EXPERIMENT 1
Calibration of Volumetric Glassware
Introduction
Table 1.1 shows some of the tolerance values established for volumetric glassware
by the National Bureau of Standards. It may be noted that glassware meeting these
specifications is adequate for all but the most exacting work of the analytical laboratory.
Such glassware, stated by the manufacturer to conform to NBS standards, may be
purchased. For an extra fee, it is also possible to obtain glassware that has actually been
tested by the NBS. Because of the expense, however, the beginning analytical laboratory
will rarely be equipped with glassware guaranteed to meet NBS tolerance specifications.
Less expensive glassware stated by the manufacturer to meet tolerances about double
those of the NBS is available, but even this glassware may not be furnished the student.
For this reason, and also because the history of a particular item involving possible
damage may be obscure, it is often advisable for students to calibrate their volumetric
glassware. Of course, the individual instructor will make the decision in any case.
Since most analytical work involves dilute, aqueous solutions, water is generally
used as the reference material in the calibration of volumetric glassware.
The general principle in calibration is to determine the weight of water contained in
or delivered by a particular piece of glassware. Then, with the density of water known, the
correct volume is found.
The units of volume commonly employed in analytical chemistry are the liter and
the milliliter. The liter was formerly defined as the volume occupied by 1 kg of water at
the temperature of its maximum density (about 4℃) under a pressure of 1 atm. In 1964 the
Twelfth General Conference on Weights and Measurements, meeting in Paris, France,
abolished this definition and instead made the liter a special name for the cubic decimeter.
This new definition eliminates the previous discrepancy of 28 parts per million between
the milliliter and cubic centimeter (1 mL was 1.000028 cc), and these two units are now
equivalent.
1
TABLE 1.1
TOLERANCES FOR VOLUMETRIC GLASSWARE (mL)
Capacity, Less Than
and Including:
Volumetric
Flasks
Transfer
Pipets
Burets
2
0.006
5
0.01
0.01
10
0.02
0.02
25
0.03
0.03
0.03
50
0.05
0.05
0.05
100
0.08
0.08
0.10
200
0.10
0.10
500
0.15
1000
0.30
The National Bureau of Standards has specified 20℃ as the temperature at which
glassware is calibrated. Since the laboratory temperature will usually not be exactly 20℃,
glassware must, strictly speaking, be corrected when used at other temperatures because of
errors due to expansion (or contraction) of both the glass vessel itself and the solution
contained therein. The coefficient of expansion of glass is sufficiently small that the
correction required for this factor is negligible for most work (it amounts to the order of 1
part per 10,000 for a change of 5℃). The change in the volume of the solution itself, on
the other hand, is more important, but it can still be ignored in many cases if the working
temperature is not far removed from 20℃ (the volume change is of the order of 1 part per
thousand over a 5℃ range).
As noted above, calibration data are secured by converting weight of water into
volume via the density. Tables showing the density of water at various temperatures are
available in handbooks. However, the data in such tables are usually given on the bassis of
weights in vacuum, while the actual weighings are made in air. Since the water being
weighed generally displaces more air than do the weights, it is necessary to correct the
weighings for the buoyancy effect of the air if such handbook tables are to be used. On the
other hand, we may change in vacuum densities into densities that would be obtained in
air with steel weights, and use these directly with our weighings obtained in air. The
values in Table 1.2, which are the reciprocals of such adjusted densities, may be used
directly by the student without taking the buoyancy effect into consideration.
Methods of Calibration Commonly Employed
There are three general approaches to the calibration of volumetric glassware that
2
are in wide use and with which the student should be familiar.
Table1.2 VOLUME OF 1G OF WATER WEIGHED IN AIR WITH STEEL WEIGHTS
AT VARIOUS TEMPERATURES
℃
ml
℃
ml
10
11
12
13
14
1.0013
1.0014
1.0015
1.0016
1.0018
21
22
23
24
25
1.0030
1.0033
1.0035
1.0037
1.0040
15
16
17
1.0019
1.0021
1.0022
26
27
28
1.0043
1.0045
1.0048
18
19
20
1.0024
1.0026
1.0028
29
30
1.0051
1.0054
1. The first method, which we may designate as a direct, absolute calibration, is
based on the principles outlined above. The volume of water delivered by a buret or pipet,
or contained in a volumetric flask, is obtained directly from the weight of the water and its
density. Directions are given below for the calibration of a buret, a pipet, and a volumetric
flask using this method.
