NEET Chemistry Some Basic Concepts of Chemistry / रसायन की कुछ मूलभूत अवधारणाएँ Significant figures Units for measurement

Significant Figures

In the measured value of a physical quantity, the digits about the correctness of which we are surplus the last digit which is doubtful, are called the significant figures. Number of significant figures in a physical quantity depends upon the least count of the instrument used for its measurement.

(1) Common rules for counting significant figures : Following are some of the common rules for counting significant figures in a given expression:

Rule 1. All non zero digits are significant.

Example : \[x=1234\] has four significant figures. Again \[x=189\] has only three significant figures.

Rule 2. All zeros occurring between two non zero digits are significant.

Example : \[x=1007\] has four significant figures. Again \[x=1.0809\] has five significant figures.

Rule 3. In a number less than one, all zeros to the right of decimal point and to the left of a non zero digit are not significant.

Example : \[x=0.0084\] has only two significant digits. Again, \[x=1.0084\] has five significant figures. This is on account of rule 2.

Rule 4. All zeros on the right of the last non zero digit in the decimal part are significant.

Example : \[x=0.00800\] has three significant figures 8, 0, 0. The zeros before 8 are not significant again 1.00 has three significant figures.

Rule 5. All zeros on the right of the non zero digit are not significant.

Example : \[x=1000\] has only one significant figure. Again \[x=378000\] has three significant figures.

Rule 6. All zeros on the right of the last non zero digit become significant, when they come from a measurement.

Example : Suppose distance between two stations is measured to be 3050 m. It has four significant figures. The same distance can be expressed as 3.050 km or \[3.050\times {{10}^{5\,}}\,cm\]. In all these expressions, number of significant figures continues to be four. Thus we conclude that change in the units of measurement of a quantity does not change the number of significant figures. By changing the position of the decimal point, the number of significant digits in the results does not change. Larger the number of significant figures obtained in a measurement, greater is the accuracy of the measurement. The reverse is also true.

(2) Rounding off : While rounding off measurements, we use the following rules by convention:          

Rule 1. If the digit to be dropped is less than 5, then the preceding digit is left unchanged.       

Example : \[x=7.82\] is rounded off to 7.8, again \[x=3.94\] is rounded off to 3.9.

Rule 2. If the digit to be dropped is more than 5, then the preceding digit is raised by one.

Example : x = 6.87 is rounded off to 6.9, again x = 12.78 is rounded off to 12.8.

Rule 3. If the digit to be dropped is 5 followed by digits other than zero, then the preceding digit is raised by one.

Example : x = 16.351 is rounded off to 16.4, again x = 6.758 is rounded off to 6.8.

Rule 4. If digit to be dropped is 5 or 5 followed by zeros, then preceding digit is left unchanged, if it is even.

Example : x = 3.250 becomes 3.2 on rounding off, again x = 12.650 becomes 12.6 on rounding off.

Rule 5.             If digit to be dropped is 5 or 5 followed by zeros, then the preceding digit is raised by one, if it is odd.

Example : x = 3.750 is rounded off to 3.8. again x = 16.150 is rounded off to 16.2.

(3) Significant figure in calculation

(i) Addition and subtraction : In addition and subtraction the following points should be remembered :

(a) Every quantity should be changed into same unit.

(b) If a quantity is expressed in the power of 10, then all the quantities should be changed into power of 10.

(c) The result obtained after addition or subtraction, the number of figure should be equal to that of least, after decimal point.

(ii) Multiplication and division 

(a) The number of significant figures will be same if any number is multiplied by a constant.

(b) The product or division of two significant figures, will contain the significant figures equal to that of least.

 Units for measurement.

            The chosen standard of measurement of a quantity which has essentially the same nature as that of the quantity is called the unit of the quantity. Following are the important types of system for unit,

(1) C.G.S. System          :           Length (centimetre), Mass (gram), Time (second)

(2) M.K.S. System          :           Length (metre), Mass (kilogram), Time (second)

(3) F.P.S. System                       :           Length (foot), Mass (pound), Time (second)

(4) S.I. System               :           The 11th general conference of weights and measures (October 1960) adopted International system of units, popularly known as the SI units. The SI has seven basic units from which all other units are derived called derived units. The standard prefixes which helps to reduce the basic units are now widely used.

Dimensional analysis : The seven basic quantities lead to a number of derived quantities such as pressure, volume, force, density, speed etc. The units for such quantities can be obtained by defining the derived quantity in terms of the base quantities using the base units. For example, speed (velocity) is expressed in distance/time. So the unit is \[m/s\] or \[m{{s}^{-1}}\]. The unit of force (mass \[\times \] acceleration) is \[kg\ m{{s}^{-2}}\] and the unit for acceleration is \[m{{s}^{-2}}\].

Seven basic SI units

Derived Units

Standard prefixes use to reduce the basic units

Conversion factors

Matter and its classification.

            Matter is the physical material of the universe which occupies space and has mass e.g., water, sugar, metals, plants etc. Matter can be classified as,

Separation of mixtures or purification of an impure substance.

            Each component of a mixture retains its own properties and thus a mixture can be separated into its components by taking advantages of the difference in their physical and chemical properties. The different methods which are employed to separate the constituents from a mixture to purify an impure sample of a substance are,

            (1) Sedimentation : It is also called gravity separation. It is used for a mixture in which one component is a liquid and the other is insoluble solid heavier than the liquid.  Example : Sand dispersed in water.

