CPGYAN

Uncertainty in measurement chemistry

2020-02-23T12:21:00.000+05:30

UNCERTAINTY IN MEASUREMENT
What is meant by uncertainty in measurement? Let'us the study in the field of chemistry, one has to deal with experimental data as well as theoretical calculations. There are meaningful ways to handle the numbers conveniently and present the data realistically with certainty to the extent possible.how do you find the uncertainty of a measurement. These ideas are discussed below in details.
1) Scientific Notation
As chemistry is the study of atoms and
molecules which have extremely low masses
and are present in extremely large numbers,
a chemist has to deal with numbers as large
as 602, 200,000,000,000,000,000,000 for the
molecules of 2 g of hydrogen gas or as small
as 0.00000000000000000000000166 gm mass of a H atom. Similarly other constants such as Planck’s constant, speed of light,charges on particles etc., involve numbers of the above magnitude.It may look funny for a moment to write or count numbers involving so many zeros but it offers a real challenge to do simple mathematical operations of addition subtractions,multiplication or division with such numbers. You can write any two numbers of the above type and try any one of the operations you like to accept the challenge and then you will really appreciate the difficulty in handling such numbers.This problem is solved by using scientific notation for such numbers, i.e., exponential notation in which any number can be represented in the form N × 10n
where n is an exponent having positive or negative values and N is a number (called digit term) which varies between 1.000... and 9.999....
Thus, we can write 232.508 as 2.32508 ×10^2
in scientific notation. Note that while writing it, the decimal had to be moved to the left by two places and same is the exponential (2) of 10 in the scientific notation.
Similarly, 0.00016 can be written as
1.6 × 10^–4. Here the decimal has to be moved
four places to the right and ( – 4) is the exponent
in the scientific notation.Now, for performing mathematical operations on numbers expressed in scientific notation s, the following points are to be kept in mind, measurement uncertainty calculations how we find out let's see below

Multiplication and Division
These two operations follow the same rules

which are there for exponential numbers, i.e
(5.6x10^5)X(6.9x10^8)=(5.6x6.9)(10^5+8)
=(5.6x6.9)10^13
=38.64 X 10^13
=3.864 X 10^14
(9.8 X 10^-2) X (2.5x10^-6)=(9.8 X 2.5 )( 10^-2+{-6})
=(9.8x2.5)10^{-2-6}
= 24.50 X 10^-8
=2.450 X 10^-7
(2.7x 10^-3)/(5.5x10^4)=(2.7x5.5)10^-3-4
= 0.4909 X 10^-7
= 4.909 X 10^-8
Addition and Subtraction
These two operations follow the same rules
which are there for exponential numbers, i.e.
Addition and Subtraction
For these two operations, first the numbers are
written in such a way that they have same
exponent. After that, the coefficient are added
or subtracted as the case may be.
Thus, for adding 6.65 × 10^4 and 8.95 × 10^3
(6.65 × 10^4) + (0.895 × 10^4) exponent is made
same for both the numbers.
Then, these numbers can be added as follows
(6.65 + 0.895) × 10^4 = 7.545 × 10^4
Similarly, the subtraction of two numbers can
be done as shown below :
(2.5 × 10^–2) –( 4.8 × 10^–3)
= (2.5 × 10^–2) – (0.48 × 10^–2)
= (2.5 – 0.48) × 10^–2 = 2.02 × 10^–2

2) Significant Figures
Every experimental measurement has some
amount of uncertainty associated with it.
However, one would always like the results to
be precise and accurate. Precision and
accuracy are often referred to while we talk
about the measurement. Precision refers to the closeness of various measurements for the same quantity. However,accuracy is the agreement of a particular value to the true value of the result. For example, if the true value for a result is 2.00 g and a students ‘A’ takes two measurements and
reports the results as 1.95 g and 1.93 g. These
values are precise as they are close to each
other but are not accurate. Another student
repeats the experiment and obtains 1.94 g and
2.05 g as the results for two measurements.
These observations are neither precise nor
accurate. When a third student repeats these
measurements and reports 2.01g and 1.99g
as the result. These values are both precise and
accurate. This can be more clearly understood
from the data given see below
1. 2. AVG.(gm)

Student A. 1.95 1.93 1.9940
Student B. 1.94 2.05 1.9950
Student C. 2.01 1.99 2.0000

