Directly proportional

Charles s law At constant pressure the volume of a given mass of gas is directly proportional to the absolute temperature. 

Henry s law The mass of gas which is dissolved by a given volume of a liquid at constant temperature is directly proportional to the pressure of the gas. The law is only obeyed provided there is no chemical reaction between the gas and the liquid. 

Experiments on sufficiently dilute solutions of non-electrolytes yield Henry s laM>, that the vapour pressure of a volatile solute, i.e. its partial pressure in a gas mixture in equilibrium with the solution, is directly proportional to its concentration, expressed in any units (molar concentrations, molality, mole fraction, weight fraction, etc.) because in sufficiently dilute solution these are all proportional to each other. 

We know from equation A2.4.32 and equation A2.4.34 that the limiting ionic conductivities are directly proportional to the limiting ionic mobilities in fact... 

The sensitivity in an NMR experiment is directly proportional to the number of spins, making quantification of the amount of a particular element present straightforward, at least for spin / = inuclei. Furtliemiore, the... 

As before, we note that the resonance frequency of a nucleus at position r is directly proportional to the combined applied static and gradient fields at that location. In a gradient G=G u, orthogonal to the slice selection gradient, the nuclei precess (in the usual frame rotating at coq) at a frequency ciD=y The observed signal therefore contains a component at this frequency witli an amplitude proportional to the local spin density. The total signal is of the fomi... 

The mathematical form of the PEF is in almost every case a compromise between speed and accuracy. As computer power continually increases, ideally following Moore s Law, and the cost/performance ratio is getting better, one might think that there is no longer a need to sacrifice accuracy to save computational time. This is not really true, because in direct proportion to the CPU speed is the rise in the scientists interest in calculating larger and larger molecules (in fact, their interest always rises faster than the CPU speed). 

If the spring follows Hooke s law, the force it exerts on the mass is directly proportional and opposite to the excursion of the particle away from its equilibrium point Xe- The particle of mass m is accelerated by the force F = —kx of the spring. By Newton s second law, F = ma, where a is the acceleration of the mass... 

The relative weights of the two components of the vapour phase will be idaitical with the relative weights in the distillate, i.e., the weights of the two liquids collecting in the receiver are directly proportional to their vapour pressures and their molecular weights. 

Shortly after publication of Dalton s New System of Chemical Philosophy Gay-Tussac announced his observations that volumes of gas which combine with each other and the volume of the combination thus formed are in direct proportion to the sum of the volumes of the constituent gases. The volumetric proportions of Gay-Tussac and Dalton s gravimetric ratios indeed supplement each other, although they themselves contested and rejected each other s concepts. 

The rate of this reaction is observed to be directly proportional to the concentration of both methyl bromide and sodium hydroxide It is first order m each reactant or second order overall... 

Electromagnetic radiation of which visible light is but one example has the properties of both particles and waves The particles are called photons, and each possesses an amount of energy referred to as a quantum In 1900 the German physicist Max Planck proposed that the energy of a photon (E) is directly proportional to its frequency (v)... 

Energy is directly proportional to frequency electromagnetic radiation of higher frequency possesses more energy than radiation of lower frequency... 

Henry s Law. The solubility of a gas is directly proportional to the partial pressure exerted by the gas ... 

The foregoing equation reveals that essentially the concentration distribution ratio for trace concentrations of an exchanging ion is independent of the respective solution of that ion and that the uptake of each trace ion by the resin is directly proportional to its solution concentration. However, the... 

Finally, values of sx are directly proportional to transmittance for indeterminate errors due to fluctuations in source intensity and for uncertainty in positioning the sample cell within the spectrometer. The latter is of particular importance since the optical properties of any sample cell are not uniform. As a result, repositioning the sample cell may lead to a change in the intensity of transmitted radiation. As shown by curve C in Figure 10.35, the effect of this source of indeterminate error is only important at low absorbances. This source of indeterminate errors is usually the limiting factor for high-quality UV/Vis spectrophotometers when the absorbance is relatively small. 

UV/Vis detectors are among the most popular. Because absorbance is directly proportional to path length, the capillary tubing s small diameter leads to signals that are smaller than those obtained in HPLC. Several approaches have been used to increase the path length, including a Z-shaped sample cell or multiple reflections (Figure 12.44). Detection limits are about 10 M. 

In Equation 26.3, d is fixed, E is held constant in the instrument, and e is a universal constant. Thus the flight time of an ion t is directly proportional to the square root of m/z (Equation 26.4). 

Of the various parameters introduced in the Eyring theory, only r—or j3, which is directly proportional to it-will be further considered. We shall see that the concept of relaxation time plays a central role in discussing all the deformation properties of bulk polymers and thus warrants further examination, even though we have introduced this quantity through a specific model. 

Equation (2.39) is the weight average molecular weight as defined in Sec. 1.8. It is important to note that this result. My = M y, applies only in the case of nonentangled chains where 17 is directly proportional to M. A more general definition of My for the case where 17 a is... 

The various elastic and viscoelastic phenomena we discuss in this chapter will be developed in stages. We begin with the simplest the case of a sample that displays a purely elastic response when deformed by simple elongation. On the basis of Hooke s law, we expect that the force of deformation—the stress—and the distortion that results-the strain-will be directly proportional, at least for small deformations. In addition, the energy spent to produce the deformation is recoverable The material snaps back when the force is released. We are interested in the molecular origin of this property for polymeric materials but, before we can get to that, we need to define the variables more quantitatively. 

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