The Mole The mole is defined as the amount of a substance that contains as many elementary entities as there are atoms in exactly 12 g of carbon-12. This experimentally determined number is called Avogadro’s number (N A ). We normally round this to 6.022× mole = 6.022×10 23, just like 1 dozen = 12 or 1 gross = 144. N A = x

The Mole One mole each of some familiar substances: Activity: Do some research on the internet to answer the question. If you made a chain by linking 2.0 cm paperclips, how many times could the chain wrap around the earth? Aluminum Copper Water Salt (Sodium Chloride) Sugar (Sucrose) Helium (in balloon)

Calcium is the most abundant metal in the human body. A typical human body contains roughly 30 moles of calcium. Determine (a) the number of Ca atoms in a typical human body and (b) the number of moles of calcium in a sample containing 1.00×10 20 Ca atoms. Worked Example 2.3 Worked Example 2.3 Strategy Use Avogardo’s constant, 1 mole = 6.022×10 23, to convert from moles to atoms and from atoms to moles.

The molar mass ( M ) of a substance is the mass in grams of one mole of the substance. The molar mass of an element is numerically equal to its atomic mass. 1 mol C = g 1 C atom = amu The molar mass of a compound is the sum of molar masses of the elements it contains. 1 mol H 2 O = 2 ×1.008 g g = g 1 mol NaCl = g g = g Molar Mass 5.10

When expressing the molar mass of elements such as oxygen and hydrogen, we have to be careful to specify which form of the element we mean. For instance, the element oxygen exists predominantly as O 2. But we might also mean atomic oxygen (O). We must consider the context to tell which form of the element, O 2 or O, is intended. Molar Mass

Determine (a) the number of moles of C in g of carbon, (b) the number of moles of He in g of helium, and (c) the number of moles of Na in g of sodium. Worked Example 2.4 Worked Example 2.4 Strategy Molar mass of an element is numerically equal to its average atomic mass. Use the molar mass for each element to convert from mass to moles. Setup (a) The molar mass of carbon is g/mol. (b) The molar mass of helium is g/mol. (c) The molar mass of sodium is g/mol.

Interconverting Mass, Moles, and Numbers of Particles

Worked Example 5.14 Worked Example 5.14 Strategy Use molar mass to convert from mass to moles and to convert from moles to mass. The molar mass of carbon dioxide (CO 2 ) is g/mol and the molar mass of sodium chloride (NaCl) is g/mol. Determine (a) the number of moles of CO 2 in g of carbon dioxide and (b) the mass of mole of sodium chloride.

Worked Example 5.15 Worked Example 5.15 Strategy Use molar mass and Avogadro’s number to convert from mass to molecules. Use the molecular formula of water to determine the numbers of H and O atoms. (a) Determine the number of water molecules and the numbers of H and O atoms in 3.26 g of water.

The Gas Laws You are responsible for investigating the individual gas laws and for mastering all the conceptual and quantitative skills associated with them. The Ideal Gas Law can be more universally applied to solving problems involving gasses, so we will focus our lecture time on that. The properties of a gas and its quantitative behavior depend partially on the number of gas particles present. A mole is the unit we use to measure how many particles we have when we have A LOT of particles. 11.4

The Ideal Gas Equation The gas laws can be combined into a general equation that describes the physical behavior of all gases Boyle’s law Avogadro’s lawCharles’s law PV = nRT rearrangement R is the proportionality constant, called the gas constant.

The Ideal Gas Equation The ideal gas equation (below) describes the relationship among the four variables P, V, n, and T. PV = nRT An ideal gas is a hypothetical sample of gas whose pressure- volume-temperature behavior is predicted accurately by the ideal gas equation.

The Ideal Gas Equation The gas constant (R) is the proportionality constant and its value and units depend on the units in which P and V are expressed. PV = nRT

The Ideal Gas Equation Standard Temperature and Pressure (STP) are a special set of conditions where: Pressure is 1 atm Temperature is 0°C ( K) The volume occupied by one mole of an ideal gas is then L: PV = nRT

Worked Example 11.7 Strategy Convert the temperature in °C to kelvins, and use the ideal gas equation to solve for the unknown volume. Calculate the volume of a mole of ideal gas at room temperature (25°C) and 1 atm.

Worked Example 11.8 Carbon dioxide is effective in fire extinguishers partly because its density is greater than that of air, so CO 2 can smother the flames by depriving them of oxygen. (Air has a density of approximately 1.2 g/L at room temperature and 1 atm.) Calculate the density of CO 2 at room temperature (25°C) and 1.0 atm.

Study Guide for Sections 2.7, 5.10, DAY 17, Terms to know: Sections 2.7, 5.10, mole, Avogadro’s number, molar mass, Boyle’s Law, Charles’s Law, Avogadro’s law, combined gas law, ideal gas law, ideal gas, ideal gas constant, standard temperature and pressure (STP) DAY 17, Specific outcomes and skills that may be tested on exam 3: Sections 2.7, 5.10, Be able to use Avogadro’s number to convert from moles to number of items and vice versa Be able to use molar mass to convert grams to moles and vice versa Be able to use any of the conversion factors discussed so far to do multi-step conversions up to 4 steps Be able to explain how and WHY the pressure of a fixed amount of gas at a constant temperature changes when the volume of the gas is either increased or decreased Be able to explain how and WHY the volume of a fixed amount of gas at a constant pressure changes when the temperature of the gas is either increased or decreased Be able to explain how and WHY the pressure of a fixed amount of gas at a constant volume changes when the temperature of the gas is either increased or decreased Be able to explain how and WHY the volume of a gas at a constant pressure and temperature changes when the moles of gas is either increased or decreased Be able to explain how and WHY the pressure of a gas at a constant volume and temperature changes when the moles of gas is either increased or decreased Be able to use the ideal gas law to calculate any of the following four properties of a sample of gas given information about the other three: volume, pressure, moles, temperature

Extra Practice Problems for Sections 2.7, 5.10, Complete these problems outside of class until you are confident you have learned the SKILLS in this section outlined on the study guide and we will review some of them next class period

Prep for Day 18 Must Watch videos: (real vs. ideal, Isaacs) (real gas, crash course chemistry) (liquid properties, Isaacs) (liquid properties II, Isaacs) (evaporation, Tyler DeWitt) (solids, crash course chem) Other helpful videos: (UV-Berkeley, lesson 16) (gas demos) (liquid properties, HCL) 0&list=PLqOZ6FD_RQ7mco4Yb_aYDD8wHMPVYhQrUhttps:// 0&list=PLqOZ6FD_RQ7mco4Yb_aYDD8wHMPVYhQrU (UV-Irvine) Read Sections ,