Chem 109 - General Chemistry - Spring 2011

Lecture Notes 6: 31 January

The Nuclear Atom, cont.

Atomic number (Z) - the number of protons in the nucleus. This number is characteristic of a given element.
Atomic mass number (A) - the sum of the protons and neutrons in a given atom (p + n).
Atomic mass - the actual mass of an average atom in a sample. The characteristic atomic masses for Earth are shown on periodic tables.
Atomic Mass Unit: the atomic mass unit = amu is a unit of mass for atoms. It is defined as 1/12 the mass of one atom of ¹²C, where the mass of ¹²C is defined as 12 exactly.

Isotopes

Isotopes are forms of elements which differ only in the number of neutrons. This means different isotopes of the same element have essentially the same chemical properties but slightly different physical properties. They can also differ substantially in terms of their nuclear stability. Let's look at some examples of isotopes:

Symbol Z A p n e^-

¹⁴C 6 14 6 8 6

²³⁸U⁶⁺ 92 238 92 146 86

³⁵Cl^- 17 35 17 18 18

¹⁸O^2- 8 18 8 10 10

You should be able to fill in the blanks in a table like this with, the aid of a periodic table, on a quiz.

Stoichiometry

Stoichiometry is the quantitative study of the composition of compounds (e.g. determining the ratios of atoms in a molecule) and/or the ratios of substances in chemical reactions.

The Mole

This is the SI unit of amount of substance. 1 mole = the number of carbon atoms in 12 g of ¹²C. This number, called Avogadro's Number, has been measured as 6.022 x 10²³ mol^-1 (current value: 6.022 141 99 x 10²³mol^-1). Notice that this number can refer to anything (a mole of eagles, a mole of pennies, etc.). In each case we are talking about 6.022 x 10²³ items or entities.

For chemists a mole has two common uses:

It refers to Avogadro's Number of entities.
It refers to the atomic weight (or formula weight or molecular weight) of a substance expressed in grams. Thus a mole of sodium is 22.99 g of sodium (which contains 6.022 x 10²³ atoms of sodium!).

Note that Avogadro's number, 6.022 x 10²³ is thus the conversion factor from amu's to grams!

Mole Samples Demo

Atomic Mass

Determination by Mass Spectrometry: see text, pp 80-81.

Notice that atomic masses have two meanings:

At the microscopic scale (atoms, ions and molecules) it is the mass in amu's of a single atom etc.
At the macroscopic scale (visible amounts of stuff) it is the mass in grams of a mole of atoms etc.

Examples:

What is the mass of 27 atoms of oxygen

in amu's? (432.0 amu)
in grams? (7.174 x 10^-22g)

Given 3.45 grams of copper

how many moles of copper is this? (0.0543 mole)
how many atoms of copper are there in this sample? (3.27 x 10²²)

A 2.34 mole sample of sulfur contains

how many grams of sulfur? (75.0 g)
how many atoms of sulfur? (1.41 x 10²⁴)

Determination of Atomic Mass

We want to be able to figure out the atomic mass of a sample with a particular isotopic composition.

Example: Cu occurs as an isotopic mixture of 69.09% ⁶³Cu (mass = 62.93 amu) and 30.91% ⁶⁵Cu (64.93 amu). What is the atomic mass of copper in this sample?

Assume the sample consists of 1 atom for convenience, then

(0.6909 atoms)(62.93 amu/atom) + (0.3091 atoms)(64.93 amu/atoms) =

43.478 amu + 20.070 amu = 63.558 amu for 1 atom

= 63. 558 amu/atom

How about sig figs? 1 is a count, therefore exact. The two multiplications each have 4 sig figs so the calculations each have 4 sig figs (note I keep one extra, that is 5 sig figs, in the calculations to avoid rounding errors.) . For the addition we use the add/subt. rule and look at decimal place, for our four sig figs the hundredth's place is then the sig fig (again, during calculation its best to keep one extra sig fig to avoid rounding errors). The final answer then has 4 sig figs: