SCALARS & VECTORS
SCALAR QUANTITIES
Physical quantities which can completely be specified by a number (magnitude)having an appropriate unit are known as "SCALAR QUANTITIES".
Scalar quantities do not need direction for their description.Scalar quantities are comparable only when they have the same physical dimensions.Two or more than two scalar quantities measured in the same system of units are equal if they have the same magnitude and sign.Scalar quantities are denoted by letters in ordinary type.Scalar quantities are added, subtracted, multiplied or divided by the simple rules of algebra.
EXAMPLES
Work, energy, electric flux, volume, refractive index, time, speed, electric potential, potential difference, viscosity, density, power, mass, distance, temperature, electric charge etc.
VECTORS QUANTITIES
Physical quantities having both magnitude and direction with appropriate unit are known as "VECTOR QUANTITIES".
We can't specify a vector quantity without mention of deirection. vector quantities are expressed by using bold letters with arrow sign such as:vector quantities can not be added, subtracted, multiplied or divided by the simple rules of algebra.vector quantities added, subtracted, multiplied or divided by the rules of trigonometry and geometry.
EXAMPLES
Velocity, electric field intensity, acceleration, force, momentum, torque, displacement, electric current, weight, angular momentum etc.
REPRESENTATION OF VECTORS
On paper vector quantities are represented by a straight line with arrow head pointing the direction of vector or terminal point of vector.
Wednesday, October 17, 2007
Chemistry notes for Ist year
Define the following terms:
Chemistry:
Chemistry is the branch of science which deals with the properties, composition and structure of matter. Study of chemistry also includes the laws and principles related to the structure and inter-relations of elements and compound. Chemistry has the task of investigating the materials of which our universe is made. Chemistry investigates chemical changes, conditions under which chemical changes occur. Chemistry also deals with the way in which similar changes can be brought about in laboratory and on a large scale in industries. Chemistry is a very vast field. Chemistry is divided into a number of branches such as Organic chemistry, Inorganic chemistry, Physical chemistry, biochemistry, Applied chemistry, Nuclear chemistry etc.
Significant Figures
Significant figures are the reliable digits in a number or measurement which are known with certainty.
Significant figures show the accuracy in measurements. We can understand the precision of a measurement if we know exactly the significant figures in the measurement.
A measurement that contains more number of significant figures is more accurate than a measurement that contains less number of Significant figures. For example:Radius of a bob is 3.3679 cm and that of the other is 3.36 cm. In this situation the first measurement is the most accurate as it has more number of significant figures.
Rules Of Significant Figures
In order to determine significant figures in a number we must follow the following rules:
(1) All the non-zero digits are significant figures. For Example: 3.456 has four significant figures. 12.3456 has six significant figures. 0.34 has two significant figures. (2) Zeros between non-zero digits are significant. For Example: 2306 has four significant figures. 20,0894 has six significant figures. (3) Zeros locating the position of decimal in numbers of magnitude less than one are not significant. For Example: 0.2224 has only one significant figures. 0.0000034 has two significant figures. (4) Final zeros to the right of the decimal point are significant. For Example: 3.0000 has five significant figures. 1002.00 has six significant figures. (5) Zeros that locate decimal point in numbers greater than one are not significant. For Example: 30000 has only one significant figure. 120000 has two significant figures.
Rules Of Rounding Off Data
Rule # 1: If the digit to be dropped is greater than 5, then add "1" to the last digit to be retained and drop all digits farther to the right. For example: 3.677 is rounded off to 3.68 if we need three significant figures in measurement. 3.677 is rounded off to 3.7 if we need two significant figures in measurement.
Rule # 2: If the digit to be dropped is less than 5, then simply drop it without adding any number to the last digit. For example: 6.632 is rounded off to 6.63 if we need three significant figures in measurement. 6.632 is rounded off to 6.6 if we need two significant figures in measurement. Rule # 3: If the digit to be dropped is exactly 5 then: (A) If the digit to be retained is even, then just drop the "5". For example: 6.65 is rounded off to 6.6 if we need two significant figures in measurement. 3.4665 is rounded off to 6.466 if we need four significant figures in measurement. (B) If the digit to be retained is odd, then add "1" to it. For example: 6.35 is rounded off to 6.4 if we need two significant figures in measurement. 3.4675 is rounded off to 6.468 if we need four significant figures in measurement. Remember: Zero is an even number 3.05 is rounded off to 3.0 if we need two significant figures in measurement.
Use of significant figures inaddition and subtraction
In addition and subtraction we consider the significant figures on the right side of decimal point. This means that only as many digits are to be retained to the right side of decimal point as the number with fewest digits to the right of the decimal point. For example: 4.345 + 23.5 =27.845 (actual answer by using calculator) Answer after rounding off: 27.8
Use of significant figures inmultiplication and division
In multiplication and division , the number obtained after calculation of two or more numbers must have no more significant figure than that number used in multiplication or division. For example: 4.3458 x 2.7 =11.73366(actual answer by using calculator) Answer after rounding off: 12(because 2.7 has only two significant figures)
.........Introduction to fundamental concepts of chemistry Error: An error is defined as: "The difference between the measured value and the actual value." If two persons use the same instrument for measurement for finding the same measurement, it is not essential that they may get the same results. There may arises a difference between their measurements. This difference is referred to as an "ERROR". Types Of Error Errors can be divided into three categories: (1) Personal Error (2) Systematic Error (3) Random Error Personal Error www.citycollegiate.com An error comes into play because of faulty procedure adopted by by the observer is called "PERSONAL ERROR". Personal error comes into existence due to making an error in reading a scale. It is due to faulty procedure adopted by the person making measurement. Systematic Error The type of error arises due to defect in the measuring device is known as "SYSTEMATIC ERROR" Generally it is called "ZERO ERROR". it may be positive or negative error. Systematic error can be removed by correcting measurement device. Random Error The error produced due to sudden change in experimental conditions is called "RANDOM ERROR". For example: During sudden change in temperature, change in humidity, fluctuation in potential difference(voltage). It is an accidental error and is beyond the control of the person making measurement. Atomic Mass www.citycollegiate.com Atomic mass is defined as : "The mass of one atom of the element compared with the mass of one atom of C12" Atomic mass is a ratio therefore it has no unit. Generally atoms mass is expressed in ATOMIC MASS UNIT(a.m.u). One atomic mass unit is equal to 1/12 of the mass of a C12 atom. Empirical Formula "Empirical Formula is that formula which expresses the relative number of each kind of atoms present in the molecule of a compound"OR"The formula of a compound which expresses the ratio in which atoms of different elements are combined in a molecule" Empirical formula only indicates atomic ratios but it does not indicate actual number of atoms of different kinds present in the molecule of a compound. Two or more compound may have same empirical formula. Empirical formula is determined by experiment. Molecular Formula The molecular formula of a compound is defined as:"The formula of a compound which not only expresses the relative number of atoms of eachkind but also expresses the actual number of atoms of each element present in one molecule". Molecular formula and empirical formula of a compound are related as:MOLECULAR FORMULA = (EMPIRICAL FORMULA)n Where "n" is an integer and is given by: n = molecular mass of compound / Empirical formula mass of compound Molecular formula of propane = C3H8. Molecular formula of sugar = C12H22O11. Limiting Reactant The limiting reactant is defined as:" The substance which produces least amount of products when it is completely consumed in a chemical reaction".
Molewww.citycollegiate.com"The atomic mass or molecular mass of a substance expressed in grams is called mole".ORA mole may also be defined as " the gram atomic mass or gram molecular mass or gram formula massof a substance that contains 6.02 x 1023 particles." OR"The mass in grams of the atoms or molecules or ions which containsAvogadro's number of particles i.e. 6.02 x 1023 particles." For example: (1) Atomic mass of Carbon = 12 a.m.u. Therefore 12 gram of carbon = 1 mole of carbon. (2) molecular mass of nitrogen = 28 a.m.u. Therefore 28 gram of nitrogen = 1 mole of nitrogen. (3) Formula mass of NaCl = 58.5 a.m.u. Therefore 58.5 gram of NaCl = 1 mole of NaCl. Mole is denoted by "n".Formulawww.citycollegiate.comNumber of moles of substance = mass of substance (in grams) / molecular mass or atomic mass or formula massAvogadro's NumberOne mole of any substance contains equal number of particles (atoms or molecules or ions).Value of this number is 6.02 x 1023. This constant value or number is referred to as "AVOGADRO'S NUMBER" For example: One mole of hydrogen = 6.02 x 1023 molecule of hydrogen. One mole of sodium = 6.02 x 1023 sodium of hydrogen. One mole of Ca+2 = 6.02 x 1023 ions of Ca+2. It is denoted by "NA".Stoichiometrywww.citycollegiate.com Stoichiometry refers to chemical calculations. Stoichiometry is defined as: "The quantitative relationship among the reactants and products in a balanced chemical equation".Assumption of Stoichiometric Calculations There are two important assumptions for stoichiometric calculations: (1) Reactants are completely converted into products. (2) No supplementary or side-reactions occur. Suppose we want to calculate the mass of CO2 formed when a given mass of carbon burns in air. The reaction is:C + O2 è CO2 In actual practice, it is possible that we get less amount of CO2 than the calculated mass of CO2.This is because that the given mass of carbon can also form CO in addition to CO2.2C + O2 è 2CO This means that we have to avoid the formation of carbon monoxide.Types of stoichiometric calculations Stoichiometric calculations can be divided into three categories. (1) Mass - Mass Relationship (2) Mass - Volume Relationship (3) Volume - Volume Relationship Gay-Lussac's Law Of Combining Volume According to Gay-Lussac's Law Of Combining Volume:"Gases react in the ratio of small whole numbers by volume under similar conditions of temperature and pressure". For example: Nitrogen and hydrogen react to form ammonia gas.N2 + 3H2 è 2NH3 In this example one volume of nitrogen gas reacts with three volumes of hydrogen gas to produce two volumes of ammonia gas.
