U3 - Mass Relationships in Chemical Reactions

Atomic mass determined by

of protons + neutrons + electrons

Subatomic particles affecting mass

protons + neutrons mainly (electrons negligible)

Why knowing atomic mass matters

needed for lab calculations

Can one atom be weighed directly

no, too small

What can be measured instead

mass of one atom relative to another

Atomic mass (atomic weight)

atom's mass in amu

1 amu defined as

1/12 mass of carbon-12 atom

1 amu also called

1 Dalton (Da)

Carbon-12 isotope

6 protons + 6 neutrons

Atomic mass standard element

carbon-12 set to exactly 12 amu

Average atomic mass definition

weighted avg mass of naturally occurring isotopes

Why carbon atomic mass = 12.01 amu

mix of C-12 and C-13 isotopes

Carbon isotopes in natural mix

C-12, C-13

Average atomic mass calc

isotope mass × fractional abundance (sum all)

Fractional abundance meaning

decimal form of isotope % abundance

Example atomic mass info (Fe 55.85 amu)

avg Fe atom ~56× heavier than H atom

Calculation convention

use 4 sig figs for atomic masses

Simplified writing convention

often omit word "average" before atomic mass

Random Ir atom more likely

193Ir (since avg closer to 192.96 amu → higher abundance)

Atomic mass scale key idea

all atomic masses relative to C-12 = 12 amu

Relative atomic mass concept

comparison of element mass to carbon-12

Isotope definition

atoms of same element w/ different # of neutrons

Which subatomic particle differs in isotopes

neutrons

Which subatomic particle defines element identity

protons

Unit for expressing atomic mass

amu or Dalton

How atomic mass differs from mass number

mass number = whole # (p+n), atomic mass = weighted avg

What average atomic mass reflects

both isotope masses + abundance ratios

Why special unit needed for atoms

atoms too small to weigh directly

Unit used to measure atoms/molecules

atomic mass unit (amu)

Mole (mol)

amount containing 6.022×10²³ entities

Entities in a mole

atoms, molecules, or particles

Historical mole definition

of atoms in 12 g of C-12

Avogadro's number (Nₐ)

6.022×10²³ particles/mol

Who Avogadro's number named after

Amedeo Avogadro

Molar mass (M)

mass of 1 mol of substance (g or kg)

Relationship: molar mass ↔ atomic mass

molar mass (g) = atomic mass (amu) numerically

Molar mass of carbon-12

12 g/mol

of atoms in 12 g of carbon-12

6.022×10²³ atoms

Common molar mass units

g/mol or kg/mol

Avogadro's number use

convert amu ↔ grams

Conversion factor: grams → moles

1 mol X / (molar mass in g)

Conversion factor: moles → atoms

6.022×10²³ atoms / 1 mol

Mass of 1 C-12 atom (g)

1.993×10⁻²³ g

Symbol for Avogadro's number

Nₐ

Example comparison: mole to dozen

mole = large counting unit like dozen (12)

1 mol of H atoms contains

6.022×10²³ H atoms

Purpose of mole concept

link atomic scale ↔ lab-scale mass

1 mol of any element contains

same # of atoms (6.022×10²³), different mass

Unit used for atomic scale mass

amu

Unit used for lab scale mass

grams

Relationship between amu and g/mol

1 amu/atom = 1 g/mol for 1 mol of atoms

Mass spectrometry

method to determine atomic & molecular masses accurately

Purpose of mass spectrometer

measure atomic/molecular mass & isotope abundance

Sample state for mass spectrometer

gaseous

Step 1 in mass spectrometer

sample bombarded w/ high-energy electrons

Result of electron bombardment

atoms/molecules lose e⁻ → form positive ions

Ionization process

e⁻ knocked out → cation forms

Device part that accelerates ions

two oppositely charged plates

Reason ions accelerate

attraction to opposite charge

Device part that deflects ions

magnet

Ion path shape in mass spectrometer

circular

Factor determining radius of ion path

charge-to-mass ratio (e/m)

e/m ratio meaning

charge of ion ÷ mass of ion

Small e/m ratio effect

wider curve (heavier ions or smaller charge)

Large e/m ratio effect

narrower curve (lighter ions or larger charge)

Separation of ions with same charge but diff mass

based on e/m ratio difference

How ion mass determined

from degree of deflection in magnetic field

Mass spectrum

detector pattern showing ion signal by mass

Detector function

registers ions as current peaks

What current magnitude shows

of ions detected

Relationship between current & ions

directly proportional

What proportionality enables

determine relative abundance of isotopes

Relative isotope abundance

% each isotope contributes to element's mass

Why precision matters in mass spectrometry

low-abundance isotopes easy to miss (ex: Ne-21)

Why early experiments missed Ne-21

low abundance (~26 per 10,000 Ne atoms)

Use of mass spectrometry for molecules

determine molecular/molar mass

When molar mass can be found w/ mass spectrometry

even if formula unknown

Mass spectrometry key idea

atomic & molecular masses found by isotope ratios

What mass spectrometer ultimately provides

atomic mass, isotope abundance, molecular weight

Mass spectrometry category

physical method for mass determination

Ion with higher mass deflection behavior

deflects less (smaller curve)

Ion with lower mass deflection behavior

deflects more (tighter curve)

What information mass spectrum displays

isotope masses + % abundance

What chemical formula shows

atoms of each element in compound unit

Formula meaning (reverse)

if given subscripts, tells ratio of elements in 1 mol compound

Percent composition purpose

verify purity of compound by comparing to experimental %

Percent composition definition

% by mass of each element in compound

Formula for % composition

(n × molar mass element) ÷ molar mass compound × 100%

n in % composition formula

mols of element in 1 mol compound

Step 1 in % composition calc

assume 1 mol compound

Step 2 in % composition calc

find total mass of each element in 1 mol compound

Step 3 in % composition calc

divide element mass by molar mass compound × 100

Total % from all elements

should equal ~100% (small round error ok)

Unit assumed when converting % to mass

100 g sample

Why 100 g sample used

makes % = g directly

How to convert mass % to mol

divide each element's grams by atomic mass

What mole values represent

relative # mols of each element in compound

Rule for getting empirical formula

divide all mole values by smallest mole value

If mole ratios not whole numbers

multiply by factor (2, 3, etc.) to get integers

Subscripts in chemical formula represent

simplest whole-number mole ratio