Measurements in Chemistry Notes:
Chemistry is basically an experimental science, which involves measurements of physical quantities of the phenomenon under observation. Every measurement is made relative to some reference standard known as the unit of the measurement. A unit is defined as the standard of reference chosen to measure any physical quantity.
For example, the measured length of a pencil is 8.6 cm means that the length of the pencil is 8.6 times the unit of measurement, which is one cm in this case. Thus the result of any measurement is a combination of a pure number and a unit (8.6 cm here).
Significant Figures:
measurement involving only counting (the discrete variable) like the number of students in a class, number of pens in a box, etc. does not have any uncertainty. They are exact numbers.
However, every measurement, which is made by some instruments (continuous variable) like the height of a boy measured with a tape, volume of water in a beaker measured with a burette, etc. is associated with some degree of uncertainty. The extent of uncertainty depends on the accuracy of the measuring device and the skill of the operator. when the result of such a measurement is expressed it should indicate the degree of uncertainty involved. This is done in terms of significant figures. It indicates the precision of the measured quantity.
The total number of digits in a number is called the number of significant figures. the significant numbers in a number are the number of digits are certain plus one that is uncertain, beginning with the first nonzero digit. The greater the number of significant figures, the greater is the precision. For example, the volume of water in a beaker measured by using a measuring cylinder and the by using a burette, has been reported as 160 cm^{3} and 160.0 cm^{3}. The number of significant figures in these cases are three and four respectively. This implies that in the first volume (160 cm^{3}) the digits 1 and 6 are certain and the third digit 0 is uncertain. The precision of the apparatus is 1 cm^{3}. Therefore the true value lies between 159 and 161 cm^{3}. But in the second volume, (160.0 cm^{3}) the digits 1,6 and 0 are certain and only the last digit 0 is uncertain. Here the precision is 0.1 cm^{3}. Therefore the true volume lies between 159.9 cm^{3} and 160.1 cm^{3}. The second measurement is more precise in these cases.
Rules for determining Significant Figures in a number
The total number of digits in a number is called the number of significant figures. the significant numbers in a number are the number of digits are certain plus one that is uncertain, beginning with the first nonzero digit. The greater the number of significant figures, the greater is the precision. For example, the volume of water in a beaker measured by using a measuring cylinder and the by using a burette, has been reported as 160 cm^{3} and 160.0 cm^{3}. The number of significant figures in these cases are three and four respectively. This implies that in the first volume (160 cm^{3}) the digits 1 and 6 are certain and the third digit 0 is uncertain. The precision of the apparatus is 1 cm^{3}. Therefore the true value lies between 159 and 161 cm^{3}. But in the second volume, (160.0 cm^{3}) the digits 1,6 and 0 are certain and only the last digit 0 is uncertain. Here the precision is 0.1 cm^{3}. Therefore the true volume lies between 159.9 cm^{3} and 160.1 cm^{3}. The second measurement is more precise in these cases.
Rules for determining Significant Figures in a number
The following rules are observed to determine the number of significant figures in a number.
1. All non zero digits as well as the zeros between the nonzero digits are significant. For example, 168 cm has three significant figures and the number 180045 has six significant figures.
2. When the numbers start with a decimal, zeros to the left of the first non zero digit are not significant. Thus 0.5412, 0.05412, 0.005412, all have four significant figures. However zeros to the right of the first nonzero digits are significant. For example, 0.50, 0.050, 0.500 and 0.5100 have two, two, three and four significant figures respectively.
3. If a number has an integral part and a decimal part, all zeros in the number are significant. For example, 7.05, 75.10, 75.050 have three, four and five significant figures respectively.
4. When there is no decimal point in a number, the last zeros may or may not be significant. For example, 20200 g may have three, four or five significant figures depending upon the precision.
In such cases expressing the numbers in scientific notation helps to remove the ambiguity regarding the number of significant figures. in scientific notation, the number is written in the standard exponential form as N x 10^{n}, where N is a number with a single nonzero digit to the left of the decimal point, and n is an integer. In exponential notation, the numeric portion indicates the number of significant figures. For example, the above mass may be written as 2.02 x 10^{4 }g which has three significant figures. But if it is precise to four or five significant figures, then the number should be written as 2.020 x 10^{4} g and 2.0200 x 10^{4} g respectively. Thus Avogadro's constant 6.023 x 10^{23} mol^{ 1} and Planck's constant 6.62 x 10^{34} Js have four and three significant figures respectively.
Example :
Express the following in scientific notations (a) 8614 (b) 0.00178
(a) 8.614 x 10^{3}
(b) 1.78 x 10^{3}
Example :
Find the significant figures in each of the following
(a) 0 0656 g (b) 451 cm^{3} (c) 4.0062
(d) 0.070 (e) 6.02 x 10^{23 } (f) 3.50 x 10^{3}g
Answers (a) 3 (b) 3 (c) 5 (d) 2 (e) 3 (f) 3
Computation Rules:
To compute the final result of an experiment, mathematical manipulations such as addition, subtraction, multiplication and division are required. When several numbers of varying precisions are computed (added, subtracted, multiplied, or divided) the final answer cannot be more precise than the least precise number involved in the computation. Following rules are used for the purpose of determining the number of significant figures in the results.
Rounding off the results
I While reporting the results, the last digits may be rounded off, if required, to avoid figures that are not significant.
2 All digits to be rounded off are removed together (however, rounding is done separately for mixed calculations involving additionsubtraction, and multiplicationdivision).
3. If the digit following the last digit to be retained is less than 5, the last digit is left unchanged. However, if the digit is greater than 5, the last digit to be retained is increased by one.
4. If the left most digit to be removed is 5, the last digit retained is not altered if it is even but increased by one if it is odd.
Example :
Round off the number 58.69536 to three significant figures.
Answer: The number is rounded off to three significant figures as 58.7 because the number to be dropped (9) is greater than 5.
Example :
Round off the following numbers 57.250 and 57.350 to three significant .figures.
Answer: 57.250 is rounded off as 57.2; 57.350 is rounded off as 57.4
In addition and subtraction, the result should be reported to the same number of decimal places as that of the term with the least number of decimal places.
Example:
(a) Addition 24.2 14.3042 154.2
2.22 3.0258 6.1
0.222 0.0016 23
Actual value = 26.642 17.3316 183.3
Reported value 26.6 17.3316 183
(b) Subtraction 5.2848 13.64 26.382
5.2822 0.0016 8.4593
Actual value = 0.0026 13.6384 17.9227
Reported value = 0.0026 13.64 17.923
The answers in the case of (a) are reported to
(1) one decimal place
(2) four decimal places
(3) nearest whole number
The answers in the case of (b) are reported to
(1) same decimal places
(2) two decimal places
(3) three decimal places.
In multiplication and division, the result should be reported to the same number of significant figures as the least precise term in the computation.
Example : (a) 50.122 x 1.21 = 60.6;
(b) 0.364 ÷ 4.974 = 0.072
The presence of exact numbers in an expression does not affect the
number of significant figures in the answer.
Example :
Here '3' is an exact number and the answer is reported to 3 significant figures.
SI Units:
In order to have consistency in the scientific recording, IUPAC has recommended the use of international system of units. It is popularly known as the SI units (after the French expression System Internationally).
The SI has seven basic units which are dimensionally independent. All other units are derived from these basic units.
The Seven basic SI Units:
Name of Unit

