# Stoichiometry: Moles, Atoms, & Formulae

### Atomic Mass

• Determination by Mass Spectrometry: see text, pp 80-81. Basically have an "ion gun" to provide a focused beam, then a magnetic selection system (recall how we could move electron beam in Crooke's tube) to select/determine mass, and finally a detection system (measures current from ions). Mass spectrometry today is a key tool in environmental chemistry analysis and monitoring as well as a super-senstive system for detecting isotopes such as 14C.

Recall 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? (27 atoms)(16.00g/atom) = 432.0 amu
• in grams? (27atoms)(16.00g/atom)(1g/[6.022 x x 1023]) = 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? (3.45g)(1mol/63.55g)(6.022 x 1023atom/mol) = 3.27 x 1022atoms
• A 2.34 mole sample of sulfur contains
• how many grams of sulfur? (2.34mol)(32.06g/mol) = 75.0 g
• how many atoms of sulfur? (4.52 x 1025)

### 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:

= 63. 56 amu/atom

An example of the reverse problem can be found on the posted Final, number II.3.

Most samples of matter consist of combinations of atoms or ions to give compounds characterized by molecules or formulae. We are thus interested in molecular masses, formula masses etc.

Examples:

• What is the weight of 0.25 mole of:
• KBr?

0.25 mole x (39.10 g/mole + 79.90 g/mole) = 29.75 g = 3.0 x 101g

• glucose? (C6H12O6)

so weight = 0.25 mole x (6 [12.01]g/mole + 12 x [1.008 g/mole] + 6 [16.00] g/mole) = 45.04 g = 45 g

• How many moles are there in 23.5 g of:
• sucrose (C12H22O11)

so MW = (12 [12.01]g/mole + 22 x [1.008 g/mole] + 11 [16.00 ] g/mole) = 342.30 g/mole

and moles = (23.5 g)/(342.30 g/mole) = 6.865 x 10-2mole = 6.87 x 10-2mole.

• How many moles are there in 23.5 g of NaCl?
• How many moles are there in 23.5 g of propane (C3H8)?

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