Evaluate 2,3,3-trimethyl-1-butene as a candidate for free-radical bromination. How many allylic bromides would you expect to result from its treatment with N-bromosuccinimide?

Consider an interphase mass-transfer process for the chlorine dioxide ($ClO_{2}$)-air-water system at $20 ^{\circ } \mathrm {C}$, where $ClO_ {2}$ gas (solute A) is sparingly soluble in water. At the current conditions of operation, the mole fraction of $\mathrm{ClO}_{2}$ in the bulk gas phase is $y_{A}=0.040$ and the mole fraction of $\mathrm{ClO}_{2}$ in the bulk liquid phase is $x_{A}=0.00040$. The mass density of the liquid phase is $992.3 \mathrm{kg} / \mathrm{m}^{3}$ and is not dependent on the very small amount of $\mathrm{ClO}_{2}$ dissolved in it. The molecular weight of water is $18 \mathrm{g/gmole}$, and the molecular weight of $\mathrm{ClO}_{2}$ is 67.5 g/gmole. The total system pressure is 1.5 atm. The liquid film mass-transfer coefficient for $\mathrm{ClO}_{2}$ in water is $k_{x}=1.0$ gmole/m$^{2} \cdot \mathrm{ s }$, and the gas film mass-transfer coefficient $\mathrm{ClO}_{2}$ in air is $k_{G}=0.010$gmole/m$^{2} \cdot s \cdot atm$. The equilibrium distribution data for the $\mathrm{ClO}_{2}$-water-air system at $20^{\circ} \mathrm{C}$ are provided below:

$$\begin{array}{llllllll}\hline \scriptstyle{p_{A}} & \scriptstyle{{100E-02}} & \scriptstyle{{3.00E - 02}} & \scriptstyle{{5.00 \mathrm{E} - 02}} & \scriptstyle{{7.00 \mathrm{E} - 02}} & \scriptstyle{{1.00 \mathrm{E} - 01}} & \scriptstyle{{1.10 \mathrm{E} - 01}} \\ \scriptstyle{{x_{\mathrm{A}}}} & \scriptstyle{{2.40 \mathrm{E} - 04}} & \scriptstyle{{7.19 \mathrm{E} - 04}} & \scriptstyle{{1.15 \mathrm{E} - 03}} & \scriptstyle{{1.64 \mathrm{E} - 03}} & \scriptstyle{{2.34 \mathrm{E} - 03}} & \scriptstyle{2.58\mathrm{E} - 03} \\ \scriptstyle{{p_{\mathrm{A}}}} & \scriptstyle{{1.20 \mathrm{E} - 01}} & \scriptstyle{{1.30 \mathrm{E} - 01}} & \scriptstyle{{1.40 \mathrm{E} - 01}} & \scriptstyle{{1.50 \mathrm{E} - 01}} & \scriptstyle{{1.60 \mathrm{E}-01}} \\ \scriptstyle{{x_{\mathrm{A}}}} & \scriptstyle{{2.81 \mathrm{E}-03}} & \scriptstyle{{3.06 \mathrm{E}- 03}} & \scriptstyle{{3.28 \mathrm{E} - 03}} & \scriptstyle{{3.52 \mathrm{E} - 03}} & \scriptstyle{{3.78 \mathrm{E} - 03}} \\ \hline\end{array}$$

a. Plot out the equilibrium line in $p_{A}-c_{A L}$ coordinates, and the operating point $\left(p_{A}, c_{A L}\right)$. Is the process gas absorption or liquid stripping? b. What is the equilibrium relationship as n equal to? c. What is $k_{L}$ for the liquid film? d. If the $\mathrm{ClO}_{2}$ mole fraction in the bulk gas phase is maintained at 0.040 under 1.5 am total system pressure, what is the maximum possible dissolved $\mathrm{ClO}_{2}$ concentration (gmole A/$\mathrm{m}^{3}$) in the liquid phase that could possibly exit the process-i.e., $c_{A L}^{\circ}$? e. What are the compositions at the gas-liquid interface, $p_{A, i}$ and $c_{A L, i}$? f. What is $K_{y}$, the overall mass-transfer coefficient based upon the overall gas-phase mole fraction driving force? There are several valid approaches for calculating $K_{y}$ based on the information provided. Show at least two approaches that lead to the same result. g. What is the mass-transfer flux $N_{A}$ for $\mathrm{ClO}_{2}$ in units of gmole/m$^{2} \cdot$s?

