223- Which comparison of vapor pressure (P), boiling point (t), and freezing point ($t'$) of a 1 molar solution of table salt (B) and a 1 molar solution of sugar (A) is correct?

• [(1)] $t'_B < t'_A\ ,\quad t_A < t_B\ ,\quad P_A > P_B$
• [(2)] $t'_B > t'_A\ ,\quad t_A > t_B\ ,\quad P_A > P_B$
• [(3)] $t'_B < t'_A\ ,\quad t_A < t_B\ ,\quad P_A < P_B$
• [(4)] $t'_B > t'_A\ ,\quad t_A > t_B\ ,\quad P_A < P_B$

224- Reaction rate: $\mathrm{NO_2(g) + CO(g) \to NO(g) + CO_2(g)}$, follows the relation $\bar{R} = k[\mathrm{NO_2}]^2$. Which graph about the progress of the reaction is correct? (Initial concentration of reactants is one mole per liter.)
[Figure: Four graphs showing $\bar{R}/k$ vs. $t$. Graph (1): decreasing curve starting at 1. Graph (2): decreasing straight line starting at 1. Graph (3): decreasing curve starting above 1. Graph (4): decreasing curve starting at 1 with different curvature.]

225- In the hypothetical reaction $\mathrm{A(g) + B(g) \to C(g)}$, by doubling the molar concentration of A and keeping the concentration of B constant, the reaction rate doubles; and by doubling the molar concentration of B while keeping the concentration of A constant, the rate becomes 4 times. What is the rate law and the unit of the rate constant?

• [(1)] $\mathrm{k[A][B]^2}$, unit: $\mathrm{mol^{-1}.L.s}$
• [(2)] $\mathrm{k[A][B]^2}$, unit: $\mathrm{mol^{-2}.L^2.s^{-1}}$
• [(3)] $\mathrm{k[A][B]}$, unit: $\mathrm{mol^{-1}.L.s^{-1}}$
• [(4)] $\mathrm{k[A]^2[B]^4}$, unit: $\mathrm{mol^{-2}.L^2.s}$

%% Page 24 Page 23 120-C Chemistry

226 – In the reaction $A(aq)$: $A(aq) \rightarrow D(aq) + 2X(aq) + H^+(aq)$, in a solution with 1 molar concentration of $HCl$, 2 molar $X(aq)$ and 1 molar $A(aq)$, the concentration $[A]$ is shown in the figure below.
Which of the following graphs shows the pH change of this solution over time?
(D has no acidic or basic character.)
[Figure: Graph showing $[A]$ (mol/L) on y-axis with values 0.8, 0.6, 0.4, 0.2 and time (s) on x-axis with values 100, 200, 300, 400. The curve decreases from about 0.8 and levels off asymptotically.]
[Figure: Four pH vs. time graphs labeled (1), (2), (3), (4):

• Graph (1): pH starts around 5 and increases in an S-shaped curve, leveling off near 7, x-axis 0 to 300.
• Graph (2): pH increases linearly from about 1 to 7, x-axis 0 to 300.
• Graph (3): pH starts low and increases in a concave-up curve leveling near 7, x-axis 0 to 300.
• Graph (4): pH starts around 5 and increases in a concave-down curve leveling near 7, x-axis 0 to 300.

]

227 – 1.6 mol of gas $\mathrm{SO_2Cl_2}$ is placed in a 2-liter closed container and heated until equilibrium is reached: $$\mathrm{SO_2Cl_2(g) \rightleftharpoons SO_2(g) + Cl_2(g)}$$ If at equilibrium, the total number of moles of gas in the container is 2.4 mol, what is the equilibrium constant $K_c$ (mol$\cdot$L$^{-1}$) under the experimental conditions?
(1) $2/2$ (2) $1/6$ (3) $0/22$ (4) $0/4$

228 – If the equilibrium reaction: $K = 2\,\mathrm{mol\cdot L^{-1}}$, $A(g) \rightleftharpoons 2B(g)$, starting with 1 molar concentration of substance $A$, at most what percentage of this reaction proceeds?
(1) $50$ (2) $52/5$ (3) $60$ (4) $62/5$
%% Page 25 Chemistry 120-C Page 24

229- If the pH of a weak acid HA solution is $2.5 \times 10^{-7}$ mol per milliliter, and 5 mol of it exists, what is the percent ionic dissociation of HA under experimental conditions?
(1) $0/f$ (2) $0/Y$ (3) $f$ (4) $Y$

230- If the pH of a 0.1 molar KX solution is smaller than the pH of a 0.1 molar $\text{KX}'$ solution, which of the following is always correct?
(1) HX is a stronger acid than $\text{HX}'$. (2) KX is acidic and $\text{KX}'$ is a basic salt.
(3) $K_a$ of HX is smaller than $K_a$ of $\text{HX}'$. (4) X can be a hydroxide ion and $\text{X}'$ can be a cyanide ion.

