Physics section test (5)

MCAT Section Tests
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Physical Sciences
Test 3

Time: 38 Minutes
Number of Questions: 29


MCAT

PHYSICAL SCIENCES
DIRECTIONS: Most of the questions in the following
Physical Sciences test are organized into groups, with
a descriptive passage preceding each group of
questions. Study the passage, then select the single
best answer to each question in the group. Some of
the questions are not based on a descriptive passage;
you must also select the best answer to these
questions. If you are unsure of the best answer,
eliminate the choices that you know are incorrect,
then select an answer from the choices that remain.
Indicate your selection by blackening the
corresponding circle on your answer sheet. A periodic
table is provided below for your use with the
questions.
PERIODIC TABLE OF THE ELEMENTS
1
H
1.0

2

He
4.0

3
Li
6.9

4
Be
9.0

5
B
10.8

6
C
12.0

7
N
14.0

8
O
16.0

9
F
19.0

10
Ne
20.2

11
Na
23.0

12
Mg
24.3

13
Al
27.0

14
Si
28.1

15
P
31.0

16
S
32.1

17

Cl
35.5

18
Ar
39.9

19
K
39.1

20
Ca
40.1

21
Sc
45.0

22
Ti
47.9

23
V
50.9

24
Cr
52.0

25
Mn
54.9

26
Fe
55.8

27
Co
58.9

28
Ni
58.7

29
Cu
63.5

30
Zn
65.4

31
Ga
69.7

32

Ge
72.6

33
As
74.9

34
Se
79.0

35
Br
79.9

36
Kr
83.8

37
Rb
85.5

38
Sr
87.6

39
Y
88.9

40
Zr
91.2

41
Nb
92.9

42
Mo
95.9

43
Tc
(98)

44
Ru
101.1

45
Rh
102.9

46
Pd
106.4

47

Ag
107.9

48
Cd
112.4

49
In
114.8

50
Sn
118.7

51
Sb
121.8

52
Te
127.6

53
I
126.9

54
Xe
131.3

55
Cs
132.9

56
Ba
137.3

57
La *
138.9

72
Hf
178.5

73
Ta
180.9

74
W
183.9

75
Re
186.2

76

Os
190.2

77
Ir
192.2

78
Pt
195.1

79
Au
197.0

80
Hg
200.6

81
Tl
204.4

82
Pb
207.2

83
Bi
209.0

84
Po
(209)

85
At
(210)

86
Rn
(222)

87
Fr
(223)

88
Ra
226.0

89
Ac †
227.0

104
Rf
(261)

105

Ha
(262)

106
Unh
(263)

107
Uns
(262)

108
Uno
(265)

109
Une
(267)

*

58
Ce
140.1

59
Pr
140.9

60

Nd
144.2

61
Pm
(145)

62
Sm
150.4

63
Eu
152.0

64
Gd
157.3

65
Tb
158.9

66
Dy
162.5

67
Ho
164.9

68
Er
167.3

69
Tm
168.9

70
Yb
173.0

71
Lu
175.0

†

90
Th
232.0

91
Pa
(231)

92
U
238.0

93
Np
(237)

94
Pu
(244)

95
Am
(243)

96
Cm
(247)

97
Bk
(247)

98
Cf
(251)

99
Es
(252)

100

Fm
(257)

101
Md
(258)

102
No
(259)

103
Lr
(260)

GO ON TO THE NEXT PAGE.

2

as developed by


Physical Sciences 3
Passage I (Questions 1–5)

1.

