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♥ It is a general term for a method in quantitative chemical
analysis in which the amount of a substance is
determined by the measurement of the volume that the
♥ It is commonly used to determine the unknown
concentration of a known reactant.
♥Volumetric analysis is often referred to as titration, a
laboratory technique in which one substance of known
concentration and volume is used to react with another
substance of unknown concentration.
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Involves the preparations, storage, and measurement of
volume of chemicals for analysis
Quantitative chemical analysis which determines
volume of a solution of accurately known concentration
required to react quantitatively with the analyte (whose
concentration to be determined).
The volume of titrant required to just completely react
with the analyte is theTITRE.
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A process in which a standard reagent is added to a
solution of analyte until the reaction between the two is
A reagent solution of accurately known concentration is
called a standard solution.
A process to determine the concentration of a solution
of known concentration by titrating with a primary
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The point at which the reaction is observed to be
completed is the end point
The end point in volumetric method of analysis is the
signal that tells the analyst to stop adding reagent and
make the final reading on the burette.
Endpoint is observed with the help of indicator
The point at which an equivalent or stoichiometric
amount of titrant is added to the analyte based on the
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Volumetric analysis involves a few
pieces of equipment:
Pipette – for measuring accurate and precise volumes of
Burette – for pouring measured volumes of solutions
Conical flask – for mixing two solutions
Wash bottles – these contain distilled water for cleaning
Funnel – for transfer of liquids without spilling
Volumetric flasks – a flask used to make up accurate
volumes for solutions of known concentration
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Reaction must be stoichiometric, well defined reaction
between titrant and analyte.
Reaction should be rapid.
Reaction should have no side reaction, no interference
from other foreign substances.
Must have some indication of end of reaction, such as color
change, sudden increase in pH, zero conductivity, etc.
Known relationship between endpoint and equivalence
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Concentration: is a general term expressing the
amount of solute contained in a given material.
Expressed by different ways
Molarity(M):The number of moles of solute
divided by the number of liters of solution
containing the solute. (is gram molecular weight
dissolved in one liter of solution)
Molarity = moles of solute / volume in liters
Milli moles of solute / volume in milliliters.
Moles = weight (gms) / MW or
Millimoles = weight(mg) / MW
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Defined as no of equivalents of solute divided
by the number of liters of solution containing
the solute. ( gm equivalent weight dissolved
in one liter of solution)
Normality = equivalents of solute / volume in
Milli eq. of solute / volume in milliliters.
Equivalents = weight (gms) / EW or
Milliequivalent = weight(mg) / EW
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Molarity = weight / MW xVolume
MW =Weight / Molarity x volume similarly
Normality = weight / EW xVolume
EW =Weight / normality x volume
EW = MW / h
Where h reacting unit.
For acid H+ is reacting unit and for base OH-
For Oxdn redn e- is reacting unit
For Ionic species valences
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Is defined as part by wt of substance which is
chemically equivalent to one part by wt of
hydrogen or 8 part by wt of oxygen or 35.5
part by wt of chlorine.
Thus in finding out equlent. wt we find out
how many grams of that sub are directly or
indirectly eq to one gm of hydrogen
It depends on reaction in which it takes place
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Weight percent (w/w) = weight of analyte x 100
weight of sample
Volume percent (v/v) = volume of analyte x 100
volume of sample
Weight percent (w/v) = weight of analyte x 100
volume of sample
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Ppm = weight analyte x 10 6
weight of sample
Or ie 1 gm / 10 liters
Or 1mg / Liter
Or microgram / ml
Molal Solution: Gram molecular wt dissolved
in 1000gm of solution
Formal solution: gram formula wt dissolved in
1000ml of solution.
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Commercial acid and basis are available in %
by wt, and by further dilutions solution are
Density = wt / unit volume at sp temp (20OC)
unit gm / ml or gram / cm3
Sp. Gravity = mass / mass of eq volume of
water at 20OC or
At 4OC density of water is 1.00000gm/ml
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The branch of chemistry which deals with
weight relation between reactant and
product is called stoichiometry.
HCl react with NaOH according to eq
HCl + NaOH H2O + NaCl
36.5 40 18 58.5 gm
Ie 36.5 gm of HCl = 1000ml of 1M NaOH
0.0365 gm of HCl = 1 ml of 1M NaOH and
0.00365 gm of HCl = 1 ml of 0.1 M NaOH
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A solution whose con is accurately known
Prepared by dissolving an accurately wt
quantity of highly pure material called
primary std. and diluted to an accurately
volume in volumetric flask.
