Mole Concept  What is moleA mole concept or mole refers to the amount of a substance that has the same number of particles, atoms or molecules as the number of atoms present in 12 grams of C12 atom, which is an isotope of carbon. So, the mole concept generally tells the number of atoms or such particles which are equal in number to the atoms present in the 12 grams of C12. We can say that C12 atom is taken as a standard to compare the number of atoms or molecules or particles present in the given amount of a substance. The number of particles present in one mole of any substance = 6.023×10^{23}. This is because the number of atoms present in C12 with mass 12 grams is equal to the 6.023×10^{23}. This number is known as an Avogadro's number. So, 1 mole of a substance will contain Avogadro's no. of particles or 6.0222 x 10^{23} particles of that substance. It can be atoms, molecules or any other particles. For example, 1 mole of iron will contain 6.0222 x 10^{23} atoms of iron, similarly, 1 mole of water will contain 6.0222 x 10^{23} molecules of water. So, we can say that as per the definition of mole, the number of atoms present in 1 mole of iron is equal to the number of atoms of C12 present in 12 grams of C12. So, the mole concept was introduced as a convenient method to expressing the number of particles in the given amount of a substance at an atomic or molecular level such as one gram of a pure element which contains a large number of atoms. We can say that mole is just like a measurement that comprises two main parts that include the numerical magnitude and the units to express the magnitude. For example, if the mass of a ball is 2 kg, the magnitude is 2 and the unit is kilogram. Similarly, a mole is used as a unit of measurement for measuring the number of elementary entities like atoms, molecules, etc., just like kg is used for measuring weight, and meter is used for measuring length. Furthermore, the mass of one mole of a substance is called the molar mass of that substance. 1 mole of all elements do not have the same mass, however, they have the same number of atoms. For example, the molar mass of a gold is different from the molar mass of carbon. The mole concept was introduced by a scientist named Lorenzo Romano Amedeo Carlo Avogadro. So, the 1 mole of particles 6.0222 x 10^{23} is known as Avogadro's number which represents 6.0222 x 10^{23} number of particles just like a pair represents 2 and a dozen represents 12. For example, a boy goes to a shop and ask for Avogadro's number of chocolates then he wants 6.0222 x 10^{23} chocolates. However, it has no practical use in daily life. So, it is introduced to represent quantities related to atoms, molecules, electrons, etc. The number 6.0222 x 10^{23} is also known as the Avogadro constant and is denoted by the symbol NA or N0. The number of moles of a given substance in a pure sample can be represented by the below formula; n = N/N_{A} n= number of moles of the substance N= total number of particles in the given sample N_{A} is the Avogadro constant or number. The term 'mole' was introduced by the German chemist Wilhelm Ostwald. He derived this term from the Latin word 'moles' whose meaning is heap or pile. Furthermore, the number of moles of a molecule may not be equal to the number of moles of its constituting elements. For example, one mole of carbon dioxide contains N_{A} number of CO_{2} molecules. But, each molecule of carbon dioxide contains 2 oxygen atoms and one carbon atom. So, one mole of CO_{2} contains 2 moles of oxygen and 1 mole of carbon. Number of atoms or molecules = number of moles x 6.022 x 10^{23} Furthermore, the atomic mass unit and mole both are based on the same reference substance C 12, so, the molar mass of a substance in gram is numerically equal to its atomic mass in amu. Let us solve some numerical to understand the mole conceptCalculate the number of moles in the following cases;i) In 52 gram of Helium (He) Solution: 1 mole of He = 66.0222 x 10^{23} He atoms The atomic mass of 1 He atom = 4 u The mass of 6.0222 x 10^{23} atoms of He = 4g, which is equal to gram atomic mass of He 1 mole of He = 4 gram or gram atomic mass of He Now, 4 gram of He = 1 mole So, 52 gram of He will contain = ¼ x 52 = 13 moles ii) To find out number of moles in 12.044 x 10^{23} atoms of He Solution: 6.022 x 10^{23} atom of He is equal to 1 mole of He So, 12.044 x 10^{23} atom will be equal to 1/6.022 x 10^{23} x 12.044 x 10^{23} moles = 2 moles iii) Calculate the mass of 0.5 mole of N_{2} gas Solution: One molecule of N_{2} gas consists of two N atoms. mass of one N atoms = 14 u So, atomic mass of 2 N atoms (one molecule of nitrogen) = 14 u + 14 u = 28 u Now, one mole of Nitrogen gas will contain 6.0222 x 10^{23} molecules = 28 g, which is gram molecular mass of Nitrogen gas So, 1 mole of N_{2} contains 28 grams of N2 gas So, 0.5 mole of N gas will contain = 