Experiment #5

Avagadro’s Number 6.02 x 10 23

And The Standard Deviation

x S

Introduction

► Purpose: Relate a gram formula weight to Avogadro’s number by

using the dimensional analysis approach and determine the

correct number of significant figures in your applications.

Compute the standard deviation for the volume of water

delivered by a 10 mL Graduate Cylinder.

Key Ideas

►Amu Vs. Gram –►Atom Vs. Ion – ►Atom Vs. Mole – ►Formula Weight –►GFW,GAW,GMW –►Dimensional Analysis –►Standard Deviation –

Just How Big is a Mole?Just How Big is a Mole?

► Enough soft drink cans to Enough soft drink cans to cover the surface of the earth to cover the surface of the earth to a depth of over 200 miles. a depth of over 200 miles.

► If we were able to count atoms If we were able to count atoms at the rate of 10 million per at the rate of 10 million per second, it would take about 2 second, it would take about 2 billion years to count the atoms billion years to count the atoms in one mole. in one mole.

Volume of a penny - 3.60 x Volume of a penny - 3.60 x mm mm 33

Volume of Earth = Volume of Earth = ~1.0832073×10~1.0832073×101818 mm³  mm³

Volume of Volume of JupiterJupiter = = 1.43128×101.43128×102121 mm³  mm³

Atom Vs. Mole

Mole

6.02X10 23 Atoms

Larger mass measured in grams

Larger in size Can be seen

Atom

1 Atom

Very small mass measured in Amus

Very Small in sizeCan’t be seen

Amu Vs. Gram

Amu – We use if we are talking about the mass of an atom. Ex. the mass of an iron atom is 55.8 amus.

Gram – We use if we are talking about the mass of a moleor fraction of a mole. Ex. The mass of one mole of iron is55.8 grams.

Formula weight – the mass of the collection of atoms represented by a chemical formula. For Ex. water contains two hydrogen atoms and one oxygen atom.

1 x 16.00 (mass of O) = 16.00

2 x 1.01 (mass of H) = + 2.02

Formula Weight 18.02

The formula weight tells us the mass of one mole of our substance.

Formula Weight

GFW – Gram Formula Weight

This refers to the mass of an ion or ionic compound Ex. Mass of a Cl-

GAW – Gram Atomic Weight

This refers to the mass of a atomEx. Mass of a Cl atom

GMW Gram Molecular WeightThis refers to the mass of a

molecule or molecular compound Ex. Mass of one molecule of H2O

How do Avagadro’s number, Mole and GAW Apply to each

other? ►One mole of Tin has a mass of

118.69g. ►One atom of Tin has a mass of 118.69

Amu.►One mole of Tin contains 6.02X1023

atoms.

Dimensional Analysis

1000mm

1mor

1m

1000mm

Convert 10 m to mm Remember 1 m = 1000mm

They both mean the same thing it all depends on what you need.

Dimensional Analysis

mm100001m

1000mm

1

10m

1

10m# 1

# 3

# 2

Mult. left to rightdivide top to bottom

What you are given always over 1

The 1 is a filler.

The unit you want to eliminate is placed in the lower right so it will cancel out with your original unit.

Keep in mind

X going and / going

t want don'you

needyou

1

start with

Ex#1 pg 51

MW

Gm

Find the # of moles in the sample of Tin. Giventhe sample has a mass of 29.04g mw

1gm

Sn of .245mSn of 118.70g

Sn of 1m

1

Sn of 29.04g

Chart on pg 55

“Everything is based off of one mole”

To determine the g formula wt.determine the atomic mass of all atoms present

Example 1 mole of H2O – 18.00grams

Chart on pg 55

“Everything is based off of one mole”

To determine #g / moleculeFind the # grams per mole / number of molecules

Example 2 1 mole of H2O = 18.00grams

18.00grams / 6.02x1023 molecules = 2.9x10-23

#g/molecule = 2.9x10-23

Chart on pg 55

“Everything is based off of one mole”

To determine # of moles use dimensional analysis

Grams to moles

Example 3

35.4 g Cu 1 mol Cu 63.5 g Cu

= .58mol

Chart on pg 55

“Everything is based off of one mole”

To determine the number of atoms per mole add up the number of atoms in the formula

Example 4

H2O = 3 atoms

Standard Deviation

► This is how much your value is off from the actual answer. Can be used as a correction factor.

► Ex. A 1mL pipette delivers 1mL + or - .007mL So the pipette

delivers .9993mL or 1.007 mL. X = Avg

Standard Deviation Ex.

1 mL Pipette

1.02gM H2O

1.01g1.01g1.01g 1.02g

Density of H20 = 0.9982 g/mL

1.02mL1.02mL

1.01mL

1.02mL1.01mLVol. of pipet

Use V= M/D to determine volume delivered

Mass of

Beaker &

water

109.50g

111.53g

109.50g

109.50g

111.53g

110.51g

Mass of

Beaker

110.51g

110.51g

110.51g

110.51g

N= number of trials

∑(Xi-X avg.)2

1-n

x - x2

iS

Xi-Xavg. (a)1.01-1.02=.01(b)1.02-1.02= 0(c)1.01-1.02=.01(d)1.02-1.02= 0(e)1.02-1.02= 0

X avg.= 1.02 mL#1

#2

#3 (Xi-Xavg.)2

(a).01 =1.0X10-4

(b) 0 = 0(c).01 =1.0X10-4(d) 0 = 0(e) 0 = 0

#4 #5 ∑(Xi-X avg.)2 /N-1

#6 Take Square Root of Step #5

Final Answer: +/- 0.007 mL.

Due Next Week

►Pages 51 & 53 we are determining the number of atoms / ions or moles that are asked for.

►YOU MUST SHOW ALL WORK FOR CREDIT!!

►Page 55 complete the table and show all work.

►Pages 61 determine the St. Dev. for 1 mL pipette ( I do as a example)

►Page 63 determine the St. Dev. for a 10mL. graduated cylinder.