2. Volumetric glassware is sometimes calibrated by comparison with another
vessel previously calibrated directly. We may refer to this as an indirect, absolute
calibration, or calibration by comparison. This method is especially convenient if many
pieces of glassware are to be calibrated, and it is sufficiently accurate for all ordinary
usages provided that the reference vessel itself has been accurately calibrated. Calibrating
bulbs are not available in many student laboratories, and specific directions for their use
are not included in this chapter. They are not difficult to use if proper care is taken.
Students may obtain directions from their instructors if they are to use such equipment.
3. Sometimes it is necessary to know only the relationship between two items of
glassware without knowing the absolute volume of either one. This situation arises, for
example, in taking an aliquot portion of a solution. Suppose that is desired to titrate
one-fifth of an unknown sample. The unknown might be dissolved, appropriately treated
preparatory to the titration, and diluted to volume in a 250-mL volumetrc flask. A 50-mL
pipet would then be used to withdraw an aliquot for titration. For the calculations in this
analysis, it would not be necessary to know the exact volume of the flask or the pipet, but
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it would be required that the pipet hold exactly one-fifth as much solution as the flask. The
method used for a relative calibration of this sort simply involves discharging the pipet
five times into the flask and marking the level of the meniscus on the flask.
Calibration of Buret
The buret should be thoroughly cleaned so that it drains well, and the stopcock
should be properly lubricated. Fill the buret with water and test for leakage, making a
reading to the nearest 0.01 mL and repeating the reading after waiting at least 5 min. No
noticeable change should have occurred. During the waiting period, weigh a stoppered
125-mL Erlenmeyer flask (or other suitable container) to the nearest milligram. Record
this weight.
Fill the buret with distilled water that is at the temperature of the laboratory. This
temperature must be measured and recored. Then sweep any air bubbles from the tip of the
buret by opening the stopcock to permit rapid outflow. Now withdraw water more slowly
until the meniscus is at, or slightly below, the zero mark on the buret. After drainage is
complete (at least 30 s), read the buret to the nearest 0.01 mL. Record this "initial" reading.
Remove any hanging drop of water from the tip of the buret by touching it lightly to the
side of a vessel such as a beaker. Now run about 10 mL of water from the buret into the
weighed flask. The tip of the buret should extend somewhat into the mouth of the flask,
and care should be taken against spattering. The neck of the flask where contact with the
stopper is made should not be wet. Quickly stopper the flask. Read the buret after allowing
time for drainage and record this "final" reading. Then weigh the stoppered flask to the
nearest milligram. Record this weight. Tabulation of the data as suggested in Table 1.3 is
convenient.
Now refill the buret and obtain another "initial" reading. Run about 20 mL of water
into the flask, obtain the "final" buret reading, and reweigh the flask. Note that we are
calibrating the buret in 10-mL intervals, but starting each time from an initial reading near
zero since in titrations we generally start near this point.
This process is repeated for the 30-, 40-, and 50-mL volumes. The flask, of course,
should never be allowed to exceed the capacity of the balance. It should first be emptied,
the neck dried with a clean towel, and reweighed.
For each calibration interval, multiply the weight of water by the appropriate value
from Table 1.2 to obtain the actual volume of the water.
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TABLE 1.3 SAMPLE DATA FOR CALIBRATION OF BURET
Initial buret reading
Final buret reading
Apparent volume. ml
Initial weight of flask
Final weight of flask
Weight of water, g
Temperature, ℃
Actual volume, ml
Correction, ml
0.38
10.16
9.78
62.576
72.311
9.735
24
9.77
-0.01
0.49
20.16
19.67
72.311
91.832
19.521
24
19.59
-0.08
The difference between this actual volume and the apparent volume (from the buret
readings) is, of course, the correction. If the actual volume is larger than the apparent
volume, the correction obtained by subtracting in this way will be positive, which means
that it is to be added to the buret reading in future work with the buret.