The Kjeldahl method for determining the
percentage of nitrogen in a substance is an important
tool in industrial research. It is commonly used to

determine the protein content of meats, grains,
fertilizers, drugs, and other biological substances.
Because proteins from a particular source tend to
contain the same percent nitrogen, the percentage of
protein in the sample can be estimated quite accurately
by multiplying the percentage of nitrogen by a known
factor. This factor is 6.25 for meats, 6.38 for dairy
products, and 5.70 for cereals.
The sample to be analyzed is first decomposed in
hot, concentrated sulfuric acid (H2SO4), which
oxidizes carbon and hydrogen to CO2 and H2O
respectively. Amine and amide nitrogens are
quantitatively converted to ammonium ion (NH4+).
The hot sulfuric acid decomposition, or digestion,
proceeds slowly, especially with substances that are
resistant to H2SO4 (e.g., heterocyclic compounds like
pyridine). Digestion times for these compounds can
often be decreased by adding a neutral salt, such as
potassium sulfate (K2SO4), to the digestion mixture.
The digest is then cooled, and made basic with 50%
NaOH. This process liberates ammonia:

A technician is analyzing 0.1 g of beef using the
Kjeldahl procedure. The final titration of the
borate requires 5.5 mL of 0.01 M HCl. Which of
the following represents the percentage of protein
in the sample?

0.01× 0.0055× 14
× 100

0.1
0.01× 0.0055× 2 × 14
× 100
B.
0.1
0.01× 0.0055× 14
× 100× 6.25
C.
0.1
0. 01× 0.055× 14
× 100× 6.25
D.
0.1

A.

2.

According to the Brønsted-Lowry acid-base
theory, which of the following pairs shows the
conjugate acid of NaOH and the conjugate base
H3BO3, respectively?
A.
B.
C.
D.

NH4+ + OH– → NH3(g) + H2O
Reaction 1

H2O and NH3
NH3 and NH4+
H2SO4 and H2BO3–
H2O and H2BO3–

This gaseous ammonia is then distilled into a
flask containing an excess of boric acid, which
converts the ammonia back to the ion as follows:
H3BO3 + NH3 ? NH4+ H2BO3–
Reaction 2
Reaction 2 produces an acidic solution
containing the borate ion. The borate ion is then
titrated with standardized HCl to find the percent
nitrogen.

3.

Which of the following acid-base indicators
would be used to find the endpoint in the titration
of the H2BO3– produced in Reaction 2 with
standardized HCl?
A. Bromocresol green (pH of transition = 3.8 to
5.4)
B. Cresol purple (pH of transition = 7.6 to 9.2)
C. Phenolphthalein (pH of transition = 8.3 to
10.0)
D. Phenol red (pH of transition = 6.8 to 7.4)

GO ON TO THE NEXT PAGE.
KAPLAN

3


MCAT
4.

Which of the following compounds is least likely
to need K2SO4 added to its digestion mixture?
A.
B.
C.
D.

5.

A guanine base
A cyclic alkene
A furan compound
A pyrrole derivative

H3BO3 can be classified as:
A.
B.
C.
D.

a polyprotic acid
a polyprotic organic acid
the conjugate base of H2BO3–

a reducing agent

Passage II (Questions 6–10)
Food is digested by the body in a series of steps,
and the body uses the energy released at each step for
body functions. This is the process of metabolism.
The overall energy released by the metabolic process
equals the energy released in the equivalent
combustion process. Thus, by measuring the amount
of energy released during combustion, we can find the
energy that a particular food provides to the body.
A constant-volume calorimeter, shown in Figure
1, measures the energy content of a substance. The
bomb, which holds the sample to be measured, is a
container filled with oxygen gas at a given pressure.
The bomb itself resides in a thermally isolated
container, which holds 2000 g of water. The sample is
ignited electrically, and its combustion produces heat,
which the water and bomb absorb. The energy content
of the sample can be determined by measuring the
change in temperature of the water with a simple
thermometer.
However, before the heat or energy produced by
the reaction can be calculated, it is necessary to
calibrate the calorimeter: that is, the heat capacity of
the bomb must be determined. The heat capacity of the
bomb is the product of the specific heat and the mass
of the bomb. (Note: The specific heat of water is
4,190 J/kg • K.)

Figure 1

6.

