89 -- Considering the given reactions, for the reaction: $4N_\gamma(g) + 3H_\gamma O(l) \rightarrow 2NH_\gamma(g) + 2N_\gamma O(g)$, how many kilojoules is $\Delta H$?
$$4NH_\gamma(g) + 3O_\gamma(g) \rightarrow 2N_\gamma(g) + 6H_\gamma O(l) \quad , \quad \Delta H = -1530 \ \text{kJ}$$ $$N_\gamma O(g) + H_\gamma(g) \rightarrow N_\gamma(g) + H_\gamma O(l) \quad , \quad \Delta H = -376 \ \text{kJ}$$ $$2H_\gamma(g) + O_\gamma(g) \rightarrow 2H_\gamma O(l) \quad , \quad \Delta H = -572 \ \text{kJ}$$

(1) $-988$	(2) $-1035$
(3) $-1105$	(4) $-1058$

90 -- Which two compounds are isomers of each other and have a higher boiling point than the other compounds?
[Figure: Four organic compounds labeled Alef, B, T, P:

• Alef: a carboxylic acid (with OH group on carbonyl)
• B: an ester (cyclic, with two C=O groups)
• T: a ketone (with C=O in chain, labeled H)
• P: a ketone (simple, C=O in chain)

]

(1) ``Alef'' and ``B'' -- ``T''	(2) ``Alef'' and ``T'' -- ``Alef''
(3) ``B'' and ``P'' -- ``T''	(4) ``P'' and ``T'' -- ``Alef''

%% Page 14 Chemistry 122A Page 13

91-- From burning a quantity of carbon, gases CO and CO$_2$ are formed. Considering the following reactions, if 5.6 liters of gas CO is formed at STP conditions, and a total of 201.5 kilojoules of energy is released, how many grams of carbon are consumed in reaction (II)? $(C = 12\ \text{g.mol}^{-1})$
\begin{align*} \text{I)}\ \ 2\text{C(s)} + \text{O}_2\text{(g)} &\rightarrow 2\text{CO(g)}, \Delta H = -564\ \text{kJ} \text{II)}\ \ \text{C(s)} + \text{O}_2\text{(g)} &\rightarrow \text{CO}_2\text{(g)}, \Delta H = -393\ \text{kJ} \end{align*}

(1) 8

(2) 6

(3) 4

(4) 15

92-- Considering the given structures of polymers, the molar mass of the monomer forming polymer A is approximately how many times the molar mass of the monomer forming polymer B? $(H = 1,\ C = 12,\ N = 14\ :\ \text{g.mol}^{-1})$
[Figure: Polymer A shows a polyamide structure with repeating units containing carbonyl groups and NH linkages; Polymer B shows a polystyrene-like structure with phenyl groups]

(1) $0.48$

(2) $0.50$

(3) $0.52$

(4) $0.58$

93-- Considering the structure of the given molecule, how many of the following statements are correct? $(H = 1,\ C = 12,\ N = 14,\ O = 16,\ Cl = 35.5\ :\ \text{g.mol}^{-1})$
[Figure: A molecule containing two chlorine atoms on a benzene ring, an NH group connecting to another benzene ring, and a $-$COOH group]

• The number of $\text{C}-\text{H}$ bonds is 5 times the number of $\text{C}-\text{N}$ bonds.
• Approximately, 15 percent of the molar mass of the compound is contributed by oxygen.
• The difference between the number of lone pairs between atoms and the number of $\text{C}-\text{H}$ bonds equals the number of chlorine atoms.
• The number of non-bonding electron pairs on atoms is 2.75 times the number of carbon atoms that have an oxidation number of $+1$.

(1) 4

(2) 3

(3) 2

(4) 1

Calculation Space
%% Page 15

94 -- Regarding the given reaction, which is used to prepare phosphorus, which of the following balanced equations is correct?
$(C = 12,\ O = 16,\ P = 31\ \text{g.mol}^{-1})$
$$\mathrm{Ca_3(PO_4)_2(s) + SiO_2(s) + C(s) \rightarrow CaSiO_3(s) + P_4(s) + CO(g)}$$
(1) The average rate of formation of $\mathrm{CO(g)}$ 21 grams, with the average rate of formation of $\mathrm{P_4(s)}$ 9.3 grams, and the average rate of consumption of carbon is 15 grams equal.
(2) The average rate of consumption of the reactant containing Si, equals the average rate of formation of the formula containing Si, and equals the rate of reaction.
(3) If in a certain time, 4 moles of carbon are consumed, in half of this time, $\frac{1}{2}$ mole of $\mathrm{CaSiO_3(s)}$ is formed.
(4) The time of consumption of 0.4 moles of salt, equals the time of formation of 0.2 moles of $\mathrm{P_4(s)}$.