Otherwise a solution of approximately
desired con is titrated against the primary
standard solution and concentration is
determine, this is called standardization
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Measurements are made with reference to standards
The accuracy of a result is only as good as the quality and accuracy
of the standards used
A standard is a reference material whose purity and composition are
well known and well defined
Primary Standards – Used as titrants or used to standardize titrants
Eg. Acid base titration Na2CO3, KHP, Succinic acid, Benzoic acid,
Eg for redox titration: K2Cr2O7, Potassium bromate, KIO3,
Sodium Oxilate, arsionus trioxide
Eg for PPT titrations: NaCl, KCl, KBr, Silver nitrate
Eg for Complometric titration: Pure matels like Zn,Mg, Mn and its
salts9/9/2018 17Deokate UA
It should be 100% pure or with known purity
Should be stable to drying temp.
Usually solid to make it easier to weigh
Easy to obtain, purify and store, and easy to dry
Inert in the atmosphere
High formula weight so that it can be weighed with high
It should not absorb moisture, or should not react with oxygen
Reaction with analyte should be single, rapid complete and
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True or correct or actual value are known only when
the count object or when a quantity is assigned a
particular value such as atomic weight. Otherwise the
true value of a quantity is never known.
Standard value is observed value given by the expert
using a suitable method and good quality apparatus
Observed value is the result obtained
Error:The difference between true value or standard
value is called error
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The Accuracy of an analytical procedure expresses
the closeness of agreement between the value, which
is accepted either as a conventional true value or an
accepted reference value and the value observed
(individual observation or mean of measurements).
The Precision (VARIABILITY) of an analytical
procedure is nearness between several
measurements of the same quantity usually
expressed as the standard deviation (S), variance (S2),
or coefficient of variation (= relative standard
deviation, R.S.D.) of a series of measurements
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imprecise Accurate and precisePrecise Accurate
Inaccurate and imprecise
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Two analysis (I & II) of substance whose true value is 100% is given below;
100.00, 99.60, 99.70,
Average value is 99.60%
Error is (100.00-99.60) =
The precision is poor but
accuracy is good
98.80, 98.82, 98.84,
Average value is 98.82%
Error is (100.00-98.82) =
The accuracy is poor but
precision is better
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Since analytical chemistry is the science of
making quantitative measurements, it is
important that raw data is manipulated and
reported correctly to give a realistic estimate of
the uncertainty in a result.
Simple data manipulations may only require
keeping track of significant figures. More
complicated calculations require propagation-
The uncertainity in a result can be categorized
into random error and systematic error.
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The term error is used to show the difference
between measured and true value.
Since the true value are never known one has
to make use standard value.
The standard value can be obtained by
Absolute Method: sample is synthesized using
know quantities to obtain a primary standard.
Comparative method: standard data is obtained.
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DETERMINATE OR SYSTEATIC ERRORS
Instrumental or reagent error
INDTERMINATE OR RANDOM ERRORS
The cause of a random error may not be known
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Propositional error: the magnitude of error
depends upon sample size
Additive error:The value of error is constant
is independent of amount of sample taken for
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Proper calibration of apparatus
Running a blank determination
Carrying out a control determination (use of
standard and reference)
Use of independent method. (results of two
different methods are compared)
Reparative determination and statistical
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Average is measure of central tendency
It is the arithmetic mean of different values
obtained by measuring the same quantity
Arithmetic mean = sum of different value
Number of times determination is made
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Deviation (d): difference between the measured value
and average value d =(x1-x-)
Average or mean deviation (d-) is arithmetic mean of
different deviation observed
d- = d1+d2+dn
Relative Mean deviation is =
Mean deviation x 100
The positve or negative sing of individual deviation is
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The standard deviation is square root of the
sum of the squared individual deviation
divided by (n-1)
s = √ d1
2 + d2
2 + d3
2 + dn
The square of standard deviation is called
Variance and coefficient of variation (C.V)
(also known as relative Std dev.) is defined as
C.V. = s x 100
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The number of significant figures in a result is
simply the number of figures that are known
with some degree of reliability.The number
13.2 is said to have 3 significant figures.The
number 13.20 is said to have 4 significant
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All measurements are approximations--no
measuring device can give perfect measurements
without experimental uncertainty. By convention, a
mass measured to 13.2 g is said to have an absolute
uncertainty of 0.1 g and is said to have been
measured to the nearest 0.1 g.