4

A heater is placed in the calorimeter to calibrate
it. Which
of ON
the following
GO
TO THEphysical
NEXTquantities
PAGE.
need to be determined?

as developed by


Physical Sciences 3
A. The change in temperature only
B. The change in temperature and the power of
the heater
C. The power of the heater and the time the
heater operated
D. The change in temperature, the power of the
heater, and the total time it operated
7.

A.

B.
C.
D.

(1620 + 2) ∞ 2
(1620 + 2 ∞ 4190) ∞ 275
(1620 + 2 ∞ 4190) ∞ 2
It cannot be determined unless the mass of
the calorimeter is known.

Why must the container be thermally isolated ?
A. So all the heat released by the sample will be
absorbed by the water
B. So all the heat released by the sample will be
absorbed by the bomb and the water
C. So that the system will always be in thermal
equilibrium
D. So that the system will not conduct
electricity

8.

increases by 2°C when the sample is ignited, what
is the heat released in joules?

10. What happens to the entropy of the calorimeter
system after the combustion of a sample?
A.
B.
C.

D.

It increases.
It decreases.
It remains the same.
It increases and then decreases.

If the bomb is not sufficiently thermally isolated
and lets heat escape, how would it affect the
calculated energy content of the food being
measured?
A. The calculated value would be less than the
actual value because the enthalpy change of
combustion is maximized under adiabatic
conditions.
B. The calculated value would be less than the
actual value because the observed
temperature change of the water would be
lower.
C. The calculated value would be higher than
the actual value because the reaction would
release more heat to compensate for the heat
loss in accordance with le Châtelier’s
principle.
D. The calculated value would be higher than
the actual value because the heat capacity of
the calorimeter would decrease.

9.

A sample of 2-methyl-naphthalene is submerged
in a bomb with a heat capacity of 1,620 J/°C
which is submerged in a calorimeter containing 2
kg of water. If the temperature of the water

KAPLAN

Passage III (Questions 11–16)
Titration is a common procedure used in
quantitative analysis. Two reagents that are often used
for this purpose are potassium iodide and sodium
thiosulfate. Iodide is used to standardize, or establish

5


MCAT
the molarity of, a thiosulfate solution. First, an
aqueous solution of iodine is prepared by adding an
excess of potassium iodide to a known volume of an
acidic solution of potassium iodate.
IO3– + 5 I– + 6 H+ ? 3 I2 + 3 H2O
Reaction 1
The iodine combines with excess iodide to form
triiodide, by the following reaction:
I2 + I–

I3–

Reaction 2

Keq = 7.1 ∞ 102

calculation indicates
thiosulfate solution?

the

molarity

of

the

(0.01)(0.05)(3)
32. 60
(0.01)(0.05)(6)
B.
(214.0)(0.03260)
(0.01)(0.05)(6)
C.
(0.03260)
(2)(0.01)(0.05)(6)
D.
(166.0)(0.03260)

A.

Triiodide solutions are commonly referred to as
iodine solutions since this terminology adequately

explains the stoichiometry of this reagent (I2 + 2e– ?
2I–).
The iodine solution resulting from Reaction 1 is
titrated with the thiosulfate solution that is to be
standardized. The two half-reactions that occur are:
E°(V)
2 S2O3

? S4O6 + 2
Reaction 3

2–

2–

e–

–0.09

I2+ 2 e– ? 2 I–
Reaction 4

12. In the reaction between iodine and thiosulfate,
which species are reducing agents?
A.
B.
C.
D.

I2 and S4O62–

S4O62– and S2O32–
S2O32– and I2
S2O32– only

0.54

The endpoint of this titration is determined by
adding starch, a common iodine indicator, and
watching for disappearance of the deep blue
starch/iodine complex. The molarity of thiosulfate is
then determined from the amount of iodate consumed
in Reaction 1.
An application of this technique is the use of a
standardized thiosulfate solution, together with
potassium iodide, to determine the percentage of
copper in brass. A weighed sample of brass is
dissolved in nitric acid, and an excess of KI is added
to the acidified solution. This produces the following
reaction:

