The Mole

CA Standards

A dozen If I have a dozen eggs, how many is that? 12 If I have a dozen pencils, how many is that? 12 If there are a dozen people in the room, how many is that? Still 12. So if we were to say that a “dozen” is a specific quantity of anything, would that be right? A mole is like that – it is a quantity.

The Mole 1 dozen = 1 pair = 1 ream = 1 mole = 12 items 2 items 500 items x items So if we have a mole of pencils, how many is that? x pencils If we have a mole of water molecules, how many is that? x molecules

Avogadro’s Number x is called “Avogadro’s Number” in honor of the Italian chemist Amedeo Avogadro ( ). Amedeo Avogadro I didn’t discover it. Its just named after me! Basis for a mole:. There are exactly 12 grams of carbon-12 in one mole of carbon-12.

How much is a mole? The number x is a huge number. 1 mole of seconds represents a span of time 4 million times as long as the earth has already existed. 1 mole of marbles is enough to cover the entire earth to a depth of 50 miles! However, since atoms are so tiny, a mole of atoms or molecules is a perfectly manageable quantity to use in a reaction.

How much is a mole? copper aluminum iron iodine sulfur mercury

Let’s go back to the dozen eggs, dozen pencils, dozen people.... Table 3.1 Zumdahl Comparison of Mass of Various Elements ElementNumber of Atoms Present Mass of sample in grams Aluminum6.022 x Copper6.022 x Iron6.022 x Sulfur6.022 x Iodine6.022 x Mercury6.022 x

Representative Particles A representative particle is a general term that refers to one of these three choices: an atom:a single element, no bonds examples: He, Na, Cu a molecule: a molecular or covalent compound with only nonmetals examples: CO 2, H 2 O, NH 3 a formula unit: an ionic compound with a metal + cation and a nonmetal – anion. examples: NaCl, KI, Mg(OH) 2 A mole of He atoms would be 6.02 x He atoms. A mole of H 2 O molecules would be 6.02 x H 2 O molecules. A mole of NaCl would be 6.02 x NaCl formula units

Try a few… Specify whether each one of these is an atom, a molecule or a formula unit: LiF CH 4 MgCl 2 CH 3 COOH Ca(OH) 2 Fe NH 4 NO 3

Dimensional Analysis Before we start on any examples or calculations, let’s remind ourselves about our dimensional analysis strategy for solving problems. Our goal is to make units cancel out. We start with writing the “given” on the left side of the page, including units. Next we write the units we are trying to find on the right side of the paper, on the far side of the equals sign. Then we use conversion factors (all of which equal one) and organize them such that the units cancel out to give us our answer. One chain. No intermediates. All units written.

This is the Mole Roadmap. We will use it to convert between 1) moles, 2) representative particles, 3) mass and 4) volume of a gas.

Sample problem 7-2 atoms to moles conversion Sample problem 7-2 atoms to moles conversion

Representative Particles Watch out for these tricks: How many molecules are there in a mole of water?  1 mole of water = 6.02 x molecules of water How many atoms are there in a mole of water (H 2 O)?  1 mole of water has 6.02 x atoms of O and 2 x (6.02 x ) atoms of H  So all together there are 3 x (6.02 x ) atoms in one mole of H 2 O. That’s because there are 3 atoms per molecule of H 2 O.

Sample Problem 7-3 – atoms in a compound

Calculating Molecular Mass (or Molar Mass) Calculate the Molecular mass of carbon dioxide, CO 2. 1(12.0 g/mol) + 2(16.0 g/mol) =44.0 g/mol  One mole of CO 2 (6.02 x molecules) has a mass of 44.0 grams. That is the “molar mass” of CO 2.

Molar Mass There are actually three names for calculating the molar mass of a substance: –Gram atomic mass (gam) use for single atoms like Ar: 39.9 grams/mole –Gram molecular mass (gmm) use for covalent/molecular compounds such as H 2 O 2 (1.0) + 1 (16.0) = 18.0 grams/mole H 2 O –Gram formula mass (gfm) use for ionic compounds such as NaCl 1 (23.0) + 1 (35.5) = 58.5 grams/mole NaCl –All three are really the same idea. Just add up the masses for each atom in the substance to get the total.

Sample problem 7-5 – molar mass

Sample Problem 7-6 Conversion: moles to grams

Sample Problem 7-7 grams to moles conversion

Calculations with Moles: Converting moles to grams How many grams of lithium are in 3.50 moles of lithium? 3.50 mol Li = g Li 1 mol Li 6.94 g Li 24.3 This method with the lines is called the ladder method. Just thought I’d expose you to it, since some college teachers use it.

Calculations with Moles: Converting grams to moles How many moles of lithium are in 18.2 grams of lithium? 18.2 g Li = mol Li 6.94 g Li 1 mol Li 2.62

Calculations with Moles: Using Avogadro’s Number How many atoms of lithium are in 3.50 moles of lithium? 3.50 mol = atoms 1 mol 6.02 x atoms 2.11 x 10 24

Calculations with Moles: Using Avogadro’s Number How many atoms of lithium are in 18.2 g of lithium? 18.2 g Li = atoms Li 1 mol Li x atoms Li 1.58 x g Li1 mol Li (18.2)(6.022 x )/6.94

Standard Molar Volume Equal volumes of all gases at the same temperature and pressure contain the same number of molecules – Amedeo Avogadro At STP (Standard Temperature and Pressure is 0 o C and 1 atm or 101kPa) 1 mole of any gas occupies 22.4 liters of volume. So how many molecules are there in 22.4 L of N 2 at STP? How many atoms are there?

Calculations with Moles: Using Standard Molar Volume How many moles of hydrogen are in 100 L of hydrogen at STP? 100 L = mol 22.4 L 1 mol 4.64

Calculations with Moles: Using Standard Molar Volume How many liters are occupied by 3 moles of oxygen gas at STP? 3 mol = L 1 mol 22.4 L 67.2

The Mole Road Map

7.3 Percent Composition and Chemical Formulas

Example 7-10

Example 7-11

Empirical Formulas Percent composition data can be used to calculate the empirical formula of a compound. Percent composition data can be used to calculate the empirical formula of a compound. The empirical formula gives the lowest whole- number ratio of the atoms of the elements in a compound. The empirical formula gives the lowest whole- number ratio of the atoms of the elements in a compound. Empirical formulas can be interpreted at the microscopic or macroscopic level. Empirical formulas can be interpreted at the microscopic or macroscopic level. For example CO 2 can be interpreted as one carbon atom and two oxygen atoms For example CO 2 can be interpreted as one carbon atom and two oxygen atoms Or, it can be interpreted as one mole of carbon atoms and two moles of oxygen atoms. Or, it can be interpreted as one mole of carbon atoms and two moles of oxygen atoms. An empirical formula may or may not be equal to a molecular formula. For example hydrogen peroxide is H 2 O 2 but it’s empirical formula is HO. An empirical formula may or may not be equal to a molecular formula. For example hydrogen peroxide is H 2 O 2 but it’s empirical formula is HO.

Example 7-13

Example 7-13 continued