The calibration should be repeated as a check on the work. Duplicate results should
agree within 0.04 mL. With the weighings carried out to the nearest milligram, as directed
above, errors in weighing should not affect the results because the weight is actually
needed only to the nearest 0.01 g. Hence failure of duplicate results to agree is generally
due to (1) leakage around the buret stopcock, (2) failure to wait for drainage before
reading the buret, or (3) careless technique in collecting or handing the container and
stopper.
Since our calibration is performed over 10-mL intervals, students often ask about
the correction to be applied to a buret reading of an intermediate value such as 46ml.
Ordinarily, applying the correction of the nearest interval, in this case 50mL, will be
sufficient. It is perhaps somewhat better to interpolate between the known corrections.
This is done most conveniently by a graphical method. The student may plot corrections
against intervals 10, 20 mL,..., connecting the points with straight lines so as to obtain
linear interpolations by simple inspection of the graph. Such an interpolation obviously is
not likely to reflect the true situation within the buret, but it will usually be more than
sufficiently accurate for the need at hand. The student must use good judgment in
consideration of the precision desired in the buret reading. For example, an error of 0.04
mL in a 40-mL buret reading represents only 1 ppt.
Calibration of Pipet
The method is essentially the same as that described above for a buret. The pipet
should naturally be carefully cleaned and rinsed before calibration. Weigh to the neareat
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milligram a clean, stoppered Erlenmeyer flask of adequate capacity. Now fill the pipet to a
level above the etched line, using a beaker of distilled water that is at the temperature of
the laboratory. This temperature must be measured, of course. Dry the outside of the pipet
with a clean towel, and then release the finger pressure to allow the liquid level to fall to
the etched line. The pipet should be held in a vertical position with the etched line at
eye-level for this operation. Hold the liquid level so that the bottom of the meniscus
coincides with the etched line, and touch the tip of the pipet to the side of the beaker to
remove any hanging drop. Then discharge the contents of the pipet into the weighed
container. It is best to insert the tip of the pipet well into the container and to keep the tip
touching the inner wall of the container during the delivery. With the tip still touching the
container, allow the pipet to drain for 20 to 30 s after the flow ceases. Do not disturb the
last portion of water remaining in the tip. Then stopper the container and reweigh it.
Calculate the volume of water delivered by the pipet from the weight and the appropriate
value taken from Table 1.2. The calibration should be repeated, and the duplicate results
should not differ by more than 1 ppt. Common errors are (1) warming the contents of the
pipet by holding the enlarged portion in the palm of the hand, (2) failure to allow sufficient
drainage time, (3) disturbing the residue of water that should remain in the tip of the pipet,
and (4) general carelessness in handling the weighed container and stopper.
6
實
驗
一
容器體積的校正
一、目的
1. 學習電子天平的正確操作及秤重方法。
2. 了解玻璃器皿容積的校正方法與操作技巧。
3. 學習數據處理及分析技巧
二、原理
實驗室中常使用之器皿多為玻璃材質，由於玻璃材質稍高溫加熱易軟化變
形，使玻璃器皿上的刻度改變，故有精確刻度之玻璃器皿不可放入烘箱加熱乾燥，
如玻璃器材之吸量管、滴定管、定量瓶及量筒等。在大部分的分析實驗中，常選擇
水作為溶劑，由於水的密度隨溫度而異（如Table 1-2所示），以及玻璃本身熱脹冷縮
等因素而導致玻璃器皿視容積發生偏差。故為了得到準確的體積測量，玻璃器皿在
使用前須先校正。
校正過程包括用體積容器來測定已知密度液體的重量，其中體積受溫度影響
最大，其影響可分為兩方面：第一，液體的體積隨溫度改變而有所不同。第二，玻
璃器皿的體積會隨溫度而改變。玻璃的溫度係數很小，故校正體積時，除非須做更
精密之量測，否則可將玻璃器皿的體積變化因素忽略。
三、實驗器材與藥品
器材：50mL 三角錐形瓶 13 個、溫度計、50mL 滴定管、25mL 吸量管、天平
藥品：R.O 水
四、實驗步驟
A. 滴定管的校正（了解滴定管的正確使用方式）
(每組領取十三個50 mL三角錐形瓶)
1. 徹底清洗滴定管，並使活塞可順暢轉動。
取約 500mL 水，靜置到室溫，並測量溫度。
將滴定管裝滿水，打開活栓讓水快速流出以除去尖端的氣泡。
將液面(新月型凹處)流至刻度 0.00mL 處，並去除滴定管尖端的水滴。
（了解微量天平的正確使用方式）秤重一 50mL三角錐形瓶讀取至 0.1mg。
從滴定管中取 10mL 水，盡量精確取10.00mL，待水完全沉靜下來後(至少30
秒)再精確讀值到0.01ml。
7. 稱量三角錐形瓶加水的重量 (使用同一天平)。
8. 計算水的重量。
2.