The uncertainty in the experimental or the
calculated values is indicated by mentioning
the number of significant figures. Significant
figures are meaningful digits which are known
with certainty. The uncertainty is indicated by
writing the certain digits and the last uncertain
digit. Thus, if we write a result as 11.2 mL, we
say the 11 is certain and 2 is uncertain and
the uncertainty would be +1 in the last digit.
Unless otherwise stated, an uncertainty of +1
in the last digit is always understood.
There are certain rules for determining the
number of significant figures. These are stated
below:
(1) All non-zero digits are significant. For
example in 285 cm, there are three
significant figures and in 0.25 mL, there
are two significant figures.
(2) Zeros preceding to first non-zero digit are
not significant. Such zero indicates the
position of decimal point.
Thus, 0.03 has one significant figure and
0.0052 has two significant figures.
(3) Zeros between two non-zero digits are
significant. Thus, 2.005 has four significant
figures.
(4) Zeros at the end or right of a number are
significant provided they are on the right
side of the decimal point. For example,
0.200 g has three significant figures.
But, if otherwise, the terminal zeros are not
significant if there is no decimal point. For
example, 100 has only one significant
figure, but 100. has three significant
figures and 100.0 has four significant
figures. Such numbers are better
represented in scientific notation. We can
express the number 100 as 1×10^2
for one significant figure, 1.0×10^2 for two
significant figures and 1.00×10^2 for three
significant figures.
(5) Counting numbers of objects, for example,
2 balls or 20 eggs, have infinite significant
figures as these are exact numbers and can
be represented by writing infinite number
of zeros after placing a decimal i.e.,
2 = 2.000000 or 20 = 20.000000
In numbers written in scientific notation,
all digits are significant e.g., 4.01×10^2
has three significant figures, and 8.256 × 10^–3 has four significant figures.
Addition and Subtraction of Significant
Figures
The result cannot have more digits to the right
of the decimal point than either of the original
numbers.
12.11
18.0
+ 1.012
Total 31.122
Here, 18.0 has only one digit after the decimal
point and the result should be reported only
up to one digit after the decimal point which
is 31.1

Multiplication and Division of Significant
Figures
In these operations, the result must be reported
with no more significant figures as are there in
the measurement with the few significant
figures.
2.5×1.25 = 3.125
Since 2.5 has two significant figures, the
result should not have more than two
significant figures, thus, it is 3.1.
While limiting the result to the required
number of significant figures as done in the
above mathematical operation, one has to keep
in mind the following points for rounding off
the numbers
1). If the rightmost digit to be removed is more
than 5, the preceding number is increased
by one. for example, 1.386
If we have to remove 6, we have to round it
to 1.39
2). If the rightmost digit to be removed is less
than 5, the preceding number is not changed.
For example, 4.334 if 4 is to be removed,
then the result is rounded upto 4.33.
3). If the rightmost digit to be removed is 5,
then the preceding number is not changed
if it is an even number but it is increased
by one if it is an odd number. For example,
if 6.35 is to be rounded by removing 5, we
have to increase 3 to 4 giving 6.4 as the
result. However, if 6.25 is to be rounded
off it is rounded off to 6.2.

3) Dimensional Analysis
Often while calculating, there is a need to
convert units from one system to other. The
method used to accomplish this is called factor
label method or unit factor method or
dimensional analysis. This is illustrated
below.
Example
A piece of metal is 3 inch (represented by in)
long. What is its length in cm?
We know that 1 in = 2.54 cm
From this equivalence, we can write
(1 in / 2.54cm) =1=(2.54cm /1 in)
thus
(1 in / 2.54cm) equals 1 and (2.54cm /1 in) also
equals 1. Both of these are called unit factors.
If some number is multiplied by these unit
factors (i.e. 1), it will not be affected otherwise.
Say, the 3 in given above is multiplied by
the unit factor. So,
3 in = 3 in × (2.54cm/1 in) = 3 × 2.54 cm = 7.62 cm
Now the unit factor by which multiplication
is to be done is that unit factor [(2.54cm/1 in) in
the above case] which gives the desired units
i.e., the numerator should have that part which
is required in the desired result.It should also be noted in the above example that units can be handled just like other numerical part. It can be cancelled,divided, multiplied, squared etc. Let us study one more example for it.
Example
A jug contains 2L of milk. Calculate the volume
of the milk in m3
Since 1 L = 1000 cm3
and 1m = 100 cm which gives
(1 m / 100cm)=1=(100 cm / 1m )
To get m3
from the above unit factors, the
first unit factor is taken and it is cubed.
( 1m / 100cm )^3=1m3 / 10^6 cm3
= (1)^3=1
Now 2 L = 2×1000 cm3
The above is multiplied by the unit factor
(2 x 1000 cm )^3 X ( 1m3/10^6 cm3 )
=(2 m3 / 10 m3 ) = 2 x 10^-3 m3

