2. Chemical Calculations
2.3. Amount of Substance, Molar Mass, and Mass
Text
The mole
What's the mass of one molecule of H2?
- Let’s have a look at the periodic table!
- One hydrogen atom weighs 1.008 u.
- One hydrogen molecule, H2, weighs 2 × 1.008u = 2.016u.
Hydrogen is up to the left of the periodic table, and oxygen is up to the right.
What’s the mass of 6.022 × 1023 H2-molecules?
- 1 u is the equivalent of 1.6605 × 10–24 g
- A single H2-molecule weighs 2.016 u =
= 2.016 u × 1.6605 × 10–24 g/u = 3.347568 × 10–24 g - 6.022 × 1023 H2-molecules weigh 6.022 × 1023 × 3.347568 × 10–24 g =
= 2.01590545 g ≈ 2.016 g
What’s the mass of one molecule of O2?
- Let’s have a look at the periodic table again!
- One oxygen atom weighs 16.00 u.
- One oxygen molecule, O2, weighs 2 × 16.00u = 32.00u.
What’s the mass of 6.022 × 1023 O2-molecules?
- 1 u is the equivalent of 1.6605 × 10–24 g
- A single O2-molecule weighs 32.00 u =
= 32.00 u × 1.6605 × 10–24 g/u = 5.3136 × 10–23 g - 6.022 × 1023 O2-molecules weigh 6.022 × 1023 × 5.3136 × 10–23 g =
= 31.9984992 g ≈ 32.00 g
1 molecule | weighs | 6.022 × 1023 molecules weigh |
H2 | 2.016 u | 2.016 g |
O2 | 32.00 u | 32.00 g |
6.022 × 1023 = 1 mol
- ”Mole” (symbol: mol) is a ”word of quantity”
- More ”words of quantities”:
- 1 pair (couple) = 2 pcs
- 1 dozen = 12 pcs
- score = 20 pcs
- gross = 144 pcs
- grand = 1,000 pcs
- myriad = 10,000 pcs
- 1 mol = 6.022 × 1023 pcs
How do you use the number 6.022 × 1023?
- The number 6.022 × 1023 is a conversion factor from u → g
- The number 6.022 × 1023 is called Avogadro’s constant. It’s written \(N_\text{A}\) and has the unit \(1/\text{mol}\).
- We write: \(N_{\text{A}} = 6.022 \times 10^{23}/\text{mol}\)
Amount of substance
The amount of substance answers the question, ”How many moles of the substance is there?”
- Written \(n\), has the unit mol.
- Example: \(n = 25 \text{mol}\)
Example 1I have a piece of iron that I know contains 2.5 moles of iron atoms. How many iron atoms is that? Solution\(N_{\text{Fe}} = n_{\text{Fe}} \times N_{\text{A}} =\) \(2.5\text{mol} \times 6.022 \times 10^{23}/\text{mol} = 1.5055 \times 10^{24} \approx 1.5 \times 10^{24}\) |
Example 2A piece of gold that I have in my lab consists of 6.1 × 1021 gold atoms. What is the amount of substance of gold, i.e. how many moles of gold are there? Solution\(n_{\text{Au}} = \frac {N_{\text{Au}}}{N_{\text{A}}} = \frac {6.2 \times 10^{21}}{6.022 \times 10^{23}/\text{mol}} = 0.0101295\text{mol} \approx 10 \times 10^{-3}\text{mol}\) |
Molar mass
1 mole of something is 6.022 × 1023 pcs.
- The molar mass of something tells us how much one mole of that substance weighs.
- The molar mass is written \(M\) and has the unit \(\text{g/mol}\).
What is the molar mass of hydrogen gas, H2?
\(M_{\text{H}_2} = m_{\text{1 H}_2\text{ molecule}} \times N_{\text{A}}\)
\(m_{\text{1 H}_2\text{ molecule}} = 2.016\text{u} \times 1.6605 \times 10^{-24}\text{g/u} = 3.347568 \times 10^{-24}\text{g}\)
\(M_{\text{H}_2} = 3.347568 \times 10^{-24}\text{g} \times 6.022 \times 10^{23}/\text{mol} ≈ 2.016\text{g/mol}\)
A mathematical relation
The molar mass indicates how much 1 mol of something weighs.
- Thus, we can write:
\[\text{molar mass} = \frac{\text{mass}}{\text{amount of substance}}\]
- Or, preferably:
\[M = \frac{m}{n}\]
Where
\(M\) is the molar mass in \(\text{g/mol}\).
\(m\) is the mass in \(\text{g}\).
\(n\) is the amount of substance in \(\text{mol}\).