In other words, we are somewhat uncertain about
that last digit —it could be a "2"; then again, it could
be a "1" or a "3". A mass of 13.20 g indicates an
absolute uncertainty of 0.01 g
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1. All nonzero digits are significant:
1.234 g has 4 significant figures,
1.2 g has 2 significant figures.
2. Zeroes between nonzero digits are significant:
1002 kg has 4 significant figures,
3.07 mL has 3 significant figures.
3. Leading zeros to the left of the first nonzero digits are
not significant; such zeroes merely indicate the position
of the decimal point:
0.001 oC has only 1 significant figure,
0.012 g has 2 significant figures.
4. Trailing zeroes that are also to the right of a decimal
point in a number are significant:
0.0230 mL has 3 significant figures,
0.20 g has 2 significant figures.9/9/2018 33Deokate UA
5. When a number ends in zeroes that are not to the right of a
decimal point, the zeroes are not necessarily significant:
190 miles may be 2 or 3 significant figures,
50,600 calories may be 3, 4, or 5 significant figures.
The potential ambiguity in the last rule can be avoided by the
use of standard exponential, or "scientific," notation. For
example, depending on whether the number of significant
figures is 3, 4, or 5, we would write 50,600 calories as:
5.06 × 104 calories (3 significant figures)
5.060 × 104 calories (4 significant figures), or
5.0600 × 104 calories (5 significant figures).
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In carrying out calculations, the general rule is that the accuracy of a calculated
result is limited by the least accurate measurement involved in the
1. In addition and subtraction, the result is rounded off to the last common
digit occurring furthest to the right in all components. Another way to state
this rules, it that, in addition and subtraction, the result is rounded off so
that it has the same number of decimal places as the measurement having
the fewest decimal places.
For example, 100 (assume 3 significant figures) + 23.643 (5 significant
figures) = 123.643, which should be rounded to 124 (3 significant figures).
2. In multiplication and division, the result should be rounded off so as to have
the same number of significant figures as in the component with the least
number of significant figures. For example,
3.0 (2 significant figures ) × 12.60 (4 significant figures) = 37.8000 which
should be rounded off to 38 (2 significant figures)
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1. If the digit to be dropped is greater than 5, the last retained digit is
increased by one. For example,
12.6 is rounded to 13.
2. If the digit to be dropped is less than 5, the last remaining digit is left as it
is. For example,
12.4 is rounded to 12.
3. If the digit to be dropped is 5, and if any digit following it is not zero, the
last remaining digit is increased by one. For example,
12.51 is rounded to 13.
4. If the digit to be dropped is 5 and is followed only by zeroes, the last
remaining digit is increased by one if it is odd, but left as it is if even. For
11.5 is rounded to 12,
12.5 is rounded to 12.
This rule means that if the digit to be dropped is 5 followed only by zeroes,
result is always rounded to the even digit.The rationale is to avoid bias in
rounding: half of the time we round up, half the time we round down.
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1. 37.76 + 3.907 + 226.4 =
2. 319.15 - 32.614 =
3. 104.630 + 27.08362 + 0.61 =
4. 125 - 0.23 + 4.109 =
5. 2.02 × 2.5 =
6. 600.0 / 5.2302 =
7. 0.0032 × 273 =
8. (5.5)3 =
9. 0.556 × (40 - 32.5) =
10. 45 × 3.00 =
11. 3.00 x 105 - 1.5 x 102 = (Give the exact numerical result, then express it the
correct number of significant figures).
12. What is the average of 0.1707, 0.1713, 0.1720, 0.1704, and 0.1715?
13. Calculate the sum of the squares of the deviations from the mean for the
five numbers gives in Question 12 above, in two different ways:
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1. 37.76 + 3.907 + 226.4 = 268.1
2. 319.15 - 32.614 = 286.54
3. 104.630 + 27.08362 + 0.61 = 132.32
4. 125 - 0.23 + 4.109 = 129
5. 2.02 × 2.5 = 5.0
6. 600.0 / 5.2302 = 114.7
7. 0.0032 × 273 = 0.87
8. (5.5)3 = 1.7 x 102
9. 0.556 × (40 - 32.5) = 4
10. 45 × 3.00 = 1.4 x 102
11. 3.00 x 105 - 1.5 x 102 = (Give the exact numerical result, then express it the correct
number of significant figures).
12. What is the average of 0.1707, 0.1713, 0.1720, 0.1704, and 0.1715?
Answer = 0.1712
13. Calculate the sum of the squares of the deviations from the mean for the five
numbers given in Question 12 above, in two different ways: (a) carrying all digits
through all the calculations;
(b) Round all intermediate result to 2 figures
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