95 -- At equal temperature and concentration, upon dissolution of each of the following substances in water, the concentration of hydroxide ions decreases and the number of existing molecules in the solution increases the most?
(1) $\mathrm{NH_3(g)}$ (2) $\mathrm{HCl(g)}$ (3) $\mathrm{HCN(g)}$ (4) $\mathrm{HCOOH(l)}$

96 -- Which statement about formic acid solution (Solution I) and acetic acid solution (Solution II) is correct?
(1) At constant temperature, if the concentration of solution (I) is less than the concentration of solution (II), the pH of solution (II) is certainly higher than the pH of solution (I).
(2) At constant temperature, if the pH of the two solutions is equal, the number of molecules of solution (I) is greater than the number of molecules of solution (II).
(3) By diluting each of the two solutions to the same extent, the degree of ionization of both acids increases by less than one fold.
(4) At different temperatures and concentrations, both solutions can react completely with sodium hydroxide.

97 -- A mixture of $a$ milliliters of strong acid solution HA ($\mathrm{pH=1/4}$) and $b$ milliliters of the same acid solution ($\mathrm{pH=1/7}$) with 200 milliliters of 0.3 molar sodium hydroxide solution becomes neutralized. $a+b$ equals how many milliliters?
(1) 500 (2) 1000 (3) 250 (4) 2000

98 -- Considering the following half-reactions at $E^\circ$, which statement is correct?
$$E^\circ(\mathrm{Cl_2/2Cl^-}) = +1.36\ \mathrm{V} \qquad E^\circ(\mathrm{Sn^{4+}/Sn^{2+}}) = +0.15\ \mathrm{V} \qquad E^\circ(\mathrm{Cu^+/Cu}) = +0.52\ \mathrm{V}$$
(1) $\mathrm{Cl^-(aq)}$ is a stronger reducing agent than $\mathrm{Sn^{2+}(aq)}$, and $\mathrm{Cu^+(aq)}$ is a stronger oxidizing agent than $\mathrm{Sn^{4+}(aq)}$.
(2) $\mathrm{Sn^{4+}(aq)}$ can oxidize $\mathrm{Cu(s)}$ under suitable conditions and produce energy.
(3) If metal X reacts naturally with $\mathrm{Sn^{4+}(aq)}$, it certainly also reacts with chlorine gas.
(4) The reaction: $\mathrm{2Cu(s) + Cl_2(g) \rightarrow 2Cu^+(aq) + 2Cl^-(aq)}$ proceeds naturally.
%% Page 16

99. The ratio of the total change in oxidation number of carbon atoms in the complete combustion reaction of one mole of naphthalene, to the total oxidation number of carbon atoms in a naphthalene molecule, is:
(1) $-6$ (2) $-3$ (3) $-4$ (4) $-12$

100. If in a galvanic cell formed from metal M and metal copper, for every 2 moles of M consumed, $3.612\times10^{24}$ electrons are exchanged, and the ratio of mass change of copper to mass change of M equals $1.84$, what is the approximate molar mass of metal M? $(\text{Cu} = 64 \text{ g.mol}^{-1})$
(1) $45$ (2) $52$ (3) $70$ (4) $59$

101. Which of the following comparisons of the properties of steel and titanium is correct?
A: Melting point: Steel $>$ Titanium
B: Corrosion resistance: Titanium $>$ Steel
C: Resistance to reaction with particles present in seawater: Steel $<$ Titanium
D: Extent of use in aircraft construction: Steel $<$ Titanium
(1) ``A'' and ``B'' (2) ``A'' and ``B'' (3) ``B'' and ``D'' (4) ``C'' and ``D''