0.5 x 28 g = 14 g of N_{2} gas iv) Calculate the mass 0.5 mole of N atoms Solution: Mass of one mole of N atoms or 6.022 x 10^{23} atoms of N = 14 g So, mass of 0.5 mole of N atoms will be = ½ x 14 g = 7 g v) Calculate the mass of 2 moles of Oxygen atoms Solution: Mass of one mole of O atoms or 6.022 x 10^{23} atoms or O = 16 g So, mass of 2 mole of O atoms will be = 2 x 16 = 32 g vi) Calculate mass of 3.011 x 10^{23} number of N atoms Solution: The mass of 6.022 x 10^{23} atoms of Nitrogen = 14 g (gram atomic mass of N) So, mass of 3.011 x 10^{23} atoms of Nitrogen = (14 / 6.022 x 10^{23}) x 3.011 x 10^{23} = 7 g vii) Calculate mass of 6.022 x 10^{23} number of N_{2} molecules Sol: Mass of one molecule of Nitrogen is 28 u as there are two N atoms. So, mass of 6.022 x 10^{23} molecules of Nitrogen (one mole of molecules molecule) or gram molecular mass of nitrogen molecules = 28 g viii) Calculate number of particles in 46 g of Na atoms Sol: One mole of Na has 6.022 x 10^{23} atoms Mass of one Na atom is 23 u. Mass of 6.022 x 10^{23} atoms or 1 mole atoms of Na = 23 g (gram atomic mass) Now, 23 g contains 6.022 x 10^{23} atoms or particles Then, 46 g of Na will contain = (6.022 x 10^{23} / 23) x 46 = 12.044 x 10^{23} atoms ix) Calculate number of molecules in 8 g of O_{2} molecules Sol: Atomic mass of one Oxygen atom = 16 u In O_{2}, the mass of two O atoms = 32 u If we take mass in grams, then mass of 1 mole or 6.022 x 10^{23} molecules of Oxygen = 32 g Now, in 32 g we have 6.022 x 10^{23} molecules So, in 8 g of O_{2}, we will have (6.022 x 10^{23} / 32) x 8 = 1.5 x 10^{23} molecules x) Calculate number of particles in 0.1 mole of carbon atoms Sol: 1 mole of carbon contains 6.022 x 10^{23} atoms So, 0.1 mole of carbon will contain = (6.022 x 10^{23} /1) x 0.1 = 0.6022 x 10^{23} atoms or particles xi) Calculate the mass of 0.5 mole of silver Sol: Mass of 1 mole of silver (Ag) = gram atomic mass of Ag = 108 g So, mass of 0.5 mole of silver (Ag) = (108/1) x 0.5 = 54 g xii) Calculate the mass of 0.5 mole of sugar ( C_{12} H_{22} O_{11}) Sol: Mass of one molecule of sugar = 12 x12 + 1 x 22 +16 x 11 = 144 + 22 + 176 = 342 u One mole of sugar contains 6.022 x 10^{23} molecules Mass of 6.022 x 10^{23} molecules or 1 mole of sugar = 342 g So, mass of 0.5 mole of sugar is = 342 x 0.5 = 171 g Mole concept formulasThere are lots of formulas in mole concept that can be used to solve numerical involving mole concept, such as; i) To convert mass in grams into moles Number of moles = given mass in grams/ molar mass in g/mol n = m / M, where m is mass given in grams and M is molar mass ii) To convert given number of moles into grams Mass in grams = number of moles x molar mass g/mol m = n x M, where n is number of moles and M is molar mass iii) To convert given number of moles of atom into number of atoms Number of atoms or molecules = number of moles x Avogadro's number N = n x N_{0}, where n is number moles and N0 is Avogadro's number, which can also be represented by N_{A} iv) To convert given number of atoms or molecules into moles Number of moles = given number of atoms or molecules / Avogadro's number n = N/ N_{0}, where n is number of moles, N is given number of atoms or molecules and N_{0} is Avogadro's number Let us see some solved examples to understand how to use the above formulas;i) Calculate the number of moles in 52 g or Helium (He) Atomic mass of He = 4u Molar mass of He = 4g So, the number of moles = given mass / molar mass n = m / M, where m is given mass in grams and M is molar mass So, n = 52 / 4 = 13 moles ii) Find number of moles in 12.044 x 10^{23} number of He atoms The number of moles = given number of particles / Avogadro's number n = N/ N_{A} = 12.044 x 10^{23} / 6.022 x 10^{23} = 2 moles iii) Calculate the mass 0.5 mole of N_{2} gas Sol. n = m / M (number of moles = mass in grams / molar mass) Gram molecular mass of N_{2} gas is 28 g. m = n x M (M is molar mass = gram molecular mass) = 0.5 x 28 g = 14 g iv) Calculate mass of 0.5 mole of N atoms m = n x M Here, M is gram atomic mass of N, which is 14 g m = 0.5 x 14 g = 7 g v) Calculate mass of 3.011 x 10^{23} number of N atoms Number of particles or atoms = number of moles x Avogadro's number N = n x N_{0} No. of moles, n = N / N_{0} = 3.011 x 10^{23} / 6.022 x 10^{23} = 0.5 mole Now, 3.011 x 10^{23} number of N atoms = 0.5 mole Now apply formula, m = n x M (mass = number of moles x molar mass) Here, M is gram atomic mass of N = 14 g m = 0.5 x 14 = 7 g vi) Calculate mass of 6.022 x 10^{23} number of N2 molecules m = n x M or (mass = number of moles x molar mass) N = n x N_{0} (given number of particles = number of moles x Avogadro's no.) 6.002 x 10^{23} = no of moles x 6.002 x 10^{23} So, no of moles (n) = 1. Mass, m = n x M = 1 x 48 g = 48 g. Here, Molar mass = gram molecular mass of Nitrogen, which is 48 g.
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