Physical Quantity

Symbol

Metre

Length

m

Kilogram

Mass

kg

Second

Time

s (sec)

Ampere

Electric Current

A

Kelvin

Temperature

K

Candela

Light Density

cd

Mole

Amount of Substance

mol

Some common SI Derived Units:
Physical Quantity

Name of Unit

Symbol for Unit

Definition in SI Basic Units

Area





m^{2}

Volume





m^{3}

Density





kg/ m^{3} or kgm^{3}

Speed





m/s or m s^{1}

Acceleration





m/s^{2 }or m s^{2}

Force

Newton

N

Kg m s^{2}

Pressure

Pascal

Pa

Kg m^{1} s^{2} or Nm^{2}

Energy

Joule

J

Kg m^{2} s^{2}

Power

Watt

W

Kg m^{2 }s^{3 }or J s^{1}

Frequency

Hertz

Hz

s^{1}

Electric Charge

Coulomb

C

A s

Electric P. D.

Volt

V

JA^{1}s^{1} or
kg m^{2} s^{3} A^{1}

Prefix

Symbol

Multiple

exa

E

10^{18}

peta

P

10^{15}

tera

T

10^{12}

giga

O

10^{9}

mega

M

10^{6}

kilo

k

10^{3}

hecto

h

10^{2}

deca

da

10

deci

d

10^{1}

centi

c

10^{2}

milli

m

10^{3}

micro

μ

10^{6}

nano

n

10^{9}

pico

p

10^{12}

femto

f

10^{15}

atto

a

10^{18}

Dimensional Analysis
Any calculation involving the use of the dimensions of physical quantities is called dimensional analysis. It is used as a problem solving technique. For example, lets consider the conversion of 3 weeks into days.
1 week = 7 days;
The above equations are called the unit conversion factor. Since the two ratios given above are equal to unity, the multiplication or division of a physical quantity by these factors does not change the value of the quantity but changes the units in which the quantity is expressed. thus to convert 3 weeks into days.
The correct conversion factor must be used for a particular conversion. The numerator of the conversion factor must be the desired unit and the denominator must be the original unit.
Example :
Let's find out how many minutes are there in 7 days
Answer:
Example:
Calculate the mass of a box in kg which weights 100 lb.
Answer:
It is also used as a very powerful tool to check the correctness of equations. In an equation, the dimensions of all the terms on either side are the same.
For example, in the equation
PV = nRT, the dimensions are
mass x length^{2} x time^{2} on both sides.
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