Chemistry:
Chemistry is the branch of science which deals with the properties, composition and structure of matter. Study of chemistry also includes the laws and principles related to the structure and inter-relations of elements and compound. Chemistry has the task of investigating the materials of which our universe is made. Chemistry investigates chemical changes, conditions under which chemical changes occur. Chemistry also deals with the way in which similar changes can be brought about in laboratory and on a large scale in industries. Chemistry is a very vast field. Chemistry is divided into a number of branches such as Organic chemistry, Inorganic chemistry, Physical chemistry, biochemistry, Applied chemistry, Nuclear chemistry etc.
Significant Figures
Significant figures are the reliable digits in a number or measurement which are known with certainty.
Significant figures show the accuracy in measurements. We can understand the precision of a measurement if we know exactly the significant figures in the measurement.
A measurement that contains more number of significant figures is more accurate than a measurement that contains less number of Significant figures. For example:Radius of a bob is 3.3679 cm and that of the other is 3.36 cm. In this situation the first measurement is the most accurate as it has more number of significant figures.
Rules Of Significant Figures
In order to determine significant figures in a number we must follow the following rules:
(1) All the non-zero digits are significant figures. For Example: 3.456 has four significant figures. 12.3456 has six significant figures. 0.34 has two significant figures. (2) Zeros between non-zero digits are significant. For Example: 2306 has four significant figures. 20,0894 has six significant figures. (3) Zeros locating the position of decimal in numbers of magnitude less than one are not significant. For Example: 0.2224 has only one significant figures. 0.0000034 has two significant figures. (4) Final zeros to the right of the decimal point are significant. For Example: 3.0000 has five significant figures. 1002.00 has six significant figures. (5) Zeros that locate decimal point in numbers greater than one are not significant. For Example: 30000 has only one significant figure. 120000 has two significant figures.
Rules Of Rounding Off Data
Rule # 1: If the digit to be dropped is greater than 5, then add "1" to the last digit to be retained and drop all digits farther to the right. For example: 3.677 is rounded off to 3.68 if we need three significant figures in measurement. 3.677 is rounded off to 3.7 if we need two significant figures in measurement.
Rule # 2: If the digit to be dropped is less than 5, then simply drop it without adding any number to the last digit. For example: 6.632 is rounded off to 6.63 if we need three significant figures in measurement. 6.632 is rounded off to 6.6 if we need two significant figures in measurement. Rule # 3: If the digit to be dropped is exactly 5 then: (A) If the digit to be retained is even, then just drop the "5". For example: 6.65 is rounded off to 6.6 if we need two significant figures in measurement. 3.4665 is rounded off to 6.466 if we need four significant figures in measurement. (B) If the digit to be retained is odd, then add "1" to it. For example: 6.35 is rounded off to 6.4 if we need two significant figures in measurement. 3.4675 is rounded off to 6.468 if we need four significant figures in measurement. Remember: Zero is an even number 3.05 is rounded off to 3.0 if we need two significant figures in measurement.