13. What is the standard potential for the redox
reaction between thiosulfate and molecular
iodine?
A. –0.63 V
B. –0.45 V
C. 0.45 V
D. 0.63 V

2 Cu 2+ + 4 I– ? 2 CuI(s) + I2
Reaction 5

The liberated iodine is then titrated with
thiosulfate to the endpoint.
11. 2 g of KI (MW 166.0) are added to 50 mL of a
0.010 M KIO3 solution. This solution is titrated
with 32.60 mL of an unstandardized sodium
thiosulfate solution (MW 158.10). Which

6

14. The reduction of copper (II) to copper (I) has a
standard half-cell potential of only 0.15 V.
Considering this fact, how is it possible for
copper to be reduced by iodide?

GO ON TO THE NEXT PAGE.
as developed by


Physical Sciences 3
I. The reaction is thermodynamically
favored, and therefore is spontaneous.
II. The reaction is forced to completion by
an excess of iodide and by the formation
of copper (I) iodide.
III. The oxidation of iodide is favored under
acidic conditions, as shown in Equation
1.
A.
B.
C.

D.

I only
II only
I and II only
II and III only

15. The titration described in the passage determined
that there were 0.01 moles of copper in 1.90 g of
brass. What is the percentage of copper in this
brass sample?
A. 1%
B. 3%
C. 33%
D. 66%

16. If sodium hydroxide were added to Reaction 1,
how would the equilibrium constant of Reaction
2 change?
A. It would increase because iodide would be
removed from the solution as NaI salt.
B. It would increase because the excess water
produced would lower the concentrations of
iodine and iodide.
C. It would remain the same because Reaction 1
and Reaction 2 are unrelated.
D. It would remain the same because the
equilibrium constant for a reaction is the
same for all concentrations of reactants and
products at the same temperate

Questions 17 through 21 are
NOT based on a descriptive
passage.
17. A thin converging lens of focal length 100 mm is
used as a magnifying glass. If the object viewed is
80 mm from the lens, how far from the lens will
the image be?

KAPLAN

A.
40 mm
B.
44 mm
C. 400 mm
D. At infinity
18. Which factors would you need to determine the
density of oxygen in a vessel containing a mixture
of gases, using the formula PV = nRT?
A. The partial pressure of oxygen and the
number of moles of oxygen in the container
B. The partial pressure of oxygen and the total
number of moles of gas in the container
C. The total pressure of gas in the container and
the number of moles of oxygen in the
container
D. The total pressure of gas in the container and
the total number of moles of gas in the
container

19. A train is moving at 30 m/s. The conductor
sounds the horn which has a frequency of 100
Hz. What is the frequency that a passenger on the
train hears?
A.
85 Hz
B. 100 Hz
C. 110 Hz
D. Cannot be determined
20. If 230 g of ethanol (C2H5OH) are added to 180 g
of water, by how much does the vapor pressure of
the water change?
A.
B.
C.
D.

It decreases by 33%.
It decreases by 50%.
It decreases by 56%.
It decreases by 67%.

21. The pressure in a non-compressible liquid:
A.
B.
C.
D.

increases with depth.
decreases with depth.

depends upon the shape of the container.
depends upon the total volume of the fluid.

Passage IV (Questions 22–29)
Circular particle accelerators, such as the
cyclotron, have been used for over 50 years to gain a
better understanding of the nature of elementary
particles. The cyclotron is depicted in a top view in
Figure 1 and in a side view in Figure 2. This
accelerator is composed of two hollow, metal, D-

7


MCAT
shaped containers, called dees. They are connected to
an alternating voltage supply. Above and below the
dees are electromagnets that create a uniform
magnetic field.
Initially, charged particles are at the center of the
cyclotron accelerator, which is point S in Figure 1.
Originally, one of the dees is at a positive potential,
and the other is at a negative potential. In the case of a
positively charged particle, the particle will be
accelerated towards the dee with a negative potential
and will enter it. Inside the dee, the electric field is
zero, due to the shielding of the dee. However, a
magnetic force is present, which causes the particle to
execute uniform circular motion. By the time the
particle comes to the edge of the dee, the alternating

voltage has changed so that the particle now faces the
negative dee, and is again accelerated by the potential
difference.
The frequency of the particle’s circular motion
can be related to the magnetic field by the equation:

