Counting by Weighing

1. Counting by Weighing

2. Who wants to count 100 M&M’s? • Suppose you work at a candy store…would you want to count out M&M’s one by one? • If you think about it, it makes way more sense to use a scale and count the M&M’s by weighing them • What would you need to know?

3. Average Mass • Obtain the mass of 5 different M&M’s. • How do we determine the average mass? • For counting purposes we assume all the items behave as though they were identical.

4. Now what if we have 2 kinds of candy? • I want one bag of gum drops and one bag of M&M’s but they both need to have EXACTLY the same number of items. • How would I figure this out?

5. MAIN IDEA!!! • Items can have different masses yet represent the same number of items.

6. Atomic Masses Counting by Weighing

7. Keep in mind the gum drop/M&M example • Atoms are extremely TINY so normal units like grams and kilograms are way to LARGE. • For example, the mass of a single carbon atom is 1.66 x 10-24 grams

8. Atomic Mass Units (amu) • To avoid using exponents like 10-24 , scientists defined a much smaller unit of mass called atomic mass units (amu) • 1 amu = 1.66 x 10-24 grams

9. Using Atomic Mass Units • Let’s think about • Average Atomic Mass = 12.01 amu • What mass of carbon atoms must we have to have 1000 carbon atoms present?

10. Using Atomic Mass Units Continued… • We weigh a pile of carbon atoms and the result is 3.00 x 1020amu. How many carbon atoms are present? • Recall 1 carbon atom = 12.01 amu

11. Using Atomic Mass Units Continued… • These principles and calculations apply to all of the other atoms • Atomic mass on the PTE refers to amu • Do the following: 1. What is the mass in amu of a sample containing 75 aluminum atoms? 2. Calculate the number of sodium atoms present in 1172.49 amu.

12. THE MOLE!!!!! • AMU’s are extremely small units • In lab, we commonly use grams. How do we count atoms in samples with masses given in grams?

13. Visual representations • If we weigh out samples of all the elements such that each sample has a mass equal to that element’s average atomic mass in grams, these samples all contain the same number of atoms

14. The Mole • This number (the number of atoms presents in all the samples) is called the mole. • Mole = the number equal to the number of carbon atoms in 12.01 grams of carbon • This number has been determined to be 6.022 x 1023 (Avogadro’s number)

15. The Mole • One mole of something always contains 6.022 x 1023 units of that substance. • Think about the concept of 1 dozen • A sample of an element with a mass equal to that element’s average atomic mass expressed in grams represents 1 mol of atoms 12.011 grams of Carbon= 1 mole of carbon

16. Using the mole in calculations • A sample of hydrogen weighs 0.500 grams. How many moles of hydrogen are present? • What is the mass of 1 mole of hydrogen? • 1 mole of hydrogen = 1.008 g

17. Calculations Continued… • We know the mass of 1 mol of H atoms so we can determine the number of moles of H atoms in any other sample by comparing its mass with the with the mass of 1 mole of H atoms. • We can follow this process for any element

18. Calculations Continued… • Once we know how many moles of something we have, we can figure out how many individual units are present • 1 mole = ? Units • 1 mole = 6.022 x 1023 units • Recall our example…0.496 moles of H. How many atoms of H are present? • DIMENSIONAL ANALYSIS

19. Now you give it a try • Compute the number of moles and the number of atoms present in 10.0g of aluminum.

20. A more complicated example… • How many silicon atoms are present in a 5.68 mg sample of silicon.