is not automatically valid for all possible geometries and experimental conditions.

## Orders of reaction and rate equations

However, a detailed account of nuclear motion can also be inferred from classical trajectories for a point moving without friction on the potential energy surface. The moving point may represent a chemically reactive system which consists of one or several molecular species.

In the latter case one considers all reactants as a "supermolecule". The forces acting on the nuclei are given by minus the gradient of the potential electronic energy at this point.PHOTOCHEMISTRY Theoretical Concepts and Reaction Mechanisms Yuri V.

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## Writing proportional equations (practice) | Khan Academy

May 10,  · Write an equation that expresses the following relationship. u varies directly with the cube of p and inversely with d In your equation, use as the constant of rutadeltambor.com: Resolved. Proportionality & Unit Rate Find the constant of proportionality and the unit rate for the data in the table.

Then write an equation to represent the relationship between time t and distance d . Home; Calculators; Differential Equations Calculators; Math Problem Solver (all calculators) Differential Equation Calculator. The calculator will find the solution of the given ODE: first-order, second-order, nth-order, separable, linear, exact, Bernoulli, homogeneous, or inhomogeneous. Identifying the Constant of Proportionality - Video & Lesson Transcript | rutadeltambor.com