The Mole Concept

Relative Mass The relative mass of an object is the mass of that object as a multiple of some other object’s mass. In the example, the mass of 5 oranges equals the mass of 2 grapefruits. The ratio (fraction) of the heavier grapefruit to the Lighter orange is 5 : 3 or 5 oranges = 1.67 oranges 3 grapefruits 1 grapefruit The mass of a grapefruit in terms of an orange is a relative mass.

Finding the Mass of Atoms: Relative Masses Since an atom is much too small to weigh on any balance, scientists have decided to express their mass compared to some atom that is arbitrarily assigned some mass number. For example, a hydrogen atom has a mass of 1.67 E -24 g. A oxygen atom has a mass of 2.66 E -23 g. If hydrogen (the lighter atom) is assigned a mass of 1, then the relative weight of the oxygen atom to the hydrogen atom is: 2.66 E -23 g oxygen atom = 15.9 O approx. = 16 O 1.67 E -24 g hydrogen atom 1 H 1 H O: H:

The Mass of Carbon Atoms Relative to Hydrogen Hydrogen atoms are the lightest so a ratio is made of the heavier carbon atom to the lighter hydrogen atom. a carbon atom = 2.0 E -23 g = 12 a hydrogen atom 1.67 E -24 g 1 A carbon atom is 12 times more massive (heavy) than a hydrogen atom. The weight of carbon as 12 is a weight relative to hydrogen which is assigned a weight of 1. C: H:

Isotopes: Atoms of the Same Kind Differing in Mass In nature atoms of one kind (like carbon atoms) are not identical. Atoms of one kind can differ slightly in their masses. Some carbon atoms have a relative mass of 12 (relative to hydrogen) while other carbon atoms have a mass of 13 and still others have a mass of 14. Atoms of the same kind that differ slightly in their masses are called isotopes. carbon isotopes: carbon-12 carbon-13 carbon-14

Percentages of Carbon Isotopes % of carbon atoms have a mass of 12. (relative to H) 1.11 % of carbon atoms have a mass of 13. (rel. to H) % of carbon atoms have a mass of 14. (rel. to H) In a typical sample of carbon the average mass of an atom is 12(.9889) + 13(.0111) = = about 12 (relative to H)

Hydrogen Makes a Poor Standard Hydrogen is the lightest element so it is convenient to assign it a value of 1. However hydrogen is not common on earth, it is explosive to work with, it is a gas at room temperature – all properties that make it an inconvenient mass standard. The IUPAC world organization of chemists decided to make the carbon-12 isotope (assigned a mass of 12u) the mass standard to which the masses of all the atoms of the various elements are compared. Carbon is a solid, fairly unreactive and very common on earth. One u is an atomic mass unit (sometimes designated as amu) and has a value of 1.67 E -24 g. A magnesium atom with a relative mass of 24u has a mass that is twice that of carbon-12.

Gay-Lussac’s Law of Combining Gas Volumes In 1802, Joseph Louis Gay-Lussac published his Law of Combining Gas Volumes. This law says that the ratio between the volumes of the reactant gases and the products can be expressed in simple whole numbers. When nitrogen gas and hydrogen gas react to form ammonia gas, 3 volumes of hydrogen combine with 1 volume of nitrogen to form 2 volumes of ammonia. Note ammonia has a chemical formula of NH 3

Another Example of Gay-Lussac’s Law Two volumes of hydrogen gas react with 1 volume of oxygen gas to produce 2 volumes of water gas (steam). 1 volume of hydrogen gas reacts with 1 volume of chlorine gas to produce 2 volumes of hydrogen chloride gas.

Other Examples of Gay-Lussac’s Reacting Gas Law Under one set of conditions of temperature and pressure, 2 L of nitrogen gas react with 1 L of oxygen gas to make 1 L of dinitrogen oxide gas (N 2 O) Under another set of conditions of temperature and pressure, 1 L of nitrogen gas react with 1 L of oxygen gas to make 1 L of nitrogen monoxide gas (NO) Under yet another set of conditions of temperature and pressure, 1 L of nitrogen gas react with 2 L of oxygen gas to make 1 L of nitrogen dioxide gas (NO 2 )

John Dalton’s Atomic Theory John Dalton, an English teacher, in 1803 read a paper in which he proposed an atomic theory – that all substances are composed of hard, indivisible particles called atoms. This paper was published in 1805 and distributed to scientists worldwide.

