CH
3
CH
2
COOH(
aq
) + H
2
O(l)
CH
3
CH
2
COO
(aq) + H
3
O
+
(aq)
Propa
noic acid, CH
3
CH
2
COOH, is a carboxylic acid that reacts with water according to the equation above.
At 25C the pH of a 50.0 mL sample of 0.20 M CH
3
CH
2
COOH is 2.79.
(a) Identify a Brønsted-Lowry conjugate acid-base pair in the reaction. Clearly label which is the acid and
which is the base.
CH
3
CH
2
C
O
OH and CH
3
CH
2
COO
acid base
OR
H
3
O
+
and
H
2
O
acid base
1 poi
n
t is earned for writing (or naming) either of the
Brønsted-Lowry conjugate acid-base pairs with a clear
indication of which is the acid and which is the base.
(
b)
Determine the value of K
a
for propanoic acid at 25C.
[H
3
O
+
] = 10
pH
= 10
2.79
= 1.6 10
3
M
[CH
3
CH
2
COO
] = [H
3
O
+
]
AND
[
C
H
3
CH
2
COOH] = 0.20 M [H
3
O
+
], OR [CH
3
CH
2
COOH] 0.20 M
(state or assume that [H
3
O
+
] << 0.20 M)
(
)
2
3
5
3 2 3
32
1.6 10
[CH CH COO ][H O ]
= = = 1.3 10
[CH CH COOH] 0.20
a
M
K
M
-
-+
-
´
´
1 poi
n
t is earned for correctly
solving for [H
3
O
+
].
1 point is earned for the
K
a
expression for
propanoic acid
OR
1 point is earned for
substituting values into the
K
a
expression.
1 point is earned for correctly
solving for the value of K
a
.
(c)
For each of the following statements, determine whether the statement is true or false. In each case,
explain the reasoning that supports your answer.
(i) The pH of a solution prepared by mixing the 50.0 mL sample of 0.20 M CH
3
CH
2
COOH with a
50.0 mL sample of 0.20 M NaOH is 7.00.
False
. The conjugate base of a weak acid undergoes
hydrolysis (see equation below) at equivalence to form a
solution with a
pH >
7.
(
)
3 2 2 3 2
CH CH COO H O CH CH COOH OH
-
+
-
+
1 poi
nt
is earned for noting that the
st
atement is false
AND pr
oviding
a
suppor
ting explanation.
(
ii) If the pH of a hydrochloric acid solution is the same as the pH of a propanoic acid solution, then the
molar concentration of the hydrochloric acid solution must be less than the molar concentration of
the propanoic acid solution.
T
rue. HCl is a strong acid that ionizes completely. Fewer
moles of
H
Cl are needed to produce the same [H
3
O
+
] as
the propanoic acid solution, which only partially ionizes.
1 poi
nt is earned for noting that the
statement is true and providing a
supporting explanation.
A
student is given the task of determining the concentration of a propanoic acid solution of unknown
conc
en
t
r
ation. A 0.173 M NaOH solution is available to use as the titrant. The student uses a 25.00 mL
volumetric pipet to deliver the propanoic acid solution to a clean, dry flask. After adding an appropriate
indicator to the flask, the student titrates the solution with the 0.173 M NaOH, reaching the end point after
20.52 mL of the base solution has been added.
(d) Calculate the molarity of the propanoic acid solution.
Let x = moles of propanoic acid
3
0.173 mol NaOH 1 mol acid
then = (0.02052 L NaOH)
1 L NaOH 1 mol NaOH
= 3.55 10 mol propanoic acid
x
-
´´
´
3
3.55 10 mol acid
= 0.142
0.02500 L acid
M
-
´
OR
Since
32
CH C
H COOH is monoprotic and, at the equivalence point,
moles H = moles OH
+
, then
=
A A
B B
M V M V
(0.173 NaOH)(20.52 mL NaOH)
= = = 0.142
25.00 mL acid
BB
A
A
MV
M
M
V
M
-
1 point is earned for correctly
calculating the number of
moles of acid that reacted at
the equivalence point.
1 point is earned for the
correct molarity of acid.
(e) The student is asked to redesign the experiment to determine the concentration of a butanoic acid
solution instead of a propanoic acid solution. For butanoic acid the value of pK
a
is 4.83. The student
claims that a different indicator will be required to determine the equivalence point of the titration
accurately. Based on your response to part (b), do you agree with the student's claim? Justify your answer.
D
isagree with the student’s claim
From
part (b) above,
p
K
a
for propanoic acid is
log(1.3 10
5
) = 4.89. Because 4.83 is so close to
4.89, the pH at the equivalence point in the titration
of butanoic acid should be close enough to the pH in
the titration of propanoic acid to make the original
indicator appropriate for the titration of butanoic acid.
1 poi
nt is earned for disagreeing with the
student’s claim and making a valid justification
using pK
a
, K
a
, or pH arguments.
1 point is earned for numerically comparing
either: the two pK
a
values, the two K
a
values,
or the two pH values at the equivalence point.
©2014 The College Board.
Visit the College Board on the Web: www.collegeboard.org.
©2014 The College Board.
Visit the College Board on the Web: www.collegeboard.org.
©2014 The College Board.
Visit the College Board on the Web: www.collegeboard.org.
©2014 The College Board.
Visit the College Board on the Web: www.collegeboard.org.
©2014 The College Board.
Visit the College Board on the Web: www.collegeboard.org.
©2014 The College Board.
Visit the College Board on the Web: www.collegeboard.org.
©2014 The College Board.
Visit the College Board on the Web: www.collegeboard.org.
AP
®
CHEMISTRY
2014 SCORING COMMENTARY
Question 2
Overview
This question was designed to assess students’ conceptual and analytical understanding of acid-base
chem
istry. Part (a) asked students to identify a Bronsted-Lowry conjugate acid-base pair from an equation
provided. Part (b) asked students to calculate the K
a
for propanoic acid given a pH and concentration. In part
(c) students were provided with two statements and asked to identify each as true or false and support their
answers with reasoning. In part (c)(i) the question assessed conceptual understanding of pH when equal
volumes of equimolar strong base and weak acid solutions were mixed. In part (c)(ii) the question assessed
conceptual understanding between concentration and pH of strong acid and weak acid solutions. Part (d)
required students to calculate the molar concentration of propanoic acid given titration data. Part (e)
assessed analytical and conceptual understanding of pK
a
values and indicators.
Sample: 2
A
Score: 10
This response earned all 10 possible points: 1 point in part (a), 3 points in part (b), 1 point in part (c)(i),
1 po
int in part (c)(ii), 2 points in part (d), and 2 points in part (e).
Sample: 2
B
Score: 8
This response earned all the points except for the two points in
part (d).
Sample: 2
C
Score: 6
This r
esponse did not earn credit in either part (c)(i) or part (c)(ii) for incorrect conclusions and reasoning.
In part (e) the response did not earn either of the two points. The student correctly calculates the value of
K
a
in part (b) but in part (e) the student incorrectly agrees with the statement that a new indicator is
needed.
© 2014 The College Board.
Visit the College Board on the Web: www.collegeboard.org.