PROPERTIES OF MATTER AND THEIR MEASUREMENT

2020-02-13T01:17:00.002+05:30

PROPERTIES OF MATTER AND THEIR MEASUREMENT
Properties of matter & their measurement are divided in Physical and chemical properties.Every substance has unique or characteristic properties. These properties can be classified into two categories — physical properties, such as colour, odour, melting point, boiling point, density, etc., and chemical properties, like composition, combustibility, ractivity with acids and bases, etc. Physical properties can be measured or observed without changing the identity or the composition of the substance. The measurement or observation of chemical properties requires a chemical change to occur. Measurement of physical properties does not require occurance of a chemical change. The examples of chemical properties are characteristic reactions of different substances; these include acidity or basicity, combustibility, etc.
1) Measurement of physical properties
Quantitative measurement of properties is required for scientific investigation. Many properties of matter, such as length, area, volume, etc., are quantitative in nature. Any
quantitative observation or measurement is represented by a number followed by units
in which it is measured. For example, length of a room can be represented as 6 m; here, 6
is the number and m denotes metre, the unit in which the length is measured.
Earlier, two different systems of measurement, i.e., the English System and the Metric System were being used in different parts of the world. The metric system, which originated in France in late eighteenth century, was more convenient as it was based on the decimal system. Late, need of a common standard system was felt by the scientific community. Such a system was established in 1960 and is discussed in detail below.
1)-A]The International System of Units (SI)
The International System of Units (in French Le Systeme International d’Unités —
abbreviated as SI) was established by the 11th General Conference on Weights and Measures (CGPM from Conference Generale des Poids et Measures). The CGPM is an inter-governmental treaty organisation created by a diplomatic treaty known as
Metre Convention, which was signed in Paris in 1875.
Prefixes used in the SI system

1)-B] Mass and Weight
Mass of a substance is the amount of matter present in it, while weight is the force exerted
by gravity on an object. The mass of a substance is constant, whereas, its weight may vary from one place to another due to change in gravity. You should be careful in using these terms.
The mass of a substance can be determined accurately in the laboratory by using an
analytical balance Seen below fig.

The SI unit of mass is kilogram. However, its fraction named as gram (1 kg = 1000 g), is used in laboratories due to the smaller amounts of chemicals used in chemical reactions.
1)-C]Volume
Volume is the amount of space occupied by a substance. It has the units of (length)3. So in
SI system, volume has units of m3. But again, in chemistry laboratories, smaller volumes are used. Hence, volume is often denoted in cm3 or dm3 units.
A common unit, litre (L) which is not an SI unit, is used for measurement of volume of
liquids.
1 L = 1000 mL , 1000 cm3 = 1 dm3

Different units used to express volume

In the laboratory, the volume of liquids or solutions can be measured by graduated
cylinder, burette, pipette, etc. A volumetric flask is used to prepare a known volume of a
solution. These measuring devices are shown in Fig.

1)-D]Density
The two properties — mass and volume discussed above are related as follows:
Density= Mass/Volume
Density of a substance is its amount of mass per unit volume. So, SI units of density can be
obtained as follows:
SI unit of density = SI unit of mass /SI unit of volume
= kg /m3
This unit is quite large and a chemist often expresses density in g cm–3, where mass is
expressed in gram and volume is expressed in cm3. Density of a substance tells us about how closely its particles are packed. If density is more, it means particles are more closely
packed.
1)-E]Temperature
There are three common scales to measure temperature — °C (degree celsius), °F (degree
fahrenheit) and K (kelvin). Here, K is the SI unit. The thermometers based on these scales
are shown in Fig.

Generally, the thermometer with celsius scale are calibrated from 0° to 100°, where these two temperatures are the freezing point and the boiling point of water, respectively. The fahrenheit scale is represented between 32° to 212°.
The temperatures on two scales are related to each other by the following relationship:
°F = (°C) * 9/5 +32
The kelvin scale is related to celsius scale as follows:
K = °C + 273.15
It is interesting to note that temperature below 0 °C (i.e., negative values) are possible
in Celsius scale but in Kelvin scale, negative temperature is not possible.