3.
4.
5.
6.
7
9. 將水的重量依表（1-2）轉換成體積（ W * Factor ＝ mL）。
10. 重覆 3-7 步驟，兩次誤差應在 0.1mL 之內。
11. 求取平均值。
12. 重覆 3-9步驟，除步驟四改取 20mL 水。
13. 重覆 3-9步驟，除步驟四改取 30mL 水。
14. 重覆 3-9步驟，除步驟四改取 40mL 水。
15. 重覆 3-9步驟，除步驟四改取 50mL 水。
16. 以修正值對刻度值作圖，畫出修正曲線（修正值＝實驗值－刻度讀值）。
B. 吸量管的校正（了解吸量管及吸球正確使用方式）
1. 稱重一 50mL三角錐形瓶(至 0.1mg)。
2. 從 25mL 吸量管中取 25mL 水到三角錐形瓶中。
3. 稱量三角錐形瓶加水的重量 (使用同一天平)。
4. 計算水的重量。
5. 將水的重量依表（1-2）轉換成體積。
6. 重覆 1-5 步驟二次 (共三次)，兩次誤差應在 0.06mL 之內。
7. 求取平均值。
8. 求出標準差，平均偏差及相對平均偏差。
(將三角錐形瓶交回放在指定的位置。)
參考公式：
i n
標準偏差 : s 
| x
i 1
 x |2
n 1
i n
平均偏差 : d 
i
| x
i 1
i

x
 ( xi ) 2 / n
n 1
x|
n
i n
d
相對平均偏差 :  100% 
x
ppt 
相對誤差 : % 
2
i
| x
i 1
i
 x| /n
 100%
x
d
 1000
x
xi  x t
 100%
xt
;
ppt 
xi：每次的測量值
x ：平均值
xt：真實值在此定為 xturevalue  x
8
xi  xt
 1000
xt
五、實驗數據與結果
A：滴定管的校正
溫度:
測量體積
次數
10 ml
1
20 ml
2
1
30 ml
2
1
40 ml
2
初刻度 (Vi)
末刻度 (Vf)
刻度體積,ml
(Va = Vf-Vi)
刻度體積平均,ml
Va= (Va1+Va2)/2
空瓶重 (W0)
瓶加水重 (W1)
水重，g
(ΔW = W1-W0)
實際體積,ml
(Vb =ΔW × F)
實際體積誤差,ml
(Vb1-Vb2)
實際體積平均
Vb=(Vb1+Vb2)/2
修正值,ml
(C = Vb-Va)
修正曲線：請用電腦作圖(XY 散佈圖中的有點折線圖)
9
1
50 ml
2
1
2
B：吸量管的校正
空瓶重(g)
空瓶加水重
(g)
水重(g)
水的
平均偏差
體積(ml)
平均值
1
25 mL
2
3
標準偏差：
平均偏差：
相對平均偏差：
六、問題與討論
問題：
一、 實驗室中，準確的體積測量常使用那些工具，應用範圍為何？
二、 測量體積之容器為何常需要校正？
三、 在 buret 的校正實驗時：兩次重覆實驗如有較大的誤差(大於 0.1mL)，可能是何
原因造成？
討論：請針對本次實驗的結果與收穫加以探討
10