102. Considering the partial periodic table below, which of the following statements about the compound formed from the combination of the two given elements (under appropriate conditions) is correct?
[Figure: Partial periodic table with elements A, D, E, Z, J, G marked in various positions]
A: Lattice enthalpy: $G < D$ and $J < D$ B: Boiling point: $A > Z < E$ and $E$
C: Polar diatomic: $Z > E > G$ and $A$ D: Number of covalent bonds: $J > A$ and $G > Z$
(1) ``A'' and ``B'' (2) ``A'' and ``D'' (3) ``B'' and ``C'' (4) ``B'', ``C'' and ``D''

103. Which of the following conditions does not increase the rate of ammonia production per unit time in the Haber process?

1. [(1)] Removing the product from the reaction vessel
2. [(2)] Using a catalyst
3. [(3)] Decreasing pressure
4. [(4)] Increasing temperature

%% Page 17

104- Gas-phase reaction: $K = 25$, $2M + 2Z \rightleftharpoons 4X + Y$, using moles of reactants equal to moles of products, the reaction is carried out in a closed container. If $0.2$ mol of gas X and $0.8$ mol of gas Y are at equilibrium, the volume of the container is how many milliliters?
(1) $250$ (2) $125$ (3) $1250$ (4) $2500$

105- The graph below shows the change in molar concentration of the product for the reaction: $\text{AD(g)} \rightleftharpoons \text{A(g)} + \text{D(g)}$, under two different conditions. Which statement is correct? ($P$ is pressure.)
[Figure: Graph of [AD] vs. temperature (°C), showing two curves $P_1$ and $P_2$, where $P_2$ is above $P_1$]

1. $P_1 < P_2$ and with decreasing temperature, the value of $K$ increases.
2. $P_2 < P_1$ and with increasing pressure, the equilibrium shifts to the right.
3. $P_2 < P_1$ and with decreasing temperature, the amounts of A and D change relative to each other.
4. $P_1 < P_2$ and with increasing volume of the container, the concentration of gas A and the amount of gas AD increase.

a) Show that among any 2-coloring (Red/Blue) of the vertices of a regular hexagon and its center, there must exist a monochromatic equilateral triangle.
b) Extend the argument to show the result holds for a larger configuration of points.

a) $n$ lines are drawn through a point $A$ inside a circle, creating chords. Show that the number of regions created inside the circle is $(n+1)^2$, assuming no three lines meet at any point other than $A$.
b) Using the result from part a), find the total number of regions when additional lines are drawn, and show the total is $(n+1)^2 + (2n+1)n$.

Three triangles are formed by drawing lines from the vertices of a triangle $ABC$ to the opposite sides, each making equal angles with the sides. Let $\Delta_1, \Delta_2, \Delta_3$ be the areas of the three smaller triangles formed at the vertices with the circumradius equal to 1.
a) Express the total area $\Delta = \Delta_1 + \Delta_2 + \Delta_3$ in terms of $A, B, C$.
b) Find the angles $A, B, C$ that maximize $\Delta$.
c) Verify that the maximum occurs for an isosceles triangle and prove $C = A$ by calculus.

Find a 4-digit number $N$ such that $N = 4M$, where $M$ is the number obtained by reversing the digits of $N$.