231- If the ratio $\dfrac{K_{a_1}}{K_{a_2}}$ for the diprotic acid $\text{H}_2\text{A}$ equals $10^4$, the pH of a 0.05 molar solution is 0.05, and the solution is 0.01 molar, by how many units does the conjugate base differ approximately?
(1) $f$ (2) $Y$ (3) $Y$ (4) $\varphi$

232- Mixing equal volumes of .............. solution with .............. solution forms a buffer solution.
(1) 0.6 molar $\text{NH}_3$, 0.2 molar $\text{H}_2\text{SO}_4$ (2) 0.4 molar NaOH, 0.2 molar $\text{HNO}_3$
(3) 0.50 molar $\text{NH}_3$, 0.4 molar $\text{HNO}_3$ (4) 0.2 molar NaOH, 0.2 molar $\text{H}_2\text{SO}_4$

233- The sum of the stoichiometric coefficients of the substances in the balanced equation for the oxidation of Fe(II) hydroxide and its conversion to Fe(III) hydroxide, in the rusting process, is which of the following?
(1) $9$ (2) $11$ (3) $1Y$ (4) $1Y$

234- In the complete combustion of stone, what is the total change in the oxidation numbers of carbon atoms?
(1) $1Y$ (2) $1f$ (3) $1\varphi$ (4) $1\Lambda$

235- Considering the figure below related to the rusting of iron, how many of the following statements are correct?
[Figure: Diagram showing rusting of iron with $\text{O}_2(\text{g})$, water droplet, $\text{Fe}^{2+}(\text{aq})$, and region A labeled on an iron piece]

• The cathode is located at point A.
• The cathodic reaction occurs where the oxygen concentration is high.
• For every mole of oxygen consumed in water, 4 moles of hydroxide ion are produced.
• The direction of movement of iron cations in the water droplet is opposite to the direction of electron movement in the iron piece.

(1) $1$ (2) $Y$ (3) $Y$ (4) $f$

120-A Page 2

130. The image of circle $C$ with center $(1, 2)$ and radius 1 unit, under the transformation $T(x,y) = (3x, 3y)$, is circle $C'$. The length of the common external tangent of these two circles is what?

• [(1)] $3$
• [(2)] $2\sqrt{3}$
• [(3)] $4$
• [(4)] $3\sqrt{2}$

131. Which converse of the following statements holds in space?

1. [(1)] If two lines $d$ and $d'$ are parallel, then every line perpendicular to $d$ is perpendicular to $d'$.
2. [(2)] If a line is parallel to one of the planes, then the line is parallel to that plane.
3. [(3)] If two planes $P$ and $Q$ are parallel, then the intersection lines of plane $R$ with them are parallel to each other.
4. [(4)] If two planes $P$ and $Q$ are parallel, then they create proportional segments on two intersecting lines.

%% Page 7 Mathematics 120-A Page 6

132. Three points $A$, $B$, and $C$ are non-coplanar and lie on a line and plane $\Delta$ is not passing through any of these three points. The number of planes parallel to $\Delta$ that are equidistant from all three points is:
(1) $1$ (2) $2$ (3) $3$ (4) $4$

133. The image of vector $\vec{a} = 7\mathbf{i} + 3\mathbf{j} - \sqrt{2}\,\mathbf{k}$, under a rotation that makes an angle of $60°$ with each of the $x$ and $y$ axes and makes an acute angle with the $z$-axis, has what components?
(1) $(1,1,\sqrt{2})$ (2) $(2,2,2\sqrt{2})$ (3) $(2,2,2\sqrt{3})$ (4) $(3,3,\sqrt{3})$

136. Using rotation of axes with appropriate scaling, the distance from the focus to the center of the conic section $x^2 + \sqrt{3}\,xy = \dfrac{3}{2}$ is:
(1) $\sqrt{3}$ (2) $\sqrt{3}$ (3) $2$ (4) $3$

145. If $n \in \mathbb{N}$ and $A_n = \{m \in \mathbb{Z} \mid m > -n,\ r^m \leq 2n\}$, then the set $A_1 \cup (A_8 - A_4)$ has how many elements?
(1) $5$ (2) $6$ (3) $7$ (4) $8$
%% Page 9 Mathematics 120-A Page 8

146- The relation $\{x - 2 \leq y \mid y \leq 2x\}$, $R = \{(x,y) \in \mathbb{Z}^2 \mid y \leq 2x,\ |y| \leq 2-x\}$, has how many ordered pairs?
(1) $8$ (2) $9$ (3) $15$ (4) $11$

149- In the graph of a regular 3-faced polyhedron, how many cycles of length 4 exist?
[Figure: regular polyhedron graph]
(1) $6$
(2) $7$
(3) $8$
(4) $9$

150- The degrees of non-1 vertices of a tree are $2,3,3,4,3,4,5$. How many vertices of degree 1 does this tree have?
(1) $7$ (2) $9$ (3) $11$ (4) $13$

151- If $(abc)_9 = (cb \circ a)_9$, then $a + b + c$ equals what?
(1) $9$ (2) $11$ (3) $12$ (4) undefined

152- For how many values of the natural number $P$, is $48P + 1$ a perfect square?
(1) $1$ (2) $2$ (3) $3$ (4) $4$