Use of significant figures inaddition and subtraction
In addition and subtraction we consider the significant figures on the right side of decimal point. This means that only as many digits are to be retained to the right side of decimal point as the number with fewest digits to the right of the decimal point. For example: 4.345 + 23.5 =27.845 (actual answer by using calculator) Answer after rounding off: 27.8
Use of significant figures inmultiplication and division
In multiplication and division , the number obtained after calculation of two or more numbers must have no more significant figure than that number used in multiplication or division. For example: 4.3458 x 2.7 =11.73366(actual answer by using calculator) Answer after rounding off: 12(because 2.7 has only two significant figures)
.........Introduction to fundamental concepts of chemistry Error: An error is defined as: "The difference between the measured value and the actual value." If two persons use the same instrument for measurement for finding the same measurement, it is not essential that they may get the same results. There may arises a difference between their measurements. This difference is referred to as an "ERROR". Types Of Error Errors can be divided into three categories: (1) Personal Error (2) Systematic Error (3) Random Error Personal Error www.citycollegiate.com An error comes into play because of faulty procedure adopted by by the observer is called "PERSONAL ERROR". Personal error comes into existence due to making an error in reading a scale. It is due to faulty procedure adopted by the person making measurement. Systematic Error The type of error arises due to defect in the measuring device is known as "SYSTEMATIC ERROR" Generally it is called "ZERO ERROR". it may be positive or negative error. Systematic error can be removed by correcting measurement device. Random Error The error produced due to sudden change in experimental conditions is called "RANDOM ERROR". For example: During sudden change in temperature, change in humidity, fluctuation in potential difference(voltage). It is an accidental error and is beyond the control of the person making measurement. Atomic Mass www.citycollegiate.com Atomic mass is defined as : "The mass of one atom of the element compared with the mass of one atom of C12" Atomic mass is a ratio therefore it has no unit. Generally atoms mass is expressed in ATOMIC MASS UNIT(a.m.u). One atomic mass unit is equal to 1/12 of the mass of a C12 atom. Empirical Formula "Empirical Formula is that formula which expresses the relative number of each kind of atoms present in the molecule of a compound"OR"The formula of a compound which expresses the ratio in which atoms of different elements are combined in a molecule" Empirical formula only indicates atomic ratios but it does not indicate actual number of atoms of different kinds present in the molecule of a compound. Two or more compound may have same empirical formula. Empirical formula is determined by experiment. Molecular Formula The molecular formula of a compound is defined as:"The formula of a compound which not only expresses the relative number of atoms of eachkind but also expresses the actual number of atoms of each element present in one molecule". Molecular formula and empirical formula of a compound are related as:MOLECULAR FORMULA = (EMPIRICAL FORMULA)n Where "n" is an integer and is given by: n = molecular mass of compound / Empirical formula mass of compound Molecular formula of propane = C3H8. Molecular formula of sugar = C12H22O11. Limiting Reactant The limiting reactant is defined as:" The substance which produces least amount of products when it is completely consumed in a chemical reaction".
Molewww.citycollegiate.com"The atomic mass or molecular mass of a substance expressed in grams is called mole".ORA mole may also be defined as " the gram atomic mass or gram molecular mass or gram formula massof a substance that contains 6.02 x 1023 particles." OR"The mass in grams of the atoms or molecules or ions which containsAvogadro's number of particles i.e. 6.02 x 1023 particles." For example: (1) Atomic mass of Carbon = 12 a.m.u. Therefore 12 gram of carbon = 1 mole of carbon. (2) molecular mass of nitrogen = 28 a.m.u. Therefore 28 gram of nitrogen = 1 mole of nitrogen. (3) Formula mass of NaCl = 58.5 a.m.u. Therefore 58.5 gram of NaCl = 1 mole of NaCl. Mole is denoted by "n".Formulawww.citycollegiate.comNumber of moles of substance = mass of substance (in grams) / molecular mass or atomic mass or formula massAvogadro's NumberOne mole of any substance contains equal number of particles (atoms or molecules or ions).Value of this number is 6.02 x 1023. This constant value or number is referred to as "AVOGADRO'S NUMBER" For example: One mole of hydrogen = 6.02 x 1023 molecule of hydrogen. One mole of sodium = 6.02 x 1023 sodium of hydrogen. One mole of Ca+2 = 6.02 x 1023 ions of Ca+2. It is denoted by "NA".Stoichiometrywww.citycollegiate.com Stoichiometry refers to chemical calculations. Stoichiometry is defined as: "The quantitative relationship among the reactants and products in a balanced chemical equation".Assumption of Stoichiometric Calculations There are two important assumptions for stoichiometric calculations: (1) Reactants are completely converted into products. (2) No supplementary or side-reactions occur. Suppose we want to calculate the mass of CO2 formed when a given mass of carbon burns in air. The reaction is:C + O2 è CO2 In actual practice, it is possible that we get less amount of CO2 than the calculated mass of CO2.This is because that the given mass of carbon can also form CO in addition to CO2.2C + O2 è 2CO This means that we have to avoid the formation of carbon monoxide.Types of stoichiometric calculations Stoichiometric calculations can be divided into three categories. (1) Mass - Mass Relationship (2) Mass - Volume Relationship (3) Volume - Volume Relationship Gay-Lussac's Law Of Combining Volume According to Gay-Lussac's Law Of Combining Volume:"Gases react in the ratio of small whole numbers by volume under similar conditions of temperature and pressure". For example: Nitrogen and hydrogen react to form ammonia gas.N2 + 3H2 è 2NH3 In this example one volume of nitrogen gas reacts with three volumes of hydrogen gas to produce two volumes of ammonia gas.
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