2. $\tan ( \alpha + B ) = 50 / \alpha = \frac { 10 / \alpha + \tan B } { 1 - 10 / d \tan B }$ solving Yan $B$ and maximizing writ $d$ you'll find $d = 10 \sqrt { 5 }$ feet and corresponding to a 3!
$$\begin{aligned} & 4 \text { SEP; } T \in Q \text { | are tangency points } \\ & C K \text { are mid points of } A B , M N \\ & \triangle P A C \cong \triangle P Q T \text { and } \triangle Q M K \cong \triangle Q P S \\ & y _ { 2 } A B = A C = P A \cdot S T / P Q = \frac { P S Q M } { P Q } = M K = 1 / 2 M N \text { QED } \\ & s = ( x + y + z ) \\ & \triangle = \sqrt { ( x + y + z ) ( x + y + z - x - y ) ( x + y + z - y - z ) ( x + y + z - x - z ) } \\ & = \sqrt { ( x + y + z ) n y z } \\ & \triangle = 1 / 2 r ( ( x + y ) + ( y + z ) + ( x + z ) ) = r ( x - y + z ) \\ & = \sqrt { ( x + y + z ) x y z } \end{aligned}$$
$$\begin{aligned} x & = \lim _ { n \rightarrow \alpha } \frac { 1 } { 2 n } \log \frac { 2 n ! } { ( n ! ) ^ { 2 } } \\ & = \lim _ { n \rightarrow \alpha } \frac { 1 } { 2 n } \lim _ { n \rightarrow \alpha } \log \frac { \frac { ( n + 1 ) ( n + 2 ) \cdots ( n + n ) } { n ^ { n } } } { \frac { 12 \cdot 3 \cdots } { n ^ { n } } } \\ & = \lim _ { n \rightarrow \alpha } \frac { 1 } { 2 n } ( \log ( 1 + 1 / n ) ( 1 + 2 / n ) ( 1 + 3 / n ) \cdots ( 1 + n / n ) - \log ( 1 / n + 2 / n + \cdots + n / n ) ) \\ & = 1 / 2 \int _ { 0 } ^ { 1 } \ln ( 1 + x ) - \ln x d x = 1 / 2 \left[ \left. \ln \log ( x + 1 ) \right| _ { 0 } ^ { 1 } - \int _ { 0 } ^ { 1 } \frac { x d x } { 1 + x } \right] - [ x \ln x \cdot x ] _ { 0 } ^ { 1 } \end{aligned}$$
$$= 1 / 2 ( ( \ln 2 + \ln 2 - 1 ) - ( - 1 ) ) = 1 / 2 \ln 4$$
7
$$\text { a) } \begin{aligned} f ( x ) & = x ^ { 5 } + x - 10 \\ f ^ { \prime } ( x ) & = 4 x ^ { 4 } + 1 > 0 \end{aligned}$$
$$\text { b) } \begin{gathered} f ( 1 ) = - 8 ; f ( 2 ) = 24 \\ f ( 1 ) f ( 2 ) < 0 \end{gathered}$$
[Figure]
$$\text { c) let } \begin{aligned} x = p / q ; & ( p / q ) ^ { 5 } + ( p / q ) = 10 \\ & \Rightarrow p 5 / q = q 10 q - p \end{aligned}$$
fraction =integer contradictian!

8. Number of pairs ew/o anykind of war $= \binom { 8 } { 2 } = 28$
The poirs that harms $= 5 f [ ( 2,4 ) , ( 2,6 ) , ( 4,6 ) , ( 6,8 ) , ( ( 2,4 ) , ( 6,8 ) ) ]$

9. $( a * b ) \quad \mathrm { lcm } = k m ; g c d = m ; a = k m ; b = k n ; c = k p$
$$\begin{array} { l l } ( a * b ) = \frac { k m n } { k } = m n ; b * c = \frac { k n p } { k } = n p & \\ ( a * b ) * c = k m n p / 1 = k m n p & a = k m \quad i = k p \\ ( a * ( b * c ) ) = k m n p / 1 = k m n p & a * i = k m p / k = m p \neq a \end{array}$$

1. 'any two similar figures have an isomerism and homethette velation which takes are figure to the other' a) have segment $A B ( A \neq B )$ and $C D ( C \not \equiv D )$. Have point $P \in A B$ with $P A / A B = \lambda \in [ 0,1 ]$; assocrate to it the point SECD with SC/CD $= \lambda$ b) have cincle $\gamma$ (of the centre $m$ and radius $r > 0$ ) and $\Gamma$ (of centre $m$ and radius $R > 0$ ). Have point $P + \gamma$ making angle $\theta \in [ 0,2 \pi )$ with the horizontal; asscerate to it point $Q \in T ^ { \prime }$ making an angle $\theta$ with the horizontal

Let $f : \mathbb{R} \rightarrow \mathbb{R}^{2}$ be a function given by $f(x) = (x^{m}, x^{n})$, where $x \in \mathbb{R}$ and $m, n$ are fixed positive integers. Suppose that $f$ is one-one. Then
(a) Both $n$ and $m$ must be odd
(b) At least one of $m$ and $n$ must be odd
(c) Exactly one of $m$ and $n$ must be odd
(d) Neither $m$ nor $n$ can be odd.