The Main Points of Dalton’s Atomic Theory 1.All matter is composed of atoms which are hard, indivisible particles. 2.Atoms cannot be made or destroyed. 3.All atoms of the same element are identical. Different elements have different types of atoms. 4.Chemical reactions occur when atoms are rearranged Compounds are formed from atoms of the constituent elements. 5.The relative masses of two atoms can be determined by using experimental mass ratios of two elements in a compound and by assuming that the simplest number ratio of 1 atom of one kind : 1 atom of the other kind applies when there is just one compound of the two elements. For example in the compound of magnesium and oxygen the experimental mass ratio is g Mg : 1 g O. If 1 atom of Mg is joined to 1 atom of O, then a Mg atom is times more massive than an O atom.

Dalton’s Theory Explained and Predicted Chemical Laws Dalton’s Atomic Theory explained the Law of Definite Composition because if atoms have definite masses and if they always combine in a fixed number ratio in a compound, then it follows that there will be a fixed mass ratio of one element to another. Ex. 1 Mg reacts with 1 O to form MgO The mass of each Mg is and the mass of each O is so the mass ratio in the compound will be 1(24.305) : 1( ) = : 1 The mass ratio in the compound water is 1(15.994) O : 2(1.0079) H = 7.94 : 1 If there is more than one compound between two elements, then the ratio by mass of one element to the second element will be in a whole number ratio between the two compounds. This is called the Law of Multiple Proportions.

Explaining Gay-Lussac’s Law: Avogadro In 1811 an Italian chemist, Amadeo Avogadro, wrote a paper making a bold assertion to explain Gay-Lussac’s Law. Avogadro proposed that: Equal volumes of gases at the same temperature and pressure contain equal numbers of atoms. This statement is referred to as Avogadro’s hypothesis. Today we use this statement changing the last word atoms to particles.

How Avogadro’s Hypothesis Explained Gay-Lussac’s Law

John Dalton Objects to Avogadro’s Explanation Dalton in his atomic theory stated that atoms can not be divided. Avogadro’s hypothesis required that in many reactions the reactant atoms must be severed in half to maintain the equal number of particles principle. Dalton strongly felt this was incorrect and in print lambasted Avogadro and Gay-Lussac for their ideas and poor experimental methods. John Dalton Amadeo Avogadro

Stanislao Cannizzaro In 1860 the Italian Stanislao Cannizzaro harmonized the indivisible atom idea of Dalton with Avogadro’s hypothesis by recognizing the existence of molecules. Cannizzaro also demonstrated how his ideas could be used experimentally to determine the relative masses of atoms.

The Atomic Mass of an Element The atomic mass of an element is a weighted average of the weights of the isotopes of that element. For example, chlorine has two main isotopes, chlorine-35 ( 75.77%) and chlorine-37 (24.23%). The weighted average of these two is.7577(35u) (37u) = 35.48u = about 35.5u

35.5 u of Cl and 35.5 g of Cl 35.5u of Cl is the mass of an average Cl atom (much too small to be weighed on a balance) 35.5 g of Cl can be weighed on a balance. Chemists have discovered that 35.5 g of Cl has 6.02 x atoms of Cl. This number of atoms of Cl is referred to as one mole (mol) of Cl or Avogadro’s number.

Mass Ratios of Single Atoms vs Equal Numbers of Atoms The mass ratio of 1 hydrogen atom to 1 oxygen atom is 1u : 16u = 1 : 16 The mass ratio of 100 H atoms to 100 O atoms is 100u : 1600u = 1 : 16 also The mass ratio of 2500 H atoms to 2500 O atoms is 2500u : u = 1 : 16 also Thus the mass ratio of equal numbers of atoms of different kinds is the same as the mass ratio of one atom of each kind.

What is True When Element Mass Ratios = Single Atom Mass Ratios? Example : 25 g of hydrogen atoms is compared to 400 g of oxygen atoms. What must be true in terms of numbers of atoms? Consider that 25g : 400g = 1 : 16

Comparing 35.5 g of Cl to 1 g of H The mass ratio of 1 H atom to 1 Cl atom is 1u : 35.5u 35.5 g of Cl contains 6.02 x atoms What must be true about 1g of H?

Expressing the Atomic Mass in g Whenever an atom’s average mass is expressed in g, this quantity has one mole or 6.02 x atoms in it. Mg has an Atomic Mass of u so g of Mg has ______________ atoms. Pb has an Atomic Mass of u so g of Pb has _______________ atoms.

The Mole: Avogadro’s Number The number 6.02 x is called the mole or Avogadro’s number. This number was determined by chemists other than Avogadro but they named this number in Avogadro’s honour.

Determining the Mass of a Mole (mol) of a Compound How much mass does one mol of H 2 O have? One mol of H 2 O has 2 mol of H which has a mass of 2(1.008 g) = g 1 mol of O which has a mass of 1( g) = g g

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