BASICS OF CHEMISTRY LIKE STATE OF MATTER & PROPERTIES

2020-02-06T00:27:00.000+05:30

CHEMISTRY
1.1 IMPORTANCE OF CHEMISTRY
Chemistry plays a central role in science and is often intertwined with other branches of science. Principles of chemistry are applicable in diverse areas, such as weather patterns, functioning of brain and operation of a computer,gs, soa production in chemical industries, manufacturing fertilizers, alkalies, acids, salts, dyes, polymers, drups, detergents, metals, alloys, etc., including new material. Chemistry contributes in a big way to the national economy. It also plays an important role in meeting human needs for food, healthcare products and other material aimed at improving the quality of life. This is exemplified by the large-scale production of a variety of fertilizers, improved variety of pesticides and insecticides. Chemistry provides methods for the isolation of lifesaving drugs from natural sources and makes possible synthesis of such drugs. Some of these drugs are cis platin and taxol, which are effective in cancer therapy. The drug AZT (Azidothymidine) is used for helping AIDS patients. Chemistry contributes to a large extent in the development and growth of a nation. With a better understanding of chemical principles it has now become possible to design and synthesize new material having specific magnetic, electric and optical properties. This has lead to the production of superconducting ceramics, conducting polymers, optical fibers, etc. Chemistry has helped in establishing industries which manufacture utility goods, like acids, alkalies, dyes, polymers metals, etc. These industries contribute in a big way to the economy of a nation and generate employment. In recent years, chemistry has helped in dealing with some of the pressing aspects of environmental degradation with a fair degree of success. Safer alternatives to environmentally hazardous refrigerants, like CFC's (chlorofluorocarbons), responsible for ozone depletion in the stratosphere, have been successfully synthesized. However, many big environmental problems continue to be matters of grave concern to the chemists. One such problem is the management of the Green House gases, like methane, carbon dioxide, etc. Understanding of biochemical processes, use of enzymes for large-scale production of chemicals and synthesis of new exotic material are some of the intellectual challenges for the future generation of chemists. A developing country, like India, needs talented and creative chemists for accepting such challenges. To be a good chemist and to accept such challenges, one needs to understand the basic concepts of chemistry, which begin with
the concept of matter. Let us start with the nature of matter.
1.2 NATURE OF MATTER
Anything which has mass and occupies space is called matter. Everything around us, for example, book, pen, pencil, water, air, all living beings, etc., are composed of matter. You know that they have mass and they occupy space.
1.2.1 States of Matter
matter can exist in three physical states viz. solid, liquid and gas. The constituent particles of matter in these three states can be represented as shown in Fig. 1.1.Particles are held very close to each other in solids in an orderly fashion and there is not much freedom of movement. In liquids, the particles are close to each other but they can move around. However, in gases, the particles are far apart as compared to those present in solid or liquid states and their movement is
easy and fast. Because of such arrangement of particles, different states of matter exhibit the following characteristics:
(I) Solids have definite volume and definite shape.
(II) Liquids have definite volume but do not have definite shape. They take the shape
of the container in which they are placed.



  Fig. 1.1 Arrangement of particles in solid, liquid and gaseous state
(III) Gases have neither definite volume nor definite shape. They completely occupy the space in the container in which they are placed. These three states of matter are inter convertible by changing the conditions of temperature and pressure.

On heating, a solid usually changes to a liquid, and the liquid on further heating changes to gas (or vapor). In the reverse process, a gas on cooling liquefies to the liquid and the liquid on further cooling freezes to the solid.

1.2.2. Classification of Matter
At the macroscopic or bulk level, matter can be classified as mixture or pure substance. These can be further sub-divided as shown in Fig. 1.2. When all constituent particles of a substance are same in chemical nature, it is said to be a pure substance. A mixture contains many types of particles. A mixture contains particles of two or more pure substances which may be present in it in any ratio. Hence, their composition is variable. Pure substances forming mixture are called its components. Many of the substances present around you are mixtures. For example, sugar solution in water, air, tea, etc., are all mixtures. A mixture may be homogeneous or heterogeneous. In a homogeneous mixture,components completely mix with each other. This means particles of components of the mixture are uniformly distributed throughout

