# Lecture 1-03 Dimensional Analysis and Mole Concepts

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```					Lecture 1-03: Dimensional Analysis and Mole Concepts                                            Examples

Quantitative Measurement: measurements associated with                                       These prefixes represent huge scale variations.
numbers
Length
Common prefixes are listed below and should be memorized.                                             - wavelength of an X-ray is 10-10 m or 0.1 nm (nanometres)
Additional prefixes may be found in Table 1.2, page 9 of Petrucci:                                    - size of universe is 1025 m (metres) or 107 Em (exametres)
x Giga                                      (G)   109
x mega                                      (M)   106                                          Mass
x kilo                                      (k)   103                                                      - mass of an electron is 10-30 kg (kilograms)
x deci                                      (d)   10-1                                                     - mass of the universe is 1020 Gg (gigagrams)
x centi                                     (c)   10-2
x milli                                     (m)   10-3                                         Time
x micro                                     (µ)   10-6                                                     - period of vibration of a radio wave is 1 s
- period of vibration of a microwave is 100 ps (picoseconds)
x nano                                      (n)   10-9
x pico                                      (p)   10-12

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Precision and Accuracy                                                                          Significant Figures in Scientific Calculations

x Precision refers to how closely individual experimental                                      x All scientific measurements have uncertainty associated with
readings agree with one another.                                                               them. The data are recorded so that only last digit has
uncertainty associated with it.
x Accuracy refers to how closely experimental readings agree
with the true values.                                                                        x See “Handout 1-03. Significant Figures Rules” to see rules for
determining the number of significant figures in a measured
value and how significant figures are treated during
calculations. Understanding this will save you 5% in this
course.

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Dimensional analysis (using units to help you make calculations)                                To use dimensional analysis, ask the following questions:
will be used in this course in most problem solving.
x What data are given in the problem?
Dimensional Analysis is your friend.                                                                  x What quantity am I trying to find?
x Never leave units off of a number                                                                 x What conversion factors do I require to take me from the
x You are better off leaving off the numerical part of the                                            given to the required quantity?
number and working ONLY with the units
Example
The units must correctly cancel out.                                                            The density of a gas is 0.0013 g/cm3. Find the density of this gas
x The units left after that process must be the correct units for                              in kg/L.

Only then should you calculate the numerical portion of your

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The Mole Concept                                                                               Avogadro’s number is 6.022 x 1023. This number is huge.

x atoms and molecules are extremely small
x measurable amounts of substance involve many atoms and                                     If Avogadro’s number of pennies was distributed evenly among
molecules                                                                                  the 4.9 x 109 human inhabitants of the earth, each person could
spend        \$1 000 000 ever hour of every day until death and
x amounts of atoms and molecules are measured in terms of                                    would still have over half of their share of the money unspent.
moles where a mole (abbreviation mol)is defined as quantity of
matter containing as many elementary particles as found in
0.012 kg of 12C.

x mole may also be thought of as quantity of matter containing

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Molar mass (M):

x mass of one mole (Avogadro’s number) of atoms, molecules
or other particles
x units of molar mass: grams per mole (g/mol or g.mol-1)

Example
Find the molar mass of sodium sulfite.

Clockwise from top are one mole quantities of graphite (C),
potassium permanganate (KMnO4), copper (II) sulfate
pentahydrate (CuSO4.5H2O), copper (Cu), sodium chloride
(NaCl)and potassium dichromate (K2Cr2O7). Antimony (Sb) is in
the centre.

Each one mole quantity has a different mass and volume.

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Molar volume:                                                                                 Mole Relationships –“the hub”
Mole, mass, volume and number of particles related as follows.
x volume occupied by 1 mol (Avogadro’s number) of a                                                            Gas Volume
Mass
substance                                                                                                                                                                Symbol m
Symbol V
(g)
x units: L or m3 ( 1 m3 = 1000 L).                                                                                 (L)

x Molar volumes are most commonly used for gases.
PV = nRT                                                     n = m/M
Number of
For example:                                                                                                                                         Moles
Symbol n
o One mole of any gas @STP (standard temperature and                                                                                           (mol)
n = # particles/No                                               C = n/V
pressure) has volume of 22.711 L
o Note: STP means 273.15 K (0oC) and 100.000 kPa (1 bar)
Number of                                                Concentration of
o STP used to be considered as 273.15 K (0oC) and                                                            Atoms or                                                    a Solution
101.326 kPa (1 atm) and had a value of 22.414 L. IUPA                                                      Molecules                                                   Symbol C
(molsolvent/Lsol)
recommends that this definition be discontinued.

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Meaning of symbols                                                                               Example #1
x R is the ideal gas constant equal to 8.3145 J/mol.K, 8.3145                                   Calculate the mass of 1.00 L of oxygen gas at 273oC and 202
kPa.L/mol.K, 0.082058 L.atm/mol.K                                                             kPa.
x P is gas pressure measured in kilopascals (kPa or atm)
x V is gas volume measured in litres (L)
x T is gas temperature in kelvins (K)
x n is the number of moles (mol)
x m is the mass in grams (g)
x M is molar mass in grams/mole (g/mol)
x No is Avogadro’s number (mol-1)
Example #2
x C is concentration in moles/litre (mol/L)
How many iron atoms would be found in 50.0 g of iron (II) sulfate?
x nsolute is the moles of solute (mol)
x Vsolution is the volume of solution (L)

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Example #3                                                                                       Example #4
A gaseous compound contains 92.30 g of carbon and 7.70 g of                                      We are often interested in determining the composition of matter.
hydrogen. The mass of 0.330 L of this gas at 120oC and 99.0 kPa                                  % composition is one way of expressing this. Find the percent
is 0.780 g. Determine the molecular formula of this compound.                                    composition (percentage of each element) in iron (III) oxide.

Suggested Homework
x Problems chapter 2: 51a, 53a, 55, 57, 59
x Handout 1-03: Significant Figures Rules
x Handout 1-04. Significant Figures Problems
x Handout 1-05. Significant Figures Answers
x Handout 1-06. Mole Problems

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