Give the structures of three isomeric dibromides that could be used as starting materials for the preparation of 3,3-dimethyl-1-butyne.

As indicated in the preceding equations, the yield of the substitution product was much better in the reaction of trans-1-chloro-2-butene than 3- chloro-1-butene. Can you suggest a reason why?

Assume that N-bromosuccinimide serves as a source of $\mathrm{Br}_{2}$, and write equations for the propagation steps in the formation of 3-bromocyclohexene by allylic bromination of cyclohexene.

Succinic anhydride, the structure of which, is a cyclic anhydride often used in FriedelCrafts acylations. Give the structure of the product obtained when benzene is acylated with succinic anhydride in the presence of aluminum chloride.

According to the Beer-Lambert Law, the light intensity at a depth of meters below the surface of the ocean is $I(x)=I_{0} a^{x}$, where $I_0$ is the light intensity at the surface and a is a constant such that 0<a<1. If $I_{0}=8$ and a=0.38, find the rate of change of intensity with respect to depth at a depth of 20 m.

Tetraethoxysilane, also called TEOS or $\operatorname{Si}\left(\mathrm{OC}_{2} \mathrm{H}_{5}\right)_{4}$, is a liquid chemical used in the semiconductor industry to produce thin films of silicon dioxide by chemical vapor deposition (CVD). In order, to deliver the TEOS vapor to the CVD reactor, liquid TEOS is fed to a wetted-wall column. The TEOS liquid uniformly coats the inner surface of the tube as a thin liquid film as it flows downward. The falling liquid film of TEOS evaporates into an inert helium carrier gas flowing upwards at a volumetric flow rate of $2000 \mathrm{cm}^{3} / \mathrm{s}$. The wetted-wall column has an inner diameter of $5.0 \mathrm{cm}$ and a length of $2.0 \mathrm{m}$. The column temperature is maintained at $333 \mathrm{K}$, and the total system pressure is 1.0 atm. At 333 K, the kinematic viscosity of helium gas is $1.47 \mathrm{cm}^{2} / \mathrm{s}$, the diffusion coefficient of TEOS vapor in helium gas $1.315 \mathrm{cm}^{2} / \mathrm{s}$, and the vapor pressure of liquid TEOS is $P_{A}=2133 \mathrm{Pa}$. a. What is the gas mass-transfer coefficient, $k_{G}$? b. What is the mole fraction of TEOS vapor exiting the column? c. What is the required mass flow rate of liquid TEOS flowing into the column if all of the liquid TEOS evaporates by the time it reaches the bottom of the column?

Find common denominators and calculate each of the following sums. $a. \frac{3}{8}+\frac{1}{4}\ b. \frac{2}{5}+\frac{1}{3}$ c. What is the least common multiple of 8 and 4? Of 5 and 3? d. Explain how finding the least common multiple of two numbers can help you add fractions.

The reaction of N-bromosuccinimide with the following compounds has been reported in the chemical literature. Each compound yields a single product in 95% yield. Identify the product formed from each starting material. (a) p-tert-Butyltoluene (b) 4-Methyl-3-nitroanisole

Solve the differential equations. $y^{\prime}=e^{x} y^{2}$

Determine the surface area of a primary settling tank sized to handle a maximum hourly flow of $0.570 m^3$. $s^{-1}$ at an overflow rate of $60.0 \mathrm{m} \cdot \mathrm{day}^{-1}.$ If the effective tank depth is 3.0 m, what is the effective theoretical detention time? Answers: Surface area= 820.80, or $821 \mathrm{m}^{2} ; t_{\mathrm{o}}=1.2 \mathrm{h}.$

True or False If a function f is defined and continuous on a closed interval [a, b], differentiable on the open interval (a, b), and if f(a)=f(b), then Rolle's Theorem guarantees that there is at least one number c in the interval (a, b) for which f(c)=0.

Differentiate. $y=\frac{c x}{1+c x}$