Examples of inversion in the following topics:
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- Boyle's Law describes the inverse relationship between the pressure and volume of a fixed amount of gas at a constant temperature.
- Boyle's Law (sometimes referred to as the Boyle-Mariotte Law) states that the absolute pressure and volume of a given mass of confined gas are inversely proportional, provided the temperature remains unchanged within a closed system.
- The law itself can be stated as follows: for a fixed amount of an ideal gas kept at a fixed temperature, P (pressure) and V (volume) are inversely proportional—that is, when one doubles, the other is reduced by half.
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- The green dashed curve in the illustration on the right represents this attraction, which increases with the inverse sixth power of the distance between the atoms (r).
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- The following chart displays many of the important regions of this spectrum, and demonstrates the inverse relationship between wavelength and frequency (shown in the top equation below the chart).
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- The examples in the green-shaded area clearly demonstrate inversion of configuration in the carbon-carbon bond forming step.
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- According to the Ideal Gas Equation, PV=nRT, pressure and volume should have an inverse relationship.
- Notice that the higher isotherms on the graph, which represent the gas' state at higher temperature, show the typical, concave decreasing curve of an inverse relationship.
- As temperature decreases, however, the isotherms on the lower portion of the graph significantly deviate from this ideal inverse relationship between P and V.
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- This temperature dependence is sometimes referred to as retrograde or inverse solubility, and exists when a salt's dissolution is exothermic; this can be explained because, according to Le Chatelier's principle, extra heat will cause the equilibrium for an exothermic process to shift towards the reactants.
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- As can be seen, a reduction in volume yields an increase in the pressure of the system, because volume and pressure are inversely related.
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- The de Broglie wavelength is inversely proportional to the momentum of a particle.
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- Amines of the type NHRR' and NR'R''R''' are chiral molecules and can undergo inversion.
- Since the barrier for inversion is quite low (~7 kcal/mol), these compounds cannot be resolved optically.
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- Returning to the examples presented at the beginning of this section, we find that reactions 2, 5 & 6 demonstrate an inversion of configuration when the cyanide nucleophile replaces the bromine.
- The consequence of rear-side bonding by the nucleophile is an inversion of configuration about the alpha-carbon.