+

Fig. 1.2 Classification of matter
the bulk of the mixture and its composition is uniform throughout. Sugar solution and air are the examples of homogeneous mixtures. In contrast to this, in a heterogeneous mixture, the composition is not uniform throughout and sometimes different components are visible. For example, mixtures of salt and sugar, grains and pulses along with some dirt (often stone pieces), are heterogeneous mixtures. You can think of many more examples of mixtures which you come across in the daily life. It is worthwhile to mention here that the components of a mixture can be separated by using physical methods, such as simple hand-picking, filtration, crystallization, distillation, etc. Pure substances have characteristics different from mixtures. Constituent particles of pure substances have fixed compositon ,copper, gold, water and glucose are some examples of pure substances. Glucose contains carbon, hydrogen and oxygen in a fixed ratio and its particles are of same composition. Hence, like all other pure substances, glucose has a fixed composition. Also, its constituents—carbon, hydrogen and oxygen—cannot be separated by simple physical methods.
Pure substances can further be classified into elements and compounds. Particles of an element consist of only one type of atoms. These particles may exist as atoms or molecules.
Sodium, copper, silver, hydrogen, oxygen, etc, are some examples of elements. Their
all atoms are of one type. However, the atoms of different elements are different in nature. Some elements, such as sodium or copper, contain atoms as their constituent particles, whereas, in some others, the constituent particles are molecules which are formed by two or more atoms. For example, hydrogen, nitrogen and oxygen gases consist of molecules, in which two atoms combine to give their respective molecules. This is illustrated in Fig.1.3

carbon atom. Thus, the atoms of different elements are present in a compound in a fixed and definite ratio and this ratio is characteristic of a particular compound. Also, the properties of a compound are different from those of its constituent elements. For example, hydrogen and oxygen are gases,whereas, the compound formed by their combination i.e., water is liquid. It is interesting to note that hydrogen burns with a pop sound and oxygen is supporter of combustion, but water is used as a fire extinguisher.
1.3 PROPERTIES OF MATTER AND THEIR MEASUREMENT
1.3.1 Physical and chemical properties
Every substance has unique or characteristic properties. These properties can be classified
into two categories — physical properties,such as colour, odour, melting point, boiling
point, density, etc., and chemical properties,like composition, combustibility, ractivity with
acids and bases, etc.Physical properties can be measured or observed without changing the identity or the composition of the substance. The measure mentor observation of chemical properties requires a chemical change to occur. Measurement of physical properties does not require occurrence a chemical change. The examples of chemical properties are characteristic reactions of different substances; these include acidity or basicity

combustibility, etc. Chemists describe, interpret and predict the behaviour of substances on the basis of knowledge of their physical and chemical properties, which are determined by careful measurement and experimentation. In the When or more atoms of different elements combine together in a definite ratio,the molecule of a compound is obtained.Moreover, the constituents of a compound cannot be separated into simpler substances by physical methods. They can be separated by chemical methods.Examples of some compounds are water,ammonia, carbon dioxide, sugar, etc. The molecules of water and carbon dioxide are represented in Fig. 1.4.Note that a water molecule comprises two hydrogen atoms and one oxygen atom.Similarly, a molecule of carbon dioxide contains two oxygen atoms combined with one

1.3.2 Measurement of physical properties
Quantitative measurement of properties reacquired for scientific investigation. Many properties of matter, such as length, area,volume, etc., are quantitative in nature. Any quantitative observation or measurement is represented by a number followed by units in which it is measured. For example, length of a room can be represented as 6 m; here,6 is the number and m denotes meter, the unit in which the length is measured.Earlier, two different systems of measurement, i.e., the English System and the Metric System were being used indifferent parts of the world. The metric system,which originated in France in late eighteenth century, was more convenient as it was base don the decimal system. Late, need of a common standard system was felt by the scientific community. Such a system was established in 1960 and is discussed in detail below.

1.3.3 The International System of Units (SI)

The International System of Units (in French Le Systeme International d’Unités —abbreviated as SI) was established by the 11th General Conference on Weights and Measures (CGPM from Conference

Generale des Poids et Measures). The CGPM is an inter-governmental treaty organization created by a diplomatic treaty known as Metre Convention, which was signed in Paris in 1875.

The SI system has seven base units and they are listed in Table 1.1. These units pertain to the seven fundamental scientific quantities. The other physical quantities, such as speed,

volume, density, etc., can be derived from these quantities

The definitions of the SI base units are given in Table 1.2.