96. Which of the following is correct?
A: If the gas-phase concentration of DOH in the solution is $0.1$ molar and its degree of ionization at room temperature is 16, the molar concentration of hydroxide ion in this solution is $6.25 \times 10^{-3}$.
B: The more carbon atoms in the molecule of a non-soap detergent, the greater its solubility in water and its cleaning ability.
C: From dissolving equal moles of $\text{Li}_2\text{O(s)}$ and $\text{N}_2\text{O}_5\text{(g)}$ in $100$ mL of water, a solution with a neutral pH is formed.
D: By increasing the concentration of acidic solution HA at constant temperature, the pH of the solution decreases and the ionization constant of the acid increases.

1. ``B'' and ``D''
2. ``P'' and ``D''
3. ``A'' and ``B''
4. ``A'' and ``B''

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97. Solutions of two weak acids HA and HD are placed in two separate containers at an equilibrium concentration of $0.05$ molar. If the ionization constant of HD to the ionization constant of HA is approximately $10^{-3}$, the pH of solution HA ................... and the pH of solution HD ................... is.

• [(1)] $1/3$ - smaller (2) $3$ - smaller (3) $1/3$ - larger (4) $3$ - larger

98. Regarding the rusting process of iron, how many of the following statements are correct?

• $E^\circ$ of the overall reaction is positive.
• The only product of the half-reaction of oxidation is dissolved in water as an anion.
• The oxidizing and reducing species in the overall reaction are gas and solid, respectively.
• For every mole of iron converted to rust, three moles of electrons are exchanged.

(1) 1 (2) 2 (3) 3 (4) 4

99. At room temperature, 8 grams of weak acid HY is dissolved in 400 mL of distilled water. If $K_a = 10^{-5}$ and $\text{HY} = 50 \text{ g·mol}^{-1}$, (ignoring the effect of adding water on the volume of the acid solution,) which statement is correct?

1. [1)] By doubling the volume of the solution by adding distilled water, the degree of ionization of the acid approximately doubles.
2. [2)] By doubling the mass of the acid and halving the volume of the solution, the pH of the solution remains constant.
3. [3)] $[\text{OH}^-]$ in the solution is approximately $5 \times 10^{-13}$.
4. [4)] The pH of the solution is $3.7$.

100. Considering the following oxidation–reduction reaction, after balancing the equation, how many of the following statements are correct?
$$\text{AuI}_2^-(aq) + \text{Cu}(s) \longrightarrow \text{Au}(s) + \text{Cu}^{2+}(aq) + \text{I}^-(aq)$$
$$E^\circ(\text{AuI}_2^- / \text{Au} + \text{I}^-) = +0.56\,\text{V}, \quad E^\circ(\text{Cu}^{2+}/\text{Cu}) = +0.34\,\text{V}$$

• This reaction proceeds spontaneously.
• In this reaction, 6 moles of electrons are exchanged.
• One polyatomic ion plays the role of oxidizing agent in this reaction.
• The sum of stoichiometric coefficients of substances in this reaction is 18.

(4) 1 (3) 2 (2) 3 (1) 4
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101 - Considering the graph below, which compares the lattice enthalpy (Fajan's lattice enthalpy) of ionic compounds a to e formed from main group elements of period 4 of the periodic table, which statement is correct?
[Figure: Bar graph showing lattice enthalpy (kJ·mol$^{-1}$) on the y-axis with values around 1000 and 4000 marked, and ionic compounds a, b, c, d, e on the x-axis. Compound d has the tallest bar (near 4000), while a, b, c, e have shorter bars (near 1000).]

1. [(1)] If the cation of compound c has a charge of $+2$, the anion of compound a cannot be a halide ion.
2. [(2)] If a and b have similar cations, the elements forming their anions can be in the same period of the periodic table.
3. [(3)] If the ions of compound e have no noble gas electron configuration, then from the charges of the cation and anion in it, we can be certain that the charge of the cation and anion is greater than in the other compounds.
4. [(4)] If the ionic radius of the anion of compound b is smaller than the ionic radius of the anion of compound d, and their electrical charges are equal, then the ratio of the ionic radius of the cation in b to the ionic radius of the cation in d is greater than $\dfrac{b}{d}$.

