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Amanda K. Cook coauthored research on isomerization.^[ref]

Interconversion of isomers without changing the overall molecular formula. Conformational interconversion can be kinetically slow when rotation is hindered.

H. Diamond coauthored research on isomerization.^[ref]

Interconversion of isomers without changing the overall molecular formula. Conformational interconversion can be kinetically slow when rotation is hindered.

Kiana E. Kawamura coauthored research on isomerization.^[ref]

Interconversion of isomers without changing the overall molecular formula. Conformational interconversion can be kinetically slow when rotation is hindered.

On releasing the tensile load, the extended chain first retracts towards less aligned conformations because they have much greater configurational multiplicity. Viscous friction and internal relaxation determine the time course; stored free energy is dissipated as heat. An unconstrained ideal chain does not shrink to a point: its mean vector is zero but its root mean square end-to-end length is $b\sqrt{N}\simeq 2.37\mathrm{nm}$ for the supplied ideal-chain parameters.

A real polypeptide also has sequence-dependent interactions. If the original native structure is the stable state in the prevailing solvent and the molecule remains intact and capable of folding, it can subsequently refold, gaining favourable intramolecular and solvent free energy. The folded state is not selected by chain entropy alone, and formation of native contacts need not be instantaneous. Kinetic traps, proline isomerization, protein aggregation, misfolding, surface attachments or chemical damage may prevent complete recovery or produce hysteresis. Thus reversible refolding is a physically motivated possibility, not guaranteed simply by removal of force. This distinction connects the recoil of a stretched polymer to the thermodynamics discussed in Question 6(c).

Let $C_{\mathrm{tot}}=[\mathrm{cis}]+[\mathrm{trans}]$, which is conserved for this closed one-to-one isomerization at fixed volume. Substitute $[\mathrm{cis}{]}_{298}=C_{\mathrm{tot}}-[\mathrm{trans}{]}_{298}$ into the equilibrium ratio:ThereforeThe equilibrium split is independent of having started with pure cis, provided equilibration is complete and no side reaction changes the total concentration.

React pentaborane with an alkyne under relatively mild conditions to obtain a nido ${\mathrm{C}}_2{\mathrm{B}}_4{\mathrm{H}}_8$ framework, conventionally nido-2,3-dicarbahexaborane(8) for acetylene. The two entering carbon atoms initially retain their adjacency. A specific mild example uses 2-butyne with triethylamine-assisted ${\mathrm{B}}_5{\mathrm{H}}_9$ at or below room temperature to give nido-$\mathrm{M}{\mathrm{e}}_2{\mathrm{C}}_2{\mathrm{B}}_4{\mathrm{H}}_6$. This is a practical route to an explicitly nido carborane, rather than an assumption that an alkyne supplies a closo cage under every condition.^[ref]

More energetic gas-phase reaction or pyrolysis promotes hydrogen loss, boron-fragment loss and cage rearrangement, giving closo carboranes, for example $1,5$-${\mathrm{C}}_2{\mathrm{B}}_3{\mathrm{H}}_5$ and $1,6$-${\mathrm{C}}_2{\mathrm{B}}_4{\mathrm{H}}_6$, with other cage sizes possible in the mixture. Thermolysis of a previously formed nido carborane is an alternative route to this stage. The point is not a clean same-composition nido-to-closo isomerization: the change of hydrogen content and sometimes cage size must be retained in the formulas.

Milder conditions favour kinetically trapped adjacent-carbon products; higher temperatures permit migration to carbon-separated arrangements, often increasing favourable B–C contacts relative to adjacent C–C/B–B contacts. Conditions and Lewis bases also influence which separated-carbon cage is isolated; temperature alone does not prescribe a single quantitative isomer distribution. Primary thermolysis studies and the small-carborane literature document both cage rearrangement and reagent-dependent product mixtures.^[ref]

Suspend starch in water, warm it to make a paste, and heat with a dilute acid, such as dilute sulfuric acid, to cause hydrolysis of the glycosidic bonds. The chemical reaction passes through shorter carbohydrates; sufficient hydrolysis ultimately gives glucose. The usual repeat-unit accounting isThis idealized polymer formula omits end-group details. The acid catalyses cleavage and is not consumed in the displayed equation. Merely using amylase from malt should not be described as necessarily producing pure glucose; it can leave maltose and shorter polysaccharides.

When sulfuric acid is used, neutralization with calcium carbonate removes the acidity and much of the sulfate as calcium sulfate. Filter out the insoluble residue, then concentrate the chemical solution gently and crystallize the glucose; further recrystallization is required to distinguish a reasonably pure chemical substance from a crude syrup. Overheating and unnecessarily prolonged strong acid treatment degrade the sugar. Hydrolysis of sucrose is a less selective preparative answer because it gives fructose alongside glucose.

For the historical copper test, use freshly mixed Fehling's reagent: an aqueous copper(II) sulfate portion and an alkaline tartrate portion. The tartrate keeps copper(II) in coordination complexes instead of allowing immediate bulk precipitation of copper(II) hydroxide. Add a suitably prepared sample to a small test portion and warm in a hot water bath. A yellow-orange to brick-red precipitate of copper(I) oxide indicates reduction of the copper(II) reagent. Run a known glucose sample and a water blank alongside it. In a simple sample, a visible difference between these controls helps distinguish a true positive from a deteriorated reagent or contamination.^[ref]

The key redox accounting on the copper side isThe required electrons come from oxidation of the sugar. This half-equation deliberately omits the changing tartrate ligands and does not assign a unique organic product. The often printed claim that hot alkaline glucose simply becomes gluconate in this test is too simple: competing isomerization, oxidation and fragmentation make the organic chemistry more complicated.^[ref]

Fructose, lactose, maltose and various other reducing substances can also give a positive Fehling's test. In particular, fructose can form aldoses by tautomerization in alkaline solution; an initial ketone functional group does not make it reliably negative.^[ref] Fermentation by suitable yeast, with carbon dioxide formation, and optical rotation can supply further historical evidence, but neither is individually specific to glucose. These are anticipated diagnostic observations, not measurements supplied by the paper. In present laboratory practice an appropriately validated enzymatic glucose assay can establish glucose more selectively; the old reducing-sugar test is not by itself a diagnosis of diabetes.^[ref]