            (2) Filtration : It is used for a mixture containing two components one of which is soluble in a particular solvent and the other is not. Example :  (i) A mixture of salt and paper using water as solvent  (ii) A mixture of sand and sulphur using carbon disulphide as solvent. (iii) A mixture of glass powder and sugar, using water as a solvent in which sugar dissolves but glass does not. (iv) A mixture of sand and sulphur, using carbon disulphide as the solvent in which sulphur dissolves but sand does not.

            (3) Sublimation : It is used for a mixture containing a solid component, which sublimes on heating from non-volatile solids.  Example : A mixture of sand + naphthalene or powdered glass + \[N{{H}_{4}}Cl\] / camphor / iodine etc. can be separated by the method of sublimation because substances like naphthalene, \[N{{H}_{4}}Cl\], iodine, camphor etc. form sublimates whereas sand, glass etc. do not.

            (4) Evaporation : It is used for a mixture in which one component is a non–volatile soluble salt and other is a liquid.  Example : Sodium chloride dissolved in sea–water.

            (5) Crystallization : It is a most common method for a mixture containing solid components and based upon the differences in the solubilities of the components of the mixture into a solvent. For separation, a suitable solvent is first selected. It is of two types :

            (i) Simple crystallization : It is applicable when there is a large difference in the solubilities of different components of a mixture. 

            (ii) Fractional crystallization : It is applicable when there is a small difference in the solubilities of different components of a mixture in the same solvent. Example : \[{{K}_{2\,}}C{{r}_{2}}{{O}_{7}}\] and \[KCl\]. Here \[{{K}_{2}}C{{r}_{2}}{{O}_{7}}\] is less soluble in water and hence crystallizes first. A series of repeated crystallization separates the two components in pure form.

            (6) Distillation : It is the most important method for purifying the liquids. It involves the conversion of a liquid to its vapours on heating (vaporisation) and then cooling the vapours back into the liquid (condensation). It can be used to separate, (i) A solution of a solid in a liquid. e.g., aqueous copper sulphate solution. (ii) A solution of two liquids whose boiling points are different. Several methods of distillation are employed.

            (i) Simple distillation : It is used only for such liquids which boil without decomposition at atmospheric pressure and contain non–volatile impurities. Example :  (a) Pure water from saline water. (b) Benzene from toluene.

            (ii) Fractional distillation : It is used for the separation and purification of a mixture of two or more miscible liquids having different boiling points. The liquid having low boiling point vaporises first, gets condensed and is collected in the receiver. The temperature is then raised to the boiling point of second so that the second liquid vaporises and is collected in other receiver. If two liquids present in a mixture have their boiling points closer to each other, a fractionating column is used. Example : (a) Crude petroleum is separated into many useful products such as lubricating oil, diesel oil, kerosene and petrol by fractional distillation. (b) A mixture of acetone and methyl alcohol.

            (iii) Vacuum distillation or distillation under reduced pressure : It is used for such liquids which decompose on heating to their boiling points. At reduced pressure, the boiling point of liquid is also reduced.

Example : Glycerol is distilled under pressure as it decomposes on heating to its boiling point.

            (iv) Steam distillation : It is used for liquids which are partially miscible with water, volatile in steam. e.g., aniline, oils etc. are purified by steam distillation. The principle involved is of reduced pressure distillation. If P_w and P_l are vapour pressures of water and liquid at distillation temperature, then \[{{P}_{w}}\,+\,{{P}_{l}}\,=\,P\,=\,76\,cm\] i.e., atmospheric pressure.  Thus, a liquid boils at relatively low temperature than its boiling point in presence of steam. Example :  Some solids like naphthalene, o-nitrophenol which are steam volatile can be purified. Nitrobenzene, chlorobenzene, essential oils are also extracted or separated by this process

            (7) Solvent extraction : It is used for the separation of a compound from its solution by shaking with a suitable solvent. The extraction follows Nernst distribution law. The solvent used must be insoluble with other phase in which compound is present as well as the compound should be more soluble in solvent. The extraction becomes more efficient if the given extracting liquid is used for more number of extractions with smaller amounts than using it once with all extracting liquid. Example : (i)  Aqueous solution of benzoic acid by using benzene.  (ii) Aqueous solution of Iodine by using chloroform or carbon tetrachloride. (iii) Flavour of tea from the tea leaves by boiling with water.

            (8) Magnetic separation : It is used for a mixture in which one component is magnetic while the other is non–magnetic. 

Example :  iron ore from the non–magnetic impurities.

            (9) Chromatography : It is based on the differences in the rates at which different components of a mixture are absorbed on a suitable solvent. It is used in separation, isolation, purification and identification of a substance. It was proposed by a Russian botanist Tswett.

            (10) Atmolysis : It is used for separation of the mixture of gases or vapours. It is based on the difference in their rates of diffusion through a porous substance. 

Example :  \[{{H}_{2}},\ S{{O}_{2}},\,\,C{{H}_{4}}\,\,and\,{{O}_{2}},\,\,{{U}^{235}}\,\And \,{{U}^{238}}\]in the form of their hexa–fluorides. 

            (11) Electrophoresis : It is based upon the differences in the electrical mobility of the different components of the mixture.

            (12) Ultracentrifugation : It is based upon the difference in sedimentation velocity of the components in a centrifugal field.