102 - For the reaction at equilibrium: $2\mathrm{NO(g)} + \mathrm{Br_2(g)} \rightleftharpoons 2\mathrm{NOBr(g)}$, at a certain temperature, 66 g of $\mathrm{NOBr}$, 18 g of $\mathrm{NO}$, and 24 g of $\mathrm{Br_2}$ exist in a 3-liter container. The equilibrium constant at these conditions is fixed, and to reach this equilibrium, 60 percent of the initial amount of $\mathrm{Br_2}$ has been consumed. With how many moles of $\mathrm{Br_2}$ was the reaction started?
$$(\mathrm{N{=}14,\ O{=}16,\ Br{=}80\ :\ g{\cdot}mol^{-1}})$$
(1) $0/25\ ,\ 2\cdot0$ (2) $0/375\ ,\ 2\cdot0$ (3) $0/375\ ,\ 0/05$ (4) $0/25\ ,\ 0/05$
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103- Which case is incorrect?

104- For the reaction: $\text{CO(g)} + 2\text{H}_2\text{(g)} \rightleftharpoons \text{CH}_3\text{OH(g)}$, given that the number of moles of its components in the reaction vessel is at equilibrium, how many of the following changes will shift the reaction forward (increase the amount)?

• Increasing pressure $\bullet$ Removing 50\% of $\text{CH}_3\text{OH}$
• Decreasing temperature $\bullet$ Simultaneously removing 50\% of $\text{H}_2$ and $\text{CO}$
• Injecting CO into the reaction vessel

(1) 5 (2) 4 (3) 3 (4) 2

105- Which comparison of ionic radii given below is correct?
(1) $S^{2-} > Cl^- > K^+ > Ca^{2+}$ (2) $Br^- > Cl^- > Mg^{2+} > K^+$
(3) $Al^{3+} > Mg^{2+} > Cl^- > S^{2-}$ (4) $K^+ > Mg^{2+} > O^{2-} > F^-$

121-A Page 2
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1. If the terms of a geometric sequence with common ratio $r$ are halved, you will obtain an arithmetic sequence with common difference $d$. What is the value of $r + d$?
   (1) zero (2) $1$ (3) $\sqrt{2}$ (4) $\dfrac{1}{2}$
   
   
2. Points $A(3,y)$ and $B(-5,y)$ lie on a parabola whose vertex is at the origin and whose latus rectum equals 1. If this parabola cuts the $x$-axis with intercepts $\alpha$ and $\beta$, and $\alpha^2 + \beta^2 = 5$, at what $y$-intercept does this parabola cut the $y$-axis?
   (1) $-\dfrac{1}{3}$ (2) $-\dfrac{2}{3}$ (3) $\dfrac{1}{3}$ (4) $\dfrac{2}{3}$
   
   
3. For the sets $A = \{a-2, 6, 2b+1, c\}$ and $B = \{\sqrt{d}, 5, -1\}$, suppose $A \times B = B \times A$. In how many cases is $a + b + c = 9$?
   (1) $1$ (2) $2$ (3) $3$ (4) zero
   
   
4. According to the truth table below, which compound proposition can be a logical tautology for proposition $X$?
   

   $p$	$q$	$r$	$X$
   د	د	د	ن
   د	د	ن	د
   د	ن	د	د
   د	ن	ن	ن
   ن	د	د	ن
   ن	د	ن	د
   ن	ن	د	د
   ن	ن	ن	ن

   
   (1) $(q \Rightarrow (p \vee r)) \Rightarrow ((p \vee \sim p) \wedge (\sim q \wedge r))$
   (2) $(r \Rightarrow (p \vee q)) \Rightarrow ((p \vee \sim p) \wedge (q \wedge \sim r))$
   (3) $[p \Rightarrow ((q \vee r) \Rightarrow (q \wedge r))] \Rightarrow (\sim (p \vee r) \wedge q)$
   (4) $(r \Rightarrow (p \vee q)) \Rightarrow [((p \Rightarrow r) \Rightarrow (\sim p \wedge r)) \wedge q]$
   
   
5. If $\alpha$ and $\beta$ are the distinct roots of the equation $ax^2 - ax - b = 0$ and $40\beta^2 + 20\alpha^2 - 20\beta = 17$ and $40\beta^2 + 20\alpha^2 - 20\beta = 17$, what is the difference of the roots of this equation?
   (1) $\dfrac{1}{5}$ (2) $\dfrac{2}{5}$ (3) $\dfrac{1}{\sqrt{5}}$ (4) $\dfrac{2}{\sqrt{5}}$
   