Example 3What is the amount of substance in 36.0 g water? SolutionLet’s use our mathematical relation: \[M = \frac {m}{n} \Leftrightarrow n = \frac {m}{M}\] \(n_{\text{H}_2\text{O}} = \frac {m_{\text{H}_2\text{O}}}{M_{\text{H}_2\text{O}}}\) \(m_{\text{H}_2\text{O}}\) \(M_{\text{H}_2\text{O}} = 1.008\text{g/mol} \times 2 + 16.00\text{g/mol} = 18.016\text{g/mol}\) \(n_{\text{H}_2\text{O}} = \frac {36.0\text{g}}{18.016\text{g/mol}} = 1.9982238\text{mol} \approx 2.00\text{mol}\) |
Contents
- 1. States of Matter. The Atom and the Periodic Table
- 1.1. Matter. States of Matter
- 1.2. Elements and Chemical Compounds. Pure Substances and Mixtures
- 1.3. The Birth of Chemistry
- 1.4. Atomic Theory. The Atomic Model
- 1.5. Atomic Number, Mass Number, and Atomic Mass
- 1.6. Electron Configurations
- 1.7. Beyond Bohr's Atomic Model
- 1.8. Redox Reactions
- 1.9. The Structure of the Periodic Table
- 1.10. The Noble Gases
- 1.11. The Alkali Metals and the Halogens
- 1.12. The Alkaline Earth Metals and the Oxygen Group
- 1.13. A Few of the Elements in Group 13, 14, and 15
- 2. Chemical Calculations
- 2.1. Physical Quantity, Magnitude, and Units
- 2.2. Atomic Mass, Molecular Mass, and Unit Mass
- 2.3. Amount of Substance, Molar Mass, and Mass
- 2.4. Stoichiometry. Conservation of mass
- 2.5. Water of Crystallization
- 2.6. Calculating the Formula of a Chemical Compound
- 2.7. From Empirical to Molecular Formulas
- 2.8. Equivalent Amounts of Substance and Masses
- 2.9. Gases and Pressure
- 2.10. Concentrations
- 2.11. Dilutions
- 2.12. Yield
- 2.13. Limiting Reactants
- 3. Chemical Bonding
- 3.1. How Ionic Compounds are Formed
- 3.2. Precipitations
- 3.3. Names and Formulas of Ionic Compounds
- 3.4. Ionic Bonds
- 3.5. Properties of Ionic Compounds
- 3.6. Metal Bonding
- 3.7. Covalent Bonds
- 3.8. Polar Covalent Bonding
- 3.9. Dipoles. Polar and non-polar Molecules
- 3.10. The VSEPR Theory
- 3.11. Hydrogen Bonding. The Peculiar Water
- 3.12. Equals Solves Equal
- 3.13. Solubility of Gases in Water
- 3.14. Solubility of Salts in Water
- 4. Thermochemistry
- 5. Chemical Equilibrium
- 5.1. Reaction Rates
- 5.2. The Law of Mass Action
- 5.3. Calculations on Chemical Equilibrium
- 5.4. Heterogenous Equilibria. Solubility Product
- 5.5. Is the System at Equilibrium? The Reaction Quotient Q
- 5.6. Changing the Concentrations in a System in Equilibrium.
- 5.7. Diluting or Compressing Systems in Equilibrium, or Changing the Temperature
- 6. Acids and bases
- 7. Oxidation and Reduction
- 8. Electrochemistry
- 9. Organic Chemistry
- 9.1. Alkanes
- 9.2. Chain Isomers. Nomenclature
- 9.3. Haloalkanes
- 9.4. Nucleophilic Substitution
- 9.5. Alkenes
- 9.6. Electrophilic Addition. Markovnikov’s Rule
- 9.7. Elimination
- 9.8. Alkynes
- 9.9. Arenes and Aromatic Compounds
- 9.10. Alcohols
- 9.11. Oxidation of Alcohols
- 9.12. Aldehydes and Ketones
- 9.13. Thiols and Disulfides
- 9.14. Ethers
- 9.15. Amines
- 9.16. Nitro Compounds and Organic Nitrates
- 9.17. Carboxylic Acids
- 9.18. More on Carboxylic Acids
- 9.19. Stereoisomerism
- 9.20. Esters
- 9.21. Lipids
- 9.22. Mono-, Oligo-, and Polysaccharides
- 9.23. Amino Acids
- 9.24. Nucleotides
- 10. Biochemistry
- 10.1. Proteins
- 10.2. Enzymes
- 10.3. Catabolic Processes
- 10.4. Carrier Molecules
- 10.5. Glycolysis
- 10.6. Beta-oxidation
- 10.7. The Citric Acid Cycle
- 10.8. The Metabolism of Amino Acids
- 10.9. The Electron Transport Chain
- 10.10. Anabolic Processes
- 10.11. Gluconeogenesis and Fatty Acid Synthesis
- 10.12. DNA: Structure and Function
- 11. Analytical chemistry