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Organic Chemistry

Eigenfunctions of a linear operator

Suppose that O1 and O2 are eigenfunctions of a linear operator A with eigenvalues a1 and a2, respectively, and that we construct a linear combination Y=C1O1 + C2O2. Under what conditions does Y became an eigenfunction of A? Show reasoning.

Prove the relationship [x,px]=ih

Prove the relationship [x,px]=ih, where px =-ihd/dx. Namely, show that applying the commutator [x,px] to any function f(x) is equal to multiplying ih to f(x).

Steps in the synthesis of compounds

The professor wants us to do the following: Outline all steps in the possible synthesis of each of the following compounds from benzene and / or toluene, using any necessary aliphatic or inorganic reagents. Assume a pure para isomer that can be separated from an ortho/para mixture a) ethylbenzene b) phenyacetylene c) iso

Chemistry

Do the following, starting from alcohol that contains four or less carbon atoms and from benzene and toluene, outline how the following can be synthesized: a) 2,3-dimethyl-2-butanol b) 2-bromo-2methyl hexane c) 1,2-diphenyl-2-propanol d) 1-parabromophenyl-1phenal-1propanol

pH Calculation of a Solution Formed During Titration

Calculate the pH of the solution formed during a titration upon adding 35.0 ml of a standard .150M NaOH solution to: a. 15.00 ml of .200 M CH3COOH Ka = 1.8 x 10^-5. b. 36.0 ml of .100 M malonic acid, (H2M) (Ka1 = 1.42 x 10^-3, ka2 = 2.01 x 10^-6

Extraction of caffeine from tea

At 25 degrees C, 1.0 gram of caffeine will dissolve in 47 ml of water, in 8.1 ml's of chloroform, in 86 ml of benzene, or in 370 of diethyl ether. Calculate the partition coefficient of caffeine between water and each of the other three solvents. Which of these three organic solvents would be the best choice for extracting caff

Naming carbon chains according to IUPAC.

The following are incorrect efforts at naming certain compounds. What are the correct IUPAC names? a) propyl chloride b) isobutyl iodide c) t-butyl bromide d) ethyl bromide