1. A mole always contains the same number of particles; however, moles of different substances have different masses. Section 2: Mass and the Mole K What I Know W What I Want to Find Out L What I Learned

2. 8(B) Use the mole concept to calculate the number of atoms, ions, or molecules in a sample of material. 8(A) Define and use the concept of a mole. 2(G) Express and manipulate chemical quantities using scientific conventions and mathematical procedures, including dimensional analysis, scientific notation, and significant figures. Mass and the Mole Copyright © McGraw-Hill Education

3. Essential Questions Why can the mass of an atom be related to the mass of a mole of atoms? How can the number of moles be converted to the mass of an element and vice versa? How can the number of moles be converted to the number of atoms of an element and vice versa? Mass and the Mole Copyright © McGraw-Hill Education

4. Review conversion factor New molar mass Mass and the Mole Copyright © McGraw-Hill Education Vocabulary

5. The Mass of a Mole 1 mol of copper (6.02 x 10 23 atoms of copper) and 1 mol of carbon (6.02 x 10 23 atoms of carbon) have different masses. One copper atom has a different mass than 1 carbon atom. Molar mass is the mass in grams of one mole of any pure substance. The molar mass of any element is numerically equivalent to its atomic mass and has the units g/mol. Mass and the Mole Copyright © McGraw-Hill Education

6. Molar Mass Concepts in Motion FPO Add link to concepts in motion animation from page 326 here. Mass and the Mole Copyright © McGraw-Hill Education

7. Using Molar Mass Moles to mass 3.00 moles of copper has a mass of 191 g. Mass and the Mole Copyright © McGraw-Hill Education

8. Mass and the Mole Copyright © McGraw-Hill Education MOLE-TO-MASS CONVERSION Use with Example Problem 2. Problem Chromium (Cr), a transition element, is a component of chrome plating. Chrome plating is used on metals and in steel alloys to control corrosion. Calculate the mass in grams of 0.0450 mol Cr. Response ANALYZE THE PROBLEM You are given the number of moles of chromium and must convert it to an equivalent mass using the molar mass of chromium from the periodic table. Because the sample is less than one-tenth of a mole, the answer should be less than one-tenth of the molar mass. KNOWN Number of moles = 0.0450 mol Cr Molar mass Cr = 52.00 g/mol Cr UNKNOWN Mass Cr = ? G

9. Mass and the Mole Copyright © McGraw-Hill Education MOLE-TO-MASS CONVERSION EVALUATE THE ANSWER The known number of moles of chromium has the smallest number of significant figures, three, so the answer is correctly stated with three digits. The answer is less than one-tenth the mass of 1 mol, as predicted, and is in grams, a mass unit.

10. Using Molar Mass Convert mass to moles with the inverse molar mass conversion factor. Convert moles to atoms with Avogadro’s number as the conversion factor. This figure shows the steps to complete conversions between mass and atoms: Mass and the Mole Copyright © McGraw-Hill Education

11. Mass and the Mole Copyright © McGraw-Hill Education MASS-TO-MOLE CONVERSION EVALUATE THE ANSWER The mass of calcium has the fewest significant figures, three, so the answer is expressed correctly with three digits. As predicted, the answer is greater than 10 mol and has the expected unit. Use with Example Problem 3. Problem Calcium (Ca), the fifth most abundant element on Earth, is always found combined with other elements because of its high reactivity. How many moles of calcium are in 525 g Ca? Response ANALYZE THE PROBLEM You must convert the mass of calcium to moles of calcium. The mass of calcium is more than ten times larger than the molar mass. Therefore, the answer should be greater than 10 mol. KNOWN Mass = 525 g Ca Molar mass Ca = 40.08 g/mol Ca UNKNOWN Number of moles Ca = ? mol

12. Mass and the Mole Copyright © McGraw-Hill Education MASS-TO-ATOMS CONVERSION Use with Example Problem 4. Problem Gold (Au) is one of a group of metals called the coinage metals (copper, silver, and gold). How many atoms of gold are in a U.S. Eagle, a gold alloy bullion coin with a mass of 31.1 g Au? Response ANALYZE THE PROBLEM You must determine the number of atoms in a given mass of gold. Because you cannot convert directly from mass to the number of atoms, you must first convert the mass to moles using the molar mass. Then, convert moles to the number of atoms using Avogadro’s number. The given mass of the gold coin is about one-sixth the molar mass of gold (196.97 g/mol), so the number of gold atoms should be approximately one-sixth Avogadro’s number. KNOWN Mass = 31.1 g Au Molar mass Au = 196.97 g/mol Au UNKNOWN Number of atoms Au = ?

13. Mass and the Mole Copyright © McGraw-Hill Education MASS-TO-ATOMS CONVERSION EVALUATE THE ANSWER The mass of gold has the smallest number of significant figures, three, so the answer is expressed correctly with three digits. The answer is approximately one-sixth Avogadro’s number, as predicted, and the correct unit, atoms, is obtained.

14. Mass and the Mole Copyright © McGraw-Hill Education ATOMS-TO-MASS CONVERSION Use with Example Problem 5. Problem Helium (He) is an unreactive noble gas often found in underground deposits mixed with methane. The mixture is separated by cooling the gaseous mixture until all but the helium has liquefied. A party balloon contains 5.50 × 10 22 atoms of helium gas. What is the mass, in grams, of the helium? Response ANALYZE THE PROBLEM You are given the number of atoms of helium and must find the mass of the gas. First, convert the number of atoms to moles, then convert moles to grams. KNOWN number of atoms He = 5.50 × 10 22 atoms He molar mass He = 4.00 g/mol He UNKNOWN mass = ? g He

15. Mass and the Mole Copyright © McGraw-Hill Education Atoms-to-Mass Conversion EVALUATE THE ANSWER The answer is expressed correctly with three significant figures and is in grams, a mass unit.

16. Mass and the Mole Copyright © McGraw-Hill Education Review Essential Questions Why can the mass of an atom be related to the mass of a mole of atoms? How can the number of moles be converted to the mass of an element and vice versa? How can the number of moles be converted to the number of atoms of an element and vice versa? Vocabulary molar mass