23.13Review of fundamental principles

Shown here is a partial listing of principles applied in the subject matter of this chapter, given for the purpose of expanding the reader’s view of this chapter’s concepts and of their general interrelationships with concepts elsewhere in the book. Your abilities as a problem-solver and as a life-long learner will be greatly enhanced by mastering the applications of these principles to a wide variety of topics, the more varied the better.

•Conservation of energy: energy cannot be created or destroyed, only converted between di erent forms. Relevant to optical analyses, particularly fluorescence where the energy of a photon emitted by fluorescence is always less (never more) than the incident photon, the di erence between the two photons’ energies being dissipated in the form of heat.

•Conservation of mass: mass is an intrinsic property of matter, and as such cannot be created or destroyed. Relevant to chemical reactions, where the total mass of the reaction’s products must precisely equal the total mass of the reactants.

•Kirchho ’s Voltage Law: the algebraic sum of all voltages in a loop is equal to zero. Relevant to conductivity and pH sensor circuits, as well as bridge circuits used in a variety of analytical instruments.

•Ideal Gas Law: P V = nRT , describing the relationship between gas pressure, chamber volume, gas quantity (in moles), and gas temperature. Relevant to expansion of gas inside Luft detectors (NDIR instruments).

•Common logarithms: used to express measurements spanning a tremendous range. Relevant to pH calculations, where the pH of an aqueous fluid is the negative logarithm of its hydrogen ion activity (molarity) pH = − log[H+]. Also used to calculate absorbance of light by di erent substances (the Beer-Lambert Law A = log II0 ).

•Self-balancing opamp circuits: all self-balancing operational amplifier circuits work on the principle of negative feedback maintaining a nearly zero di erential input voltage to the opamp. Making the “simplifying assumption” that the opamp’s di erential input voltage is exactly zero assists in circuit analysis, as does the assumption that the input terminals draw negligible current.

ion-permeable membrane by the exchange of ions across that membrane. Relevant to all forms of potentiometric chemical analysis, where sensor voltage is proportional to the logarithm of concentration quotient across the sensor membrane.

•Time constant: (τ ), defined as the amount of time it takes a system to change 63.2% of the way from where it began to where it will eventually stabilize. The system will be within 1% of its final value after 5 time constants’ worth of time has passed (5τ ). Relevant to pH measurement where signal voltage changes are damped by cable capacitance (forming an RC time constant).

•Integration (calculus): where one variable is proportional to the accumulation of the product of two others. Integration always results in a multiplication of units. Relevant to calculations of mass passing through a chromatograph detector: total mass of a species passed

R through the detector (m) equal to the integral of mass flow rate times time: m = W dt.

•Quantization of photon energy: E = hf , where the energy carried by each photon (particle of light) is a fixed quantity proportional to the frequency (color) of that photon. Relevant to spectroscopy, where di erent colors of light interact with substances depending on the energy levels associated with electrons around the atoms of the substance.

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