The 2', 3'-cyclic phosphodiester that is formed when RNA is hydrolyzed reacts with water, forming a mixture of nucleotide 2' - and 3'-phosphates. Propose a mechanism for this reaction.

Determine equilibrium values for the given dynamical systems and state whether these equilibrium values are stable. a) $A_{n+1}=3 A_n-1$ b) $B_{n+1}=0.5 B_n-3$

A frame in the shape of the simple scissors truss shown at the right below can be used to support a peaked roof. The weight of the roof compresses some parts of the frame (green), while other parts are in tension (blue). A frame made with $s$ segments joined at $j$ points is stable if $s \geq 2 j-3$. In the truss shown, 9 segments connect 6 points. Verify that the truss is stable. Then find the values of $x$ and $y$.

Draw a reaction coordinate diagram for the following reaction in which C is the most stable and B the least stable of the three species and the transition state going from A to B is more stable than the transition state going from B to C:

$$\mathrm{A} \stackrel{k_1}{\underset{k_{-1}}{\rightleftharpoons}} \mathrm{B} \underset{k_{-2}}{\stackrel{k_2}{\rightleftharpoons}} \mathrm{C}$$

a. How many intermediates are there?

b. How many transition states are there?

c. Which step has the greater rate constant in the forward direction?

d. Which step has the greater rate constant in the reverse direction?

e. Of the four steps, which has the greatest rate constant?

f. Which is the rate-determining step in the forward direction?

g. Which is the rate-determining step in the reverse direction?

Consider the ketones menthone and isomenthone. Propose an explanation for the observation that menthone is converted to a mixture of menthone and isomenthone on treatment with 90% sulfuric acid.

(a) Find all equilibrium solutions for the equation

$$\frac{d y}{d x}=0.5 y(y-4)(2+y)$$

(b) With a calculator or computer, draw a slope field for this differential equation. Use it to determine whether each equilibrium solution is stable or unstable.

Classify substance Cytosine, a component of DNA, consists of H, C, N, and O atoms bonded in a specific arrangement, as an element, compound, or mixture, and explain your answer.

A gas mixture contains $1.5 \times 10^{-5}$ mole $\mathrm{CO}$ and has a total of 1 mole. What is the $\mathrm{CO}$ concentration in ppm$_{\mathrm{v}}$?

A chromatographic procedure separates 4.0 mg of unknown mixture on a column with a length of 40 cm and a diameter of 0.85 cm.

(a) What size column would you use to separate 100 mg of the same mixture?

(b) If the flow is 0.22 mL/min on the small column, what volume flow rate should be used on the large column?

(c) The mobile phase occupies 35% of the column volume. Calculate the linear velocity for the small column and the large column

Use these words that end in the suffix -ure to answer the following questions.

mixture pleasure signature fracture

Which word can mean the result of bursting? ________________________

Classify substance Calcium chloride, used to melt ice on roads, consists of two elements, calcium and chlorine, in a fixed mass ratio as an element, compound, or mixture, and explain your answer.

Fifty gallons of a $90 \%$ alcohol solution is obtained by mixing a $100 \%$ solution with a $75 \%$ solution. How many gallons of each solution must be used to obtain the desired mixture?

A mixture containing only Al$_2$O$_3$ (FM 101.96) and Fe$_2$O$_3$ (FM 159.69) weighs 2.019 g. When heated under a stream of H2, Al2O3 is unchanged, but Fe$_2$O$_3$ is converted into metallic Fe plus H$_2$O(g). If the residue weighs 1.774 g, what is the weight percent of Fe$_2$O$_3$ in the original mixture?

When air is inhaled, it enters the alveoli of the lungs, and varying amounts of the component gases exchange with dissolved gases in the blood. The resulting alveolar gas mixture is quite different from the atmospheric mixture. The following table presents selected data on the composition and partial pressure of four gases in the atmosphere and in the alveoli:

$$\begin{array}{|c|c|c|c|c|} \hline \text { Gas } & \text { Mole \% } & \begin{array}{l} \text { Partial } \\ \text { Pressure (torr) } \end{array} & \text { Mole \% } & \begin{array}{l} \text { Partial } \\ \text { Pressure (torr) } \end{array} \\ \hline \mathrm{N}_2 & 78.6 & - & - & 569 \\ \hline \mathrm{O}_2 & 20.9 & - & - & 104 \\ \hline \mathrm{CO}_2 & 00.04 & - & - & 40 \\ \hline \mathrm{H}_2 \mathrm{O} & 00.46 & - & - & 47 \\ \hline \end{array}$$

If the total pressure of each gas mixture is $1.00 \mathrm{~atm}$, calculate:

(a) The partial pressure (in torr) of each gas in the atmosphere

(b) The mole % of each gas in the alveoli

(c) The number of $\mathrm{O}_2$ molecules in $0.50 \mathrm{~L}$ of alveolar air (volume of an average breath of a person at rest) at $37^{\circ} \mathrm{C}$