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?

Forty gallons of a $60 \%$ acid solution is obtained by mixing a $75 \%$ solution with a $50 \%$ 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?

a. Draw a reaction coordinate diagram for a reaction that is very slow and slightly exergonic. b. Draw a reaction coordinate diagram for a reaction that is very fast and slightly endergonic. c. Draw a reaction coordinate diagram for a reaction that is very slow and slightly endergonic. d. Draw a reaction coordinate diagram for a reaction that is very fast and very exergonic.

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.

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 $y$.

Which of the following statements is the most correct regarding homeostatic imbalance?

a) Positive feedback mechanisms are overwhelmed

b) The internal environment is becoming more stable

c) It is considered the cause of most diseases

A mixture of nuts contains 1 cup of walnuts for every 3 cups of peanuts.

Write a linear equation that represents the relationship between peanuts, x, and walnuts, y.

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 mixing? ________________________

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 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

Each molecular-scale scene below represents a mixture. Describe each one in terms of the number of elements and/or compounds present.

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) $B_{n+1}=0.5 B_n-3$

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 $37^{\circ} \mathrm{C}$