Workspace
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122-A Page 2

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141.12 grams of chromium(III) sulfate, what percentage yield does this reaction produce?
($\text{N}{\blacksquare}14$, $\text{O}{\blacksquare}16$, $\text{Na}{\blacksquare}23$, $\text{S}{\blacksquare}32$, $\text{Cr}{\blacksquare}52$ : $\text{g.mol}^{-1}$)
$$\text{H}_2\text{SO}_4(aq) + \text{K}_2\text{CrO}_4(aq) + \text{NaNO}_2(aq) \longrightarrow \text{Cr}(\text{SO}_4)_2(aq) + \text{K}_2\text{SO}_4(aq) + \text{NaNO}_3(aq) + \text{H}_2\text{O}(l)$$
(1) $90, 21$ (2) $75, 21$ (3) $90, 19$ (4) $75, 19$

41-- If we bombard ${}^{176}_{71}\text{Lu}$ with negative beta rays (negatron), which nucleus is the daughter nucleus?
(1) ${}^{176}_{72}\text{Hf}$ (2) ${}^{175}_{72}\text{Hf}$ (3) ${}^{176}_{69}\text{Tm}$ (4) ${}^{177}_{69}\text{Tm}$

42-- In the ``multiplication stage,'' what are the states of the input and output valves, respectively?
(1) Both open (2) Both closed
(3) Input closed, output open (4) Input open, output closed

48. A body is suspended from a string and moves vertically with downward acceleration $0.8\,\text{g}$. The tension in the string is how many times the weight of the body?
$$\frac{9}{5} \quad (1) \qquad \frac{6}{5} \quad (2) \qquad \frac{4}{5} \quad (3) \qquad \frac{1}{5} \quad (4)$$

49. A horizontal disk rotates about its own vertical axis and two persons A and B sit on the disk respectively at distances of one meter and two meters from the center. Which person has greater centripetal acceleration, and if the speed of the disk gradually increases, which surface will slide sooner? (The surface material is the same.)

• [(1)] A and A
• [(2)] B and B
• [(3)] A and B
• [(4)] B and A

50. A stationary object of mass $10\,\text{kg}$ is placed on a horizontal surface. The coefficient of static friction and kinetic friction between the object and the surface are $0.5$ and $0.25$ respectively. If a horizontal force of $55\,\text{N}$ is applied to the object, the net force on the object is how many newtons?
$$15 \quad (1) \qquad 20 \quad (2) \qquad 30 \quad (3) \qquad 5 \quad (4)$$
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1. A driver traveling on a rainy day at a speed of $36\ \dfrac{\text{km}}{\text{h}}$ is in motion, sees a red light and after traveling a distance of 10 meters comes to a stop. If the mass of the car is $1600\ \text{kg}$, what is the friction force between the tires and the road surface?
   (1) $3200$ (2) $4000$ (3) $6400$ (4) $8000$
   
2. The position–time equation of a simple harmonic oscillator in SI is $x = A\cos\dfrac{16\pi}{3}t$. At $0.5$ seconds from the start of motion, the average speed of the oscillator equals how many times its maximum speed?
   (1) $\dfrac{11}{3}$ (2) $\dfrac{11}{6}$ (3) $\dfrac{22}{3}$ (4) $6$
   
3. A mass $m$ is attached to a spring and this system performs simple harmonic motion with amplitude $A$, and its mechanical energy is $8\ \text{J}$. If we attach a mass equal to $\dfrac{m}{2}$ to the same spring and let it oscillate with the same amplitude $A$, the mechanical energy of this system will be how many joules?
   (1) $4$ (2) $8$ (3) $2\sqrt{2}$ (4) $4\sqrt{2}$
   
4. A sound source in an open space emits sound waves and the sound intensity level at a distance of 50 meters from this source is 90 dB. In this location, the average rate of sound energy transfer per square centimeter of a surface perpendicular to the direction of sound propagation is how many microwatts? $\left(I_0 = 10^{-12}\ \dfrac{\text{W}}{\text{m}^2}\right)$
   (1) $10^{-1}$ (2) $10^{-2}$ (3) $10^{-3}$ (4) $10^{-4}$
   
5. A string of length $60\ \text{cm}$ and mass $6\ \text{g}$ is fixed between two points with a tension force of $324\ \text{N}$. What is the fourth harmonic frequency of the string in hertz?
   (1) $400$ (2) $800$ (3) $600$ (4) $1200$
   
6. In a stretched rope, one part is thin and the other part is thick. According to the figure, a pulse in the thin rope is moving toward the thick part. Which figure correctly shows the subsequent state of the rope?
   [Figure: A pulse moving to the right on a thin rope connected to a thick rope]
   (1) [Figure: transmitted pulse right, reflected pulse right on thin section] (2) [Figure: transmitted pulse right, reflected pulse left on thin section]
   (3) [Figure: transmitted pulse right, reflected inverted pulse left on thin section] (4) [Figure: transmitted pulse right, reflected inverted pulse left on thin section, arrows reversed]
   

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57-- In the atomic spectrum of hydrogen in the Paschen series ($n' = 3$), the wavelength of the first spectral line is how many times the wavelength of the second spectral line of this series?
\[ \text{(1)}\ \frac{25}{64} \qquad \text{(2)}\ \frac{64}{25} \qquad \text{(3)}\ \frac{175}{276} \qquad \text{(4)}\ \frac{256}{175} \]

58-- An electron in a hydrogen atom is at level $n = 4$. This electron goes directly to level $n' = 1$ and emits a photon that hits a cesium metal with work function $5.2\ \text{eV}$. What is the maximum kinetic energy of the photoelectrons emitted from the cesium metal? ($E_R = 13.6\ \text{eV}$)
\[ \text{(1)}\ 7.55 \qquad \text{(2)}\ 6.25 \qquad \text{(3)}\ 5 \qquad \text{(4)}\ 4 \]

59-- In the figure below, if the magnitude of the electric field at point A is $5\times10^5\ \dfrac{\text{N}}{\text{C}}$, then $|q_1|$ is how many microcoulombs? $\left(k = 9\times10^9\ \dfrac{\text{N.m}^2}{\text{C}^2}\right)$

• [(1)] 8
• [(2)] 12
• [(3)] 16
• [(4)] 20

[Figure: Charge $q_1$ is located on the vertical axis, $60\ \text{cm}$ above point A. On the horizontal axis, two charges $q_2 = -4\ \mu\text{C}$ and $q_3 = +4\ \mu\text{C}$ are placed at $30\ \text{cm}$ and $60\ \text{cm}$ from point A respectively.]

60-- In the figure below, two charged particles are fixed on the x-axis. At a point on the x-axis, the net electric field from the two charged particles is zero. The distance of that point from charge $q_2$ is how many times $d$?
[Figure: Two charges $q_1$ and $q_2 = -4q_1$ are placed on the x-axis, separated by distance $2d$.]

• [(1)] $d$
• [(2)] $2d$
• [(3)] $3d$
• [(4)] $4d$

61-- Three equal point charges are placed at the vertices of a square. $q_1$ and $q_2$ are at two ends of one side, and $q_2$ and $q_3$ are at two ends of a diagonal. The magnitude of the force that $q_1$ exerts on $q_2$ is how many times the force that $q_2$ exerts on $q_3$?
\[ \text{(1)}\ \sqrt{2} \qquad \text{(2)}\ 2 \qquad \text{(3)}\ \frac{1}{2} \qquad \text{(4)}\ \frac{\sqrt{2}}{2} \]
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62. In the circuit shown below, if we connect the switch, how does the output power of the battery change?
[Figure: Circuit with $r = 2\,\Omega$ internal resistance, $2\,\Omega$, $\Delta\Omega$ (5$\Omega$), $6\,\Omega$ resistors, and switch $k$]

• [(1)] 22\% increase
• [(2)] 22\% decrease
• [(3)] 28\% increase
• [(4)] 28\% decrease

63. Two electrical resistances A and B, when connected individually to a constant electrical potential difference, the consumed power of A is twice the consumed power of B. Now if we connect them in series and apply the same potential difference across both, the consumed power of A is how many times the consumed power of B?
$$ (1)\ \frac{1}{2} \qquad (2)\ \frac{1}{4} \qquad (3)\ 2 \qquad (4)\ 4 $$