Figure 2
22. Which of the following diagrams correctly
depicts the directions of the acceleration and
velocity vectors of a charged particle traveling in
a cyclotron dee?

qB = 2? mv
where q is the charge, B is the magnetic field strength,
m is the mass of the charge and v is the frequency of
the circular motion. Note that the frequency of the
particle does not depend on its speed; faster particles
will travel in larger circles. The frequency of the
voltage supply is therefore set equal to the frequency
of the particles, and both quantities remain constant.
A particular cyclotron is used to accelerate
protons. It has a radius of 0.5 m, an oscillator
frequency of 10 MHz and a maximum voltage of 100
kV. (Note: 1 eV = 1.6 ∞ 10–l9 J. Also, the
fundamental unit of charge, e, equals 1.6 ∞ 10–l9 C
and the mass of a proton is 1.6 ∞ 10–27 kg.)

Figure 1

8

GO ON TO THE NEXT PAGE.
as developed by


Physical Sciences 3
23. If a proton travels in a clockwise direction in the
cyclotron, as shown in Figure 1, what is the
direction of the magnetic field created by the
electromagnets?
A.
B.
C.
D.

Out of the page
Into the page
Towards the top of the page
Towards the bottom of the page

24. Which of the following correctly gives the value
of the energy of a proton inside the dee in terms
of the mass, m, the charge, q, the magnetic field
strength, B, and the radius of the dee, r?

qBr
m2
q2 B2 r 2
B.
2m

qBr
C.
2m
q2 B2 r 2
D.
m2
A.

27. What is the ratio of the period of a proton 0.5 m
from the source to one 0.25 m from the source?
A.
B.
C.
D.

1:1
1:2
2:1
4:1

28. A proton in a cyclotron moving with an energy of
10 MeV and speed of 4.4 ∞ 107 m/s strikes a
stationary hydrogen ion target. After the collision
the target moves with a speed of 3.5 ∞ 107 m/s
(6.4 MeV) and the proton moves with an energy
of 0.42 MeV. Which of the following statements
about this collision is true? (Assume that the
particles move along the same path after the
collision.)
A. The collision is completely inelastic.

B. The collision is completely elastic.
C. The final speed of the incident proton is 0.9
∞ 107 m/s.
D. Momentum is not conserved.

25. Which of the following adequately describes
when the particles are accelerating?
A. Only inside the dees because only there does
the particles’ speed changes
B. Only between the dees because only there
does the particles’ speed changes
C. Throughout the entire cyclotron because the
particles are changing speed between the dees
and changing direction within the dees
D. Throughout the entire cyclotron because the
particles are changing direction between the
dees and changing speed within the dees

26. Which of the following equations correctly
describes the voltage at a given time, t, for the
cyclotron? (Note: Use units of volts and
seconds.)
A.
B.
C.
D.

29. If the magnetic field in the accelerator increases,
what factor must be changed to keep the final
velocity of the protons constant?

A.
B.
C.
D.

The oscillator frequency must be decreased.
The radius of the dees must be decreased.
The voltage must be decreased.
The radius of the dees must be increased.

END OF TEST

(7 ∞ 104) sin ((2? ∞ 107)t)
(105) sin (10–7 t)
(105) sin (107 t)
(105) sin ((2? ∞ 107)t)

KAPLAN

9


MCAT

ANSWER KEY:
1. C
11.
2. D
12.
3. A

13.
4. B
14.
5. A
15.
6.
7.
8.
9.
10.

10

D
B
B
C
A

16.
17.
18.
19.
20.

C
D
C
B
C

21.
22.
23.
24.
25.

A
A
A
B
C

D
C
A
B
A

26.
27.
28.
29.

D
A
C
B