Solvolysis of 2-bromo-2-methylbutane in acetic acid containing sodium acetate gives three organic products. What are they?

For a flow of 0.8 $m^{3} \cdot s^{-1}$, how many rapid sand filter boxes of dimensions $10 \mathrm{m} \times 10 \mathrm{m}$ are needed for a loading rate of 110 $m^{3} \cdot d a y^{-1} \cdot m^{-2}$?

A water has a pH of 8.00 and a temperature of $10^{\circ} \mathrm{C}$. A 3.00 log inactivation of Giardia cysts is required. A chlorine concentration of 1.20 $\mathrm{mg} \cdot \mathrm{L}^{-1}$ is to be used. The water is treated at a rate of 2.409 $m^{3} \cdot s^{-1}$. What is the design volume of the chlorine contacting chamber (in $m^3$)?

Students in a graduate-level environmental engineering laboratory took samples of the influent (raw sewage) and effluent (treated sewage) of a municipal wastewater treatment plant. They used these samples 10 determine the BOD rate constant (k). Would you expect the rate constants to be the same or different? If different, which would be higher and why?

In a chromatographic separation process, a bio-molecule of 20 nm diameter is diffusing into a random porous particle with void fraction ($\epsilon$) of 0.70 filled with elution solvent. However, the reduced pore diameter ($\varphi$) for the diffusion process is only 0.010 , and hindered diffusion of the solute within the solvent-filled pore can be neglected. If the desired effective diffusion coefficient $\left(D_{A c}^{\prime}\right)$ of the biomolcule inside the porous particle is $1.0 \times 10^{-7} \mathrm{cm}^{2} / \mathrm{s}$ at $30^{\circ} \mathrm{C}$, what solvent viscosity would be needed to achieve this $D_{A c}$?

Draw the elimination products obtained under E2 conditions for each of the following alkyl halides.

The reaction of 2,2-dimethyl-1-propanol with HBr is very slow and gives 2-bromo-2-methylbutane as the major product. Give a mechanistic explanation for these observations.

Identify the compound in each of the following pairs that reacts at the faster rate in an $S_N1$ reaction: (a) lsopropyl bromide or isobutyl bromide (b) Cyclopentyl iodide or 1-methylcyclopentyl iodide (c) Cyclopentyl bromide or 1-bromo-2,2- dimethylpropane (d) tert-Butyl chloride or tert-butyl iodide

a. Suggest an explanation for the fact that 1-methylcyclopropene is some 42 kJ/mol (10 kcal/mol) less stable than methylenecyclopropane. 1-Methylcyclopropene is less stable than Methylenecyclopropane b. On the basis of your answer to part (a), compare the expected stability of 3-methylcyclopropene with that of 1-methylcyclopropene and that of methylenecyclopropane.

Give the structures of two different alkyl bromides both of which yield the indicated alkene as the exclusive product of E2 elimination. (a) $\mathrm{CH}_{3} \mathrm{CH} \mathrm{\square CH}_{2}$ (c) $\mathrm{BrCH} \mathrm{\square CBr}_{2}$ (b) $\left(\mathrm{CH}_{3}\right)_{2} \mathrm{C} \mathrm{\square CH}_{2}$

Write structural formulas for all the alkene products that could reasonably be formed from each of the following compounds under the indicated reaction conditions. Where more than one alkene is produced, specify the one that is the major product. (a) 1-Bromo-3,3-dimethylbutane (potassium tert-butoxide, tert-butyl alcohol, $100^{\circ} \mathrm{C}$) (b) 1-Methylcyclopentyl chloride (sodium ethoxide, ethanol, $70^{\circ} \mathrm{C}$) (c) 3-Methyl-3-pentanol (sulfuric acid, $80^{\circ} \mathrm{C}$) (d) 2,3-Dimethyl-2-butanol (phosphoric acid, $120^{\circ} \mathrm{C}$) (e) 3-Iodo-2,4-dimethylpentane (sodium ethoxide, ethanol, $70^{\circ} \mathrm{C}$) (f) 2,4-Dimethyl-3-pentanol (sulfuric acid, $120^{\circ} \mathrm{C}$)

The reaction between 2-bromobutane and sodium ethoxide in ethanol gives rise to three E2 products. What are they? Predict their relative amounts.

Suppose that the temperature in a long thin rod placed along the x-axis is initially C/(2a) if $|X| \leqslant a$ and 0 if |x|>a. It can be shown that if the heat diffusivity of the rod is , then the temperature of the rod at the point at time is $T(x, t)=\frac{C}{a \sqrt{4 \pi k t}} \int_{0}^{a} e^{-(x-u)^{2} /(4 k t)} d u$. To find the temperature distribution that results from an initial hot spot concentrated at the origin, we need to compute $\lim _{a \rightarrow 0} T(x, t)$. Use l’Hospital’s Rule to find this